{
  "id": 1926,
  "curve_key": "87009239996171441234151767425:-32484941739463398857438105058849411956610625",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1812692499920238359044828488",
    "37598312198452856879141331946397639732592"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "naive_height": 200.37870111324233,
  "faltings_height": 14.706707574776516,
  "conductor": "7957055249285451655668179172815993925972577312050",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "19",
    "23",
    "53",
    "59",
    "71",
    "73",
    "79",
    "107",
    "331",
    "601",
    "3319",
    "5813",
    "214519",
    "3616013",
    "17506729"
  ],
  "discriminant": "-229489933413739800898518566909955415893954796036949450416087357552789560265374750000",
  "regulator": "72280614626567.07439906823765824681784663891467356962167390293613",
  "points": [
    [
      "8366842780548126",
      "765308965663908409349580"
    ],
    [
      "511158033364057022202/16410601",
      "-7084445285945617642913527026876/66479344651"
    ],
    [
      "59828716021279119/4",
      "14633990375802694038322797/8"
    ],
    [
      "487254941474136",
      "10716209233243029139884"
    ],
    [
      "64539305014470783/4",
      "16395886938695041518347217/8"
    ],
    [
      "25162104088242",
      "-88983578989818354846"
    ],
    [
      "27538112356414728/169",
      "-4431617318142953658310332/2197"
    ],
    [
      "148236534100952",
      "1739612251020893159324"
    ],
    [
      "554622147565827/4",
      "12526989911562438622551/8"
    ],
    [
      "15118052585219013318/100489",
      "56716277040164128019345692572/31855013"
    ],
    [
      "28395796033752",
      "94982083859833906524"
    ],
    [
      "-38230250287674",
      "-225881586997012113906"
    ],
    [
      "12772558913736",
      "128566254751927993284"
    ]
  ],
  "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) = (4,-1,145/6).",
  "created_at": "2026-09-25 19:16:23",
  "updated_at": "2026-09-25 19:16:23"
}