{
  "id": 1930,
  "curve_key": "6634278938605929008406436859958801:501016091689263269520717251676573912081818565521799",
  "ainvs": [
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    "-1",
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  "rank_lower_bound": 13,
  "torsion": [
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  "naive_height": 233.6326741657942,
  "faltings_height": 17.42737585073719,
  "conductor": "105282506383638544223030541052846185291174420590490",
  "bad_primes": [
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    "7",
    "13",
    "17",
    "19",
    "29",
    "59",
    "71",
    "73",
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    "307",
    "563",
    "1663",
    "1913",
    "2089",
    "4507",
    "395027",
    "468967"
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  "discriminant": "23716292678395955644377149937563549663452112811340012809826362032637434820558412308740021250000000",
  "regulator": "11468824455421.68339675014613101305977457937474985413082339617304",
  "points": [
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      "46382901088473871491393829136482365225353554218475714239617/837254030849748337209049141566587587"
    ]
  ],
  "submitter": "Alvaro Lozano-Robledo",
  "history": [],
  "commentary": "Rank exactly 13, torsion Z/2Z: 13 independent points; 2-isogeny Selmer bound 13, confirmed by a second 2-isogeny descent. Specialisation of Kihara's rank-8 family (S. Kihara, Proc. Japan Acad. 77A (2001) 11-12) with u = (s^2 - l)/(2s), (p,q,s) = (1,4,177/13).",
  "created_at": "2026-09-25 19:17:10",
  "updated_at": "2026-09-25 19:17:10"
}