{
  "schema_version": "1.0.0",
  "title": "Degree-5 unlinked analytic-rank-one boundary",
  "evidence_id": "D4D5-LMFDB-WEB-20260818T104330Z-D5",
  "generated_at_utc": "2026-08-18T12:16:14.884Z",
  "status": "excluded_from_strict_linked_inventory",
  "scope": "Direct projective-ratio-5 parent edges satisfying the source Qbar-gonality lower bound, whose genus-one target has modular analytic rank 1 but no LMFDB elliptic curve_label.",
  "summary": {
    "records": 53,
    "distinct_sources": 47,
    "distinct_targets": 53,
    "independently_certified_project_candidates": 1
  },
  "records": [
    {
      "boundary_id": "d5-boundary:30.360.21.j.1--to--30.72.1.p.1",
      "degree": 5,
      "status": "unlinked_analytic_rank_one_boundary",
      "source_label": "30.360.21.j.1",
      "source_url": "https://beta.lmfdb.org/ModularCurve/Q/30.360.21.j.1/",
      "source_genus": 21,
      "qbar_gonality_lower": 6,
      "qbar_gonality_upper": 10,
      "target_label": "30.72.1.p.1",
      "target_url": "https://beta.lmfdb.org/ModularCurve/Q/30.72.1.p.1/",
      "target_genus": null,
      "target_modular_analytic_rank": null,
      "selection_predicate": {
        "target_genus": 1,
        "target_modular_analytic_rank": 1,
        "note": "These values describe the upstream query predicate; they are not substituted into omitted row fields."
      },
      "linked_elliptic_curve_label": null,
      "independently_certified_rank_one_target": false,
      "featured": false,
      "why_excluded_from_strict_table": "LMFDB records no elliptic curve_label for the genus-one modular target, so there is no joined Mordell-Weil rank-bounds row.",
      "certification_note": null,
      "evidence_kind": "database_observation"
    },
    {
      "boundary_id": "d5-boundary:30.360.21.j.1--to--30.72.1.p.2",
      "degree": 5,
      "status": "unlinked_analytic_rank_one_boundary",
      "source_label": "30.360.21.j.1",
      "source_url": "https://beta.lmfdb.org/ModularCurve/Q/30.360.21.j.1/",
      "source_genus": 21,
      "qbar_gonality_lower": 6,
      "qbar_gonality_upper": 10,
      "target_label": "30.72.1.p.2",
      "target_url": "https://beta.lmfdb.org/ModularCurve/Q/30.72.1.p.2/",
      "target_genus": null,
      "target_modular_analytic_rank": null,
      "selection_predicate": {
        "target_genus": 1,
        "target_modular_analytic_rank": 1,
        "note": "These values describe the upstream query predicate; they are not substituted into omitted row fields."
      },
      "linked_elliptic_curve_label": null,
      "independently_certified_rank_one_target": false,
      "featured": false,
      "why_excluded_from_strict_table": "LMFDB records no elliptic curve_label for the genus-one modular target, so there is no joined Mordell-Weil rank-bounds row.",
      "certification_note": null,
      "evidence_kind": "database_observation"
    },
    {
      "boundary_id": "d5-boundary:40.480.33.bu.1--to--40.96.1.b.2",
      "degree": 5,
      "status": "unlinked_analytic_rank_one_boundary",
      "source_label": "40.480.33.bu.1",
      "source_url": "https://beta.lmfdb.org/ModularCurve/Q/40.480.33.bu.1/",
      "source_genus": 33,
      "qbar_gonality_lower": 8,
      "qbar_gonality_upper": 10,
      "target_label": "40.96.1.b.2",
      "target_url": "https://beta.lmfdb.org/ModularCurve/Q/40.96.1.b.2/",
      "target_genus": null,
      "target_modular_analytic_rank": null,
      "selection_predicate": {
        "target_genus": 1,
        "target_modular_analytic_rank": 1,
        "note": "These values describe the upstream query predicate; they are not substituted into omitted row fields."
