{
  "id": 3704,
  "curve_key": "488459443085957752790304591139138808410336:-339336105392555151638289007474087194639776932356225733922120416",
  "ainvs": [
    "0",
    "1",
    "0",
    "-10176238397624119849798012315398725175215",
    "392750121982124018096479456962466953846105445381239468832938"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    4
  ],
  "naive_height": 287.9762252143155,
  "faltings_height": 21.841413816385035,
  "conductor": "17618290971556207682545290958840926789835323960",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "23",
    "31",
    "43",
    "71",
    "73",
    "83",
    "227",
    "233",
    "359",
    "479",
    "1093",
    "1163",
    "1307",
    "1427",
    "4943",
    "71387"
  ],
  "discriminant": "806614322650607476631443999745256873912936495895224561963223330313077252622759798269982281086414472057895869300781250000",
  "regulator": "3121650657432.8677052477540521728340191038904892355751750789374",
  "points": [
    [
      "114716636197766052346",
      "857336867307199630618450837500"
    ],
    [
      "195364070310429571531",
      "2420983824233123693540174737545"
    ],
    [
      "-180686409811468638004931/3364",
      "172801161382077627803602932764296875/195112"
    ],
    [
      "-294677366174349387491/4",
      "6893989150101691940760420703125/8"
    ],
    [
      "104052664400770596961/16",
      "36589092709892255853958520115975/64"
    ],
    [
      "197155666653366737509/4",
      "835864754813879702252292984375/8"
    ],
    [
      "533729840577593012509/4",
      "9501395813659601910594788896875/8"
    ],
    [
      "10695217777023853962099/169",
      "103126133913615633929887502521875/2197"
    ],
    [
      "9707496827111768654716699/27889",
      "29094244319700487395770107368252585105/4657463"
    ],
    [
      "18322780137045138826521139/426409",
      "51956704448436928652587043883499921875/278445077"
    ],
    [
      "416356918383279285441195399/6692569",
      "366002276606927060207768605445470379025/17313676003"
    ],
    [
      "13818464431373299192706832826/112550881",
      "1190491932520025288326110663237984790510500/1194052296529"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 3549074/82573 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": "2026-09-30 01:46:31",
  "updated_at": "2026-09-30 01:46:31"
}