{
  "id": 3706,
  "curve_key": "83689037589788135305818961265851860426382065803025:-765592097655667017271264941919531256716825665292444762396431224034554693625",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-1743521616453919485537895026371913758882959704230",
    "886101964879244232952853377916898623568789978562234327233568452261401397"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    4
  ],
  "naive_height": 344.85357737996713,
  "faltings_height": 26.37219527753961,
  "conductor": "1097108044453769307704470853301745036152608455549132667550",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "31",
    "43",
    "47",
    "71",
    "109",
    "139",
    "167",
    "181",
    "227",
    "271",
    "523",
    "947",
    "1061",
    "1063",
    "11953",
    "4943153",
    "588848633"
  ],
  "discriminant": "8463795652798219847254681891108624528523966691610296553193455247881185844592110297436339102837526056208968044593576885433223519507988480000000",
  "regulator": "70420748372785316.443434931413649388959534356512950258128009794",
  "points": [
    [
      "905066969961146008229129",
      "222441735759337282248602378541794235"
    ],
    [
      "-13888899672223282560079757638599/26988025",
      "179934080509786911176943944383110133530907182889/140202789875"
    ],
    [
      "727483603247027421112825438673/1042441",
      "102254721813830093044435877500267318432223175/1064332261"
    ],
    [
      "1068131382153415551148509216764801/1414737769",
      "562937900048080698056344424901360514802588458695/53212531705397"
    ],
    [
      "7913300012304865951314863738061881/11866834225",
      "182720288847509518232902139659700947332162375052941/1292713586300375"
    ],
    [
      "464829585599352290647170121465755069/611509924081",
      "178252331348192822220981423068380873459189019026425/478195257042025271"
    ],
    [
      "55496958971043937342084287540522714681/72567619307569",
      "935672508878071963040682912384322466577080236009280525/618179093593473660247"
    ],
    [
      "529196777234928985452908403912450122021/698837933704849",
      "128238192156363742228008026084888851475545958452209792645/18474160246485685048007"
    ],
    [
      "1057036802833109188064960624213910048209/1426164182338921",
      "1707167224864848309119334816619586598493560677585573507415/53858504192550410268469"
    ],
    [
      "1092660551611250536222696470133445306009/1480726946446225",
      "2084889108516421849910983549614093643025346117257521231197/56978691255544223938375"
    ],
    [
      "39504709494583295130678050781909350270769/47300712177078361",
      "1150513374749910747897571595228124719442235039936192251450815/10287302713147817132886109"
    ],
    [
      "1889621929283145195812902630097679504941649/2438478818704569481",
      "71475546751301379555913139853042706241338229279738318374224135/3807838155702513328889203621"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 469252/945061 of the Elkies-Klagsbrun Z/4 fibration E1: y^2 + a*xy + a*c*y = x^3 + c*x^2, a = (8t-1)(32t+7), c = 8(t+1)(15t-8)(31t-7) (arXiv:2003.00077, eq. (5)), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-30 01:46:54",
  "updated_at": "2026-09-30 01:46:54"
}