{
  "id": 4251,
  "curve_key": "18021415310363681245061731648:-6915819814385424673654014051782916327172096",
  "ainvs": [
    "0",
    "1",
    "0",
    "-375446152299243359272119409",
    "8004421081464486742085823923258618005535"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    4
  ],
  "naive_height": 197.28477083957634,
  "faltings_height": 14.49347430339989,
  "conductor": "81227180467392566378365208705376",
  "bad_primes": [
    "2",
    "3",
    "11",
    "13",
    "17",
    "31",
    "43",
    "89",
    "97",
    "167",
    "683",
    "733",
    "1031",
    "12611",
    "27823"
  ],
  "discriminant": "-24291506509440501984862372559700708847292508840321386491148400337200279984231518208",
  "regulator": "822485258499.8708949900536403050358743340435729145543396349",
  "points": [
    [
      "97052251757015",
      "941124450631724927700"
    ],
    [
      "-355587895361966128897/15062161",
      "3560696613863736725643512663988/58456246841"
    ],
    [
      "-17138841305405377/841",
      "2068333791764758434470268/24389"
    ],
    [
      "846987112788604583/69169",
      "1317230633071004500854241524/18191447"
    ],
    [
      "9131265231190897217/896809",
      "61461168540317266393280603556/849278123"
    ],
    [
      "88002217373574349151/3367225",
      "782625868612195497723443201724/6178857875"
    ],
    [
      "274706952621478664621/4674244",
      "4392551294133509262344301776349/10105715528"
    ],
    [
      "540579137861245339607/22934521",
      "12156357425911616747238983791932/109833421069"
    ],
    [
      "1258662524772650177981/7856809",
      "44370304039407808421039458522584/22022635627"
    ],
    [
      "-9790612520652939115/418609",
      "17111418320999582771533376400/270840023"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -167/1118 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 the four generic sections of the fibration and a 2-descent (PARI ellrank).",
  "created_at": "2026-10-15 18:12:40",
  "updated_at": "2026-10-15 18:12:40"
}