      },
      "linked_elliptic_curve_label": null,
      "independently_certified_rank_one_target": false,
      "featured": false,
      "why_excluded_from_strict_table": "LMFDB records no elliptic curve_label for the genus-one modular target, so there is no joined Mordell-Weil rank-bounds row.",
      "certification_note": null,
      "evidence_kind": "database_observation"
    },
    {
      "boundary_id": "d5-boundary:40.480.33.bu.2--to--40.96.1.b.1",
      "degree": 5,
      "status": "unlinked_analytic_rank_one_boundary",
      "source_label": "40.480.33.bu.2",
      "source_url": "https://beta.lmfdb.org/ModularCurve/Q/40.480.33.bu.2/",
      "source_genus": 33,
      "qbar_gonality_lower": 8,
      "qbar_gonality_upper": 10,
      "target_label": "40.96.1.b.1",
      "target_url": "https://beta.lmfdb.org/ModularCurve/Q/40.96.1.b.1/",
      "target_genus": null,
      "target_modular_analytic_rank": null,
      "selection_predicate": {
        "target_genus": 1,
        "target_modular_analytic_rank": 1,
        "note": "These values describe the upstream query predicate; they are not substituted into omitted row fields."
      },
      "linked_elliptic_curve_label": null,
      "independently_certified_rank_one_target": false,
      "featured": false,
      "why_excluded_from_strict_table": "LMFDB records no elliptic curve_label for the genus-one modular target, so there is no joined Mordell-Weil rank-bounds row.",
      "certification_note": null,
      "evidence_kind": "database_observation"
    },
    {
      "boundary_id": "d5-boundary:40.480.33.cc.1--to--40.96.1.h.1",
      "degree": 5,
      "status": "unlinked_analytic_rank_one_boundary",
      "source_label": "40.480.33.cc.1",
      "source_url": "https://beta.lmfdb.org/ModularCurve/Q/40.480.33.cc.1/",
      "source_genus": 33,
      "qbar_gonality_lower": 8,
      "qbar_gonality_upper": 10,
      "target_label": "40.96.1.h.1",
      "target_url": "https://beta.lmfdb.org/ModularCurve/Q/40.96.1.h.1/",
      "target_genus": null,
      "target_modular_analytic_rank": null,
      "selection_predicate": {
        "target_genus": 1,
        "target_modular_analytic_rank": 1,
        "note": "These values describe the upstream query predicate; they are not substituted into omitted row fields."
      },
      "linked_elliptic_curve_label": null,
      "independently_certified_rank_one_target": false,
      "featured": false,
      "why_excluded_from_strict_table": "LMFDB records no elliptic curve_label for the genus-one modular target, so there is no joined Mordell-Weil rank-bounds row.",
      "certification_note": null,
      "evidence_kind": "database_observation"
    },
    {
      "boundary_id": "d5-boundary:40.480.33.cc.2--to--40.96.1.h.2",
      "degree": 5,
      "status": "unlinked_analytic_rank_one_boundary",
      "source_label": "40.480.33.cc.2",
      "source_url": "https://beta.lmfdb.org/ModularCurve/Q/40.480.33.cc.2/",
      "source_genus": 33,
      "qbar_gonality_lower": 8,
      "qbar_gonality_upper": 10,
      "target_label": "40.96.1.h.2",
      "target_url": "https://beta.lmfdb.org/ModularCurve/Q/40.96.1.h.2/",
      "target_genus": null,
      "target_modular_analytic_rank": null,
      "selection_predicate": {
        "target_genus": 1,
        "target_modular_analytic_rank": 1,
        "note": "These values describe the upstream query predicate; they are not substituted into omitted row fields."
