{
  "id": 4771,
  "curve_key": "3632575237411718188593802800:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-75678650779410795595704225",
    "0"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 190.37921801814622,
  "faltings_height": 13.933175246487009,
  "conductor": "7330890475253778201214555373723049650024030314048800",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "109",
    "173",
    "353",
    "1009",
    "1181",
    "1609",
    "4157"
  ],
  "discriminant": "27739595008941975970493171735842303123910304344963255535048054320147350809000000",
  "regulator": "7499001827716.4815733960709939379629143001266898336774597872154",
  "points": [
    [
      "-17513163291615/4",
      "125835143053829807625/8"
    ],
    [
      "-8673709284240",
      "-1965560103038231700"
    ],
    [
      "-8452322325135",
      "5984281772072580600"
    ],
    [
      "438368987131735",
      "9176439379286807197900"
    ],
    [
      "-1807788823809540/361",
      "-109184767171932965949150/6859"
    ],
    [
      "-167862964815/4",
      "-14256702039745230975/8"
    ],
    [
      "-18925708394113521/2209",
      "458447881421645369846592/103823"
    ],
    [
      "-8601183539025",
      "-3821953107932836800"
    ],
    [
      "8700196120924",
      "358371642744720682"
    ],
    [
      "103108802726479/9",
      "-681277904115856625908/27"
    ],
    [
      "67438142542225/4",
      "474388125118648406575/8"
    ],
    [
      "60954743269204015/169",
      "-15044747346590088784772500/2197"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + a x with a = -75678650779410795595704225. Source: Aguirre, Castaneda, Peral, 'High rank elliptic curves with torsion group Z/(2Z)', Math. Comp. 73 (2004) 323-331, doi:10.1090/S0025-5718-03-01547-3, https://www.ams.org/mcom/2004-73-245/S0025-5718-03-01547-3/.",
  "created_at": "2026-10-20 21:29:34",
  "updated_at": "2026-10-20 21:29:34"
}