{
  "id": 3675,
  "curve_key": "61076930323312738228036113:-473881697205465593994726663935312278041",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-1272436048402348713084086",
    "548474186580718102061552744510808380"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    4
  ],
  "naive_height": 178.12252936285904,
  "faltings_height": 12.694727432802017,
  "conductor": "2401768163536149420691858179",
  "bad_primes": [
    "3",
    "7",
    "11",
    "13",
    "23",
    "43",
    "47",
    "149",
    "991",
    "1153",
    "27031",
    "1246261"
  ],
  "discriminant": "1896408421505981725628780785658852368246230204155521023576563078226753297",
  "regulator": "889551524.31291353345982316668542702778963705773316207069",
  "points": [
    [
      "-2290989822273/4",
      "8349851907030468983/8"
    ],
    [
      "605151835488",
      "8310530636733676"
    ],
    [
      "13683287611956",
      "50448894000251952724"
    ],
    [
      "-17984990790994509/27889",
      "4886690832472759041129926/4657463"
    ],
    [
      "-1445870851058877/1681",
      "69147904042913136559526/68921"
    ],
    [
      "201869524527700/289",
      "107561613526196501972/4913"
    ],
    [
      "1900399390779600/2401",
      "22690000481046011990995/117649"
    ],
    [
      "14184161078304060/25921",
      "528563543018915142202820/4173281"
    ],
    [
      "14162137473564642405/23464336",
      "2127348013748059960789140425/113661243584"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -251/298 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": "2026-09-29 19:31:09",
  "updated_at": "2026-09-29 19:31:09"
}