{
  "id": 3696,
  "curve_key": "48870997310072778149258589856225:-338736841026456826093532629385066870181826284625",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1018145777293182878109553955338",
    "392056528965806426836847991060069035062432292"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    4
  ],
  "naive_height": 218.9002107249123,
  "faltings_height": 16.099925108534304,
  "conductor": "749928839103528874724228030523150",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "19",
    "41",
    "47",
    "53",
    "71",
    "151",
    "179",
    "449",
    "4157",
    "10357",
    "44893"
  ],
  "discriminant": "1145596260455490769045145144217755233360347118938286663380898993069794667766281666560000000",
  "regulator": "459310112709.9262660996419465318418409049950605092096836176",
  "points": [
    [
      "371861081364212",
      "8054125242692485870694"
    ],
    [
      "5517824754396212",
      "403450057460499722077094"
    ],
    [
      "-12948353606636846483404/33535681",
      "5238534675334915492938634362616730/194205128671"
    ],
    [
      "71090881864033179572/16129",
      "584895445527350229162003776090/2048383"
    ],
    [
      "96632602388112567028/208849",
      "427092503018055597087455189302/95443993"
    ],
    [
      "2330022222609685074932/5202961",
      "60415883216539884498874733614454/11867954041"
    ],
    [
      "2698276019568020256692/961",
      "140161756796921771756261787243674/29791"
    ],
    [
      "6008401135270864058068/18809569",
      "813406483556982587272022032240742/81577100753"
    ],
    [
      "9261832633174940984276/14280841",
      "114852624593541387949737490362370/53967298139"
    ],
    [
      "432453519596754366175028/141300769",
      "270538004428929692879016709805530682/1679642241103"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -7064/8413 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 01:45:05",
  "updated_at": "2026-09-30 01:45:05"
}