{
  "id": 4774,
  "curve_key": "4508297896738759042994575980336:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-93922872848724146729053666257",
    "0"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 211.75041739683638,
  "faltings_height": 15.714108528044521,
  "conductor": "31365354823671479158815749670876719302406866939637832497952",
  "bad_primes": [
    "2",
    "3",
    "11",
    "13",
    "29",
    "31",
    "43",
    "47",
    "59",
    "79",
    "83",
    "173",
    "313",
    "373",
    "1487",
    "3457"
  ],
  "discriminant": "53026636193258632499856653805489541121615449979092195130946204976111534453285788792101952",
  "regulator": "153433767881622.9688155881698244054234767371511103269461975890933",
  "points": [
    [
      "-276575640135201",
      "-2195535978875023935084"
    ],
    [
      "-5723054432289",
      "-733033603959375795948"
    ],
    [
      "-5507920096053921/25",
      "-395259427531107434812608/125"
    ],
    [
      "-304653891626084",
      "-581226593684433074378"
    ],
    [
      "23349585533550588/49",
      "2732165813058865821880866/343"
    ],
    [
      "1001302871976927",
      "30164026061532099012588"
    ],
    [
      "-844205963346119/16",
      "-140344761205244805896467/64"
    ],
    [
      "-215810114867127",
      "3196617659767052691984"
    ],
    [
      "3935217139484887/9",
      "176074852891011071539868/27"
    ],
    [
      "7399454389697142972/6889",
      "19291238531557874575134506658/571787"
    ],
    [
      "-12110862831561",
      "1065697280305629027264"
    ],
    [
      "-2756408013641711/9",
      "-5241628634863110963616/27"
    ],
    [
      "1817241281560031004639/3094081",
      "-66084895405957994264159002407996/5442488479"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + a x with a = -93922872848724146729053666257. 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 21:29:57",
  "updated_at": "2026-10-20 21:29:57"
}