{
  "id": 4765,
  "curve_key": "-5456635666500699562455504:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "113679909718764574217823",
    "0"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 170.8766239602044,
  "faltings_height": 12.307959074991858,
  "conductor": "45948877773036317495588418797306267208003055392",
  "bad_primes": [
    "2",
    "3",
    "7",
    "43",
    "47",
    "71",
    "73",
    "197",
    "199",
    "577",
    "2141",
    "3557"
  ],
  "discriminant": "-94022356984511702308503105325196023260416262965891661652406385767729088",
  "regulator": "1664736199910.2498982879759155485437612546515592832197605539342",
  "points": [
    [
      "104762203270617/4",
      "-1072365712734453758613/8"
    ],
    [
      "10655517447792",
      "34799990290591352148"
    ],
    [
      "24989725443036/169",
      "311034855129139282842/2197"
    ],
    [
      "757689992791239/3721",
      "40343337019608251813064/226981"
    ],
    [
      "7445251230832",
      "-20335923846951178348"
    ],
    [
      "733498061692",
      "-691390038441984398"
    ],
    [
      "675107014724289/7921",
      "71574546853697268494736/704969"
    ],
    [
      "652378328741199/1225",
      "19721571715238548411332/42875"
    ],
    [
      "127167789084",
      "128502666601497594"
    ],
    [
      "289395375129/4",
      "-742032218204891019/8"
    ],
    [
      "1151258506176",
      "-1287147447859797432"
    ],
    [
      "264081393534006951/570025",
      "-167843273951936378691040824/430368875"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + a x with a = 113679909718764574217823 (2-isogenous model of the curve listed there). 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 21:29:10",
  "updated_at": "2026-10-20 21:29:10"
}