{
  "id": 4772,
  "curve_key": "73247562128348539775294836320:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-1525990877673927911985309090",
    "0"
  ],
  "rank_lower_bound": 13,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 199.39092742997494,
  "faltings_height": 14.684151