      },
      "linked_elliptic_curve_label": null,
      "independently_certified_rank_one_target": false,
      "featured": false,
      "why_excluded_from_strict_table": "LMFDB records no elliptic curve_label for the genus-one modular target, so there is no joined Mordell-Weil rank-bounds row.",
      "certification_note": null,
      "evidence_kind": "database_observation"
    },
    {
      "boundary_id": "d5-boundary:40.480.33.ck.1--to--40.96.1.o.2",
      "degree": 5,
      "status": "independently_certified_project_candidate",
      "source_label": "40.480.33.ck.1",
      "source_url": "https://beta.lmfdb.org/ModularCurve/Q/40.480.33.ck.1/",
      "source_genus": 33,
      "qbar_gonality_lower": 8,
      "qbar_gonality_upper": 10,
      "target_label": "40.96.1.o.2",
      "target_url": "https://beta.lmfdb.org/ModularCurve/Q/40.96.1.o.2/",
      "target_genus": null,
      "target_modular_analytic_rank": null,
      "selection_predicate": {
        "target_genus": 1,
        "target_modular_analytic_rank": 1,
        "note": "These values describe the upstream query predicate; they are not substituted into omitted row fields."
      },
      "linked_elliptic_curve_label": null,
      "independently_certified_rank_one_target": true,
      "featured": true,
      "why_excluded_from_strict_table": "LMFDB records no elliptic curve_label for the genus-one modular target, so there is no joined Mordell-Weil rank-bounds row.",
      "certification_note": "Separately certified in the project: the pointed target has algebraic Mordell-Weil rank 1; the missing LMFDB curve_label still keeps this endpoint outside the strict linked table.",
      "evidence_kind": "database_observation_with_independent_project_certification"
    },
    {
      "boundary_id": "d5-boundary:40.480.33.ck.2--to--40.96.1.o.1",
      "degree": 5,
      "status": "unlinked_analytic_rank_one_boundary",
      "source_label": "40.480.33.ck.2",
      "source_url": "https://beta.lmfdb.org/ModularCurve/Q/40.480.33.ck.2/",
      "source_genus": 33,
      "qbar_gonality_lower": 8,
      "qbar_gonality_upper": 10,
      "target_label": "40.96.1.o.1",
      "target_url": "https://beta.lmfdb.org/ModularCurve/Q/40.96.1.o.1/",
      "target_genus": null,
      "target_modular_analytic_rank": null,
      "selection_predicate": {
        "target_genus": 1,
        "target_modular_analytic_rank": 1,
        "note": "These values describe the upstream query predicate; they are not substituted into omitted row fields."
      },
      "linked_elliptic_curve_label": null,
      "independently_certified_rank_one_target": false,
      "featured": false,
      "why_excluded_from_strict_table": "LMFDB records no elliptic curve_label for the genus-one modular target, so there is no joined Mordell-Weil rank-bounds row.",
      "certification_note": null,
      "evidence_kind": "database_observation"
    },
    {
      "boundary_id": "d5-boundary:40.480.33.cp.1--to--40.96.1.s.1",
      "degree": 5,
      "status": "unlinked_analytic_rank_one_boundary",
      "source_label": "40.480.33.cp.1",
      "source_url": "https://beta.lmfdb.org/ModularCurve/Q/40.480.33.cp.1/",
      "source_genus": 33,
      "qbar_gonality_lower": 8,
      "qbar_gonality_upper": 10,
      "target_label": "40.96.1.s.1",
      "target_url": "https://beta.lmfdb.org/ModularCurve/Q/40.96.1.s.1/",
      "target_genus": null,
      "target_modular_analytic_rank": null,
      "selection_predicate": {
        "target_genus": 1,
        "target_modular_analytic_rank": 1,
        "note": "These values describe the upstream query predicate; they are not substituted into omitted row fields."
