{
  "id": 4767,
  "curve_key": "-14569149935663089802093520:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "303523956992981037543615",
    "0"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 173.8228455206808,
  "faltings_height": 12.553477538364891,
  "conductor": "327561928777518231048733993255374727655208064800",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "103",
    "151",
    "181",
    "631",
    "661",
    "977",
    "4019"
  ],
  "discriminant": "-1789612070090496502451787786422100724771713992376875352182756335432536000",
  "regulator": "3196751624401.5216737973163515733444237502143462307635738118702",
  "points": [
    [
      "423155124540",
      "451893775348988190"
    ],
    [
      "165565843839",
      "234076267550441448"
    ],
    [
      "40659591856240",
      "259289175252550021460"
    ],
    [
      "1058045903140615/52441",
      "-940395921828290231705360/12008989"
    ],
    [
      "665743024180521/256",
      "-17558737699302388438101/4096"
    ],
    [
      "1736744050881",
      "2401176710640168216"
    ],
    [
      "2409106140",
      "-27041364802479510"
    ],
    [
      "490917930457735/729",
      "14053432975688150269280/19683"
    ],
    [
      "31377338839/9",
      "-878326015641980752/27"
    ],
    [
      "61671958230289/81",
      "597812525663662594648/729"
    ],
    [
      "3123847890625",
      "-5606424888990695000"
    ],
    [
      "2102828092820665/1296",
      "101835630353252720291885/46656"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + a x with a = 303523956992981037543615 (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 21:29:18",
  "updated_at": "2026-10-20 21:29:18"
}