{
  "id": 3701,
  "curve_key": "78568968456967502992326000769600:-738006958206007643537236377219161190832722496000",
  "ainvs": [
    "0",
    "1",
    "0",
    "-1636853509520156312340125016033",
    "854174720145841634402113003951554672311016063"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    4
  ],
  "naive_height": 220.44056487550301,
  "faltings_height": 16.31458721206736,
  "conductor": "7991717873699469142558439024164800",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "37",
    "41",
    "53",
    "67",
    "107",
    "151",
    "163",
    "283",
    "3049",
    "19231",
    "77719"
  ],
  "discriminant": "-34514769803219878082821895968549422402914288669439600325923932047485735225123096668160000000",
  "regulator": "17450379108.89054335994595193672390823791344088125802214245",
  "points": [
    [
      "-992059195235427",
      "38751310189332827723700"
    ],
    [
      "53934870329523",
      "27677574555838474784400"
    ],
    [
      "26733781602981363",
      "4366187929960852682060400"
    ],
    [
      "10340308907073844713",
      "33250659707602573267581786600"
    ],
    [
      "-8787936372180468918/10609",
      "44274727264881876234043455975/1092727"
    ],
    [
      "14363366603964907/9",
      "1296756532157386938367600/27"
    ],
    [
      "9265390560997861827/7921",
      "16381844596182561596791187952/704969"
    ],
    [
      "14965997361820245907/1089",
      "57655456534678580468063009200/35937"
    ],
    [
      "19526720333481905883/19321",
      "40921698312333192971687019600/2685619"
    ],
    [
      "67613735376705890427/76729",
      "208293227864501801473648669200/21253933"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -2333/13936 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 01:45:59",
  "updated_at": "2026-09-30 01:45:59"
}