      },
      "linked_elliptic_curve_label": null,
      "independently_certified_rank_one_target": false,
      "featured": false,
      "why_excluded_from_strict_table": "LMFDB records no elliptic curve_label for the genus-one modular target, so there is no joined Mordell-Weil rank-bounds row.",
      "certification_note": null,
      "evidence_kind": "database_observation"
    },
    {
      "boundary_id": "d5-boundary:40.480.33.cp.2--to--40.96.1.s.2",
      "degree": 5,
      "status": "unlinked_analytic_rank_one_boundary",
      "source_label": "40.480.33.cp.2",
      "source_url": "https://beta.lmfdb.org/ModularCurve/Q/40.480.33.cp.2/",
      "source_genus": 33,
      "qbar_gonality_lower": 8,
      "qbar_gonality_upper": 10,
      "target_label": "40.96.1.s.2",
      "target_url": "https://beta.lmfdb.org/ModularCurve/Q/40.96.1.s.2/",
      "target_genus": null,
      "target_modular_analytic_rank": null,
      "selection_predicate": {
        "target_genus": 1,
        "target_modular_analytic_rank": 1,
        "note": "These values describe the upstream query predicate; they are not substituted into omitted row fields."
      },
      "linked_elliptic_curve_label": null,
      "independently_certified_rank_one_target": false,
      "featured": false,
      "why_excluded_from_strict_table": "LMFDB records no elliptic curve_label for the genus-one modular target, so there is no joined Mordell-Weil rank-bounds row.",
      "certification_note": null,
      "evidence_kind": "database_observation"
    },
    {
      "boundary_id": "d5-boundary:40.480.33.cv.1--to--40.96.1.x.2",
      "degree": 5,
      "status": "unlinked_analytic_rank_one_boundary",
      "source_label": "40.480.33.cv.1",
      "source_url": "https://beta.lmfdb.org/ModularCurve/Q/40.480.33.cv.1/",
      "source_genus": 33,
      "qbar_gonality_lower": 8,
      "qbar_gonality_upper": 10,
      "target_label": "40.96.1.x.2",
      "target_url": "https://beta.lmfdb.org/ModularCurve/Q/40.96.1.x.2/",
      "target_genus": null,
      "target_modular_analytic_rank": null,
      "selection_predicate": {
        "target_genus": 1,
        "target_modular_analytic_rank": 1,
        "note": "These values describe the upstream query predicate; they are not substituted into omitted row fields."
      },
      "linked_elliptic_curve_label": null,
      "independently_certified_rank_one_target": false,
      "featured": false,
      "why_excluded_from_strict_table": "LMFDB records no elliptic curve_label for the genus-one modular target, so there is no joined Mordell-Weil rank-bounds row.",
      "certification_note": null,
      "evidence_kind": "database_observation"
    },
    {
      "boundary_id": "d5-boundary:40.480.33.cv.2--to--40.96.1.x.1",
      "degree": 5,
      "status": "unlinked_analytic_rank_one_boundary",
      "source_label": "40.480.33.cv.2",
      "source_url": "https://beta.lmfdb.org/ModularCurve/Q/40.480.33.cv.2/",
      "source_genus": 33,
      "qbar_gonality_lower": 8,
      "qbar_gonality_upper": 10,
      "target_label": "40.96.1.x.1",
      "target_url": "https://beta.lmfdb.org/ModularCurve/Q/40.96.1.x.1/",
      "target_genus": null,
      "target_modular_analytic_rank": null,
      "selection_predicate": {
        "target_genus": 1,
        "target_modular_analytic_rank": 1,
        "note": "These values describe the upstream query predicate; they are not substituted into omitted row fields."
