{
  "id": 1374,
  "curve_key": "81736772382334867489:-704534162777315542660093287857",
  "ainvs": [
    "1",
    "1",
    "1",
    "-1702849424631976406",
    "815433058060520543741414099"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2
  ],
  "naive_height": 137.55010699457264,
  "faltings_height": 9.398558969204805,
  "conductor": "274041685980626458099814310",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "41",
    "83",
    "101",
    "157",
    "163",
    "313",
    "389",
    "409",
    "613",
    "2617"
  ],
  "discriminant": "28765516653337068029166786181779192222185057587943178240",
  "regulator": "14476581915.47603780881857213181004219961152466385778786441",
  "points": [
    [
      "18501537923881/9801",
      "-63832949310588071723/970299"
    ],
    [
      "4219235049409/289",
      "8633051370115788799/4913"
    ],
    [
      "1088644391472741/1018081",
      "-15140953062258902802305/1027243729"
    ],
    [
      "12468924897",
      "-1384989071703569"
    ],
    [
      "262740962233/256",
      "49968831975279749/4096"
    ],
    [
      "1397350618342233/241081",
      "-51006041685124287408451/118370771"
    ],
    [
      "563783601196293/638401",
      "304845438785359564981/510082399"
    ],
    [
      "9136285609/9",
      "-311296393004299/27"
    ],
    [
      "962412257377/49",
      "-942119738339933623/343"
    ],
    [
      "988962334177/1089",
      "152305348520708303/35937"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Obtained by taking a rational 2-isogenous quotient of curve #1203, submitted by Noam Elkies, which has rank at least 10 and torsion \\(\\mathbf Z/2\\mathbf Z\\times\\mathbf Z/2\\mathbf Z\\). Quotienting by one of its rational 2-torsion points gives \\(y^2=x^3+10590663569x^2+10141794149802983424x\\). Its global minimal model has ainvs \\([1,1,1,-1702849424631976406,815433058060520543741414099]\\), torsion \\(\\mathbf Z/2\\mathbf Z\\), and the same conductor \\(274041685980626458099814310\\). The ten independent points on #1203 were mapped through the 2-isogeny, giving ten independent points on the quotient; the construction and invariants were verified in Magma.",
  "created_at": "2026-09-24 18:27:56",
  "updated_at": "2026-09-24 18:27:56"
}