{
  "id": 3664,
  "curve_key": "36039651674960656:-9791157463592305875096896",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-750826076561680",
    "11332358425729416579700"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    4
  ],
  "naive_height": 115.08704382116568,
  "faltings_height": 7.61563134423241,
  "conductor": "1578385609386038880",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "19",
    "31",
    "71",
    "101",
    "157",
    "281",
    "2521"
  ],
  "discriminant": "-28389137094151847682746819617320466960880524800",
  "regulator": "11416408.88265326190991398827303916597027007622670787",
  "points": [
    [
      "119492417",
      "1275844565658"
    ],
    [
      "-2765676724470495/287675521",
      "648449096088957876959870/4879264511681"
    ],
    [
      "-166805600711/7744",
      "90179158020909645/681472"
    ],
    [
      "-19034700983/576",
      "103232596200283/13824"
    ],
    [
      "-330034023/16",
      "8596833630347/64"
    ],
    [
      "19180783677/961",
      "1952982748805552/29791"
    ],
    [
      "25811558356/225",
      "4042842304672054/3375"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -140 of the Elkies-Klagsbrun Z/4 fibration E2: y^2 + a*xy + a*c*y = x^3 + c*x^2, a = -8(80t+9), c = 2(t-2)(2t-1)(18t-1)(2t-81) (arXiv:2003.00077, eq. (6)), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:29:18",
  "updated_at": "2026-09-29 19:29:18"
}