      },
      "linked_elliptic_curve_label": null,
      "independently_certified_rank_one_target": false,
      "featured": false,
      "why_excluded_from_strict_table": "LMFDB records no elliptic curve_label for the genus-one modular target, so there is no joined Mordell-Weil rank-bounds row.",
      "certification_note": null,
      "evidence_kind": "database_observation"
    },
    {
      "boundary_id": "d5-boundary:40.480.33.db.1--to--40.96.1.bb.1",
      "degree": 5,
      "status": "unlinked_analytic_rank_one_boundary",
      "source_label": "40.480.33.db.1",
      "source_url": "https://beta.lmfdb.org/ModularCurve/Q/40.480.33.db.1/",
      "source_genus": 33,
      "qbar_gonality_lower": 8,
      "qbar_gonality_upper": 10,
      "target_label": "40.96.1.bb.1",
      "target_url": "https://beta.lmfdb.org/ModularCurve/Q/40.96.1.bb.1/",
      "target_genus": null,
      "target_modular_analytic_rank": null,
      "selection_predicate": {
        "target_genus": 1,
        "target_modular_analytic_rank": 1,
        "note": "These values describe the upstream query predicate; they are not substituted into omitted row fields."
      },
      "linked_elliptic_curve_label": null,
      "independently_certified_rank_one_target": false,
      "featured": false,
      "why_excluded_from_strict_table": "LMFDB records no elliptic curve_label for the genus-one modular target, so there is no joined Mordell-Weil rank-bounds row.",
      "certification_note": null,
      "evidence_kind": "database_observation"
    },
    {
      "boundary_id": "d5-boundary:40.480.33.db.2--to--40.96.1.bb.2",
      "degree": 5,
      "status": "unlinked_analytic_rank_one_boundary",
      "source_label": "40.480.33.db.2",
      "source_url": "https://beta.lmfdb.org/ModularCurve/Q/40.480.33.db.2/",
      "source_genus": 33,
      "qbar_gonality_lower": 8,
      "qbar_gonality_upper": 10,
      "target_label": "40.96.1.bb.2",
      "target_url": "https://beta.lmfdb.org/ModularCurve/Q/40.96.1.bb.2/",
      "target_genus": null,
      "target_modular_analytic_rank": null,
      "selection_predicate": {
        "target_genus": 1,
        "target_modular_analytic_rank": 1,
        "note": "These values describe the upstream query predicate; they are not substituted into omitted row fields."
      },
      "linked_elliptic_curve_label": null,
      "independently_certified_rank_one_target": false,
      "featured": false,
      "why_excluded_from_strict_table": "LMFDB records no elliptic curve_label for the genus-one modular target, so there is no joined Mordell-Weil rank-bounds row.",
      "certification_note": null,
      "evidence_kind": "database_observation"
    },
    {
      "boundary_id": "d5-boundary:40.480.33.dd.1--to--40.96.1.bd.2",
      "degree": 5,
      "status": "unlinked_analytic_rank_one_boundary",
      "source_label": "40.480.33.dd.1",
      "source_url": "https://beta.lmfdb.org/ModularCurve/Q/40.480.33.dd.1/",
      "source_genus": 33,
      "qbar_gonality_lower": 8,
      "qbar_gonality_upper": 10,
      "target_label": "40.96.1.bd.2",
      "target_url": "https://beta.lmfdb.org/ModularCurve/Q/40.96.1.bd.2/",
      "target_genus": null,
      "target_modular_analytic_rank": null,
      "selection_predicate": {
        "target_genus": 1,
        "target_modular_analytic_rank": 1,
        "note": "These values describe the upstream query predicate; they are not substituted into omitted row fields."
      },
      "linked_elliptic_curve_label": null,
      "independently_certified_rank_one_target": false,
      "featured": false,
      "why_excluded_from_strict_table": "LMFDB records no elliptic curve_label for the genus-one modular target, so there is no joined Mordell-Weil rank-bounds row.",
      "certification_note": null,
      "evidence_kind": "database_observation"
    },
    {
      "boundary_id": "d5-boundary:40.480.33.dd.2--to--40.96.1.bd.1",
      "degree": 5,
      "status": "unlinked_analytic_rank_one_boundary",
      "source_label": "40.480.33.dd.2",
      "source_url": "https://beta.lmfdb.org/ModularCurve/Q/40.480.33.dd.2/",
      "source_genus": 33,
      "qbar_gonality_lower": 8,
      "qbar_gonality_upper": 10,
      "target_label": "40.96.1.bd.1",
      "target_url": "https://beta.lmfdb.org/ModularCurve/Q/40.96.1.bd.1/",
      "target_genus": null,
      "target_modular_analytic_rank": null,
      "selection_predicate": {
        "target_genus": 1,
        "target_modular_analytic_rank": 1,
        "note": "These values describe the upstream query predicate; they are not substituted into omitted row fields."
      },
      "linked_elliptic_curve_label": null,
      "independently_certified_rank_one_target": false,
      "featured": false,
      "why_excluded_from_strict_table": "LMFDB records no elliptic curve_label for the genus-one modular target, so there is no joined Mordell-Weil rank-bounds row.",
      "certification_note": null,
      "evidence_kind": "database_observation"
    },
    {
      "boundary_id": "d5-boundary:40.480.33.df.1--to--40.96.1.bf.2",
      "degree": 5,
      "status": "unlinked_analytic_rank_one_boundary",
      "source_label": "40.480.33.df.1",
      "source_url": "https://beta.lmfdb.org/ModularCurve/Q/40.480.33.df.1/",
      "source_genus": 33,
      "qbar_gonality_lower": 8,
      "qbar_gonality_upper": 10,
      "target_label": "40.96.1.bf.2",
      "target_url": "https://beta.lmfdb.org/ModularCurve/Q/40.96.1.bf.2/",
      "target_genus": null,
      "target_modular_analytic_rank": null,
      "selection_predicate": {
        "target_genus": 1,
        "target_modular_analytic_rank": 1,
        "note": "These values describe the upstream query predicate; they are not substituted into omitted row fields."
      },
      "linked_elliptic_curve_label": null,
      "independently_certified_rank_one_target": false,
      "featured": false,
      "why_excluded_from_strict_table": "LMFDB records no elliptic curve_label for the genus-one modular target, so there is no joined Mordell-Weil rank-bounds row.",
      "certification_note": null,
      "evidence_kind": "database_observation"
    },
    {
      "boundary_id": "d5-boundary:40.480.33.df.2--to--40.96.1.bf.1",
      "degree": 5,
      "status": "unlinked_analytic_rank_one_boundary",
      "source_label": "40.480.33.df.2",
      "source_url": "https://beta.lmfdb.org/ModularCurve/Q/40.480.33.df.2/",
      "source_genus": 33,
      "qbar_gonality_lower": 8,
      "qbar_gonality_upper": 10,
      "target_label": "40.96.1.bf.1",
      "target_url": "https://beta.lmfdb.org/ModularCurve/Q/40.96.1.bf.1/",
      "target_genus": null,
      "target_modular_analytic_rank": null,
      "selection_predicate": {
        "target_genus": 1,
        "target_modular_analytic_rank": 1,
        "note": "These values describe the upstream query predicate; they are not substituted into omitted row fields."
      },
      "linked_elliptic_curve_label": null,
      "independently_certified_rank_one_target": false,
      "featured": false,
      "why_excluded_from_strict_table": "LMFDB records no elliptic curve_label for the genus-one modular target, so there is no joined Mordell-Weil rank-bounds row.",
      "certification_note": null,
      "evidence_kind": "database_observation"
    },
    {
      "boundary_id": "d5-boundary:40.480.33.dh.1--to--40.96.1.bh.1",
      "degree": 5,
      "status": "unlinked_analytic_rank_one_boundary",
      "source_label": "40.480.33.dh.1",
      "source_url": "https://beta.lmfdb.org/ModularCurve/Q/40.480.33.dh.1/",
      "source_genus": 33,
      "qbar_gonality_lower": 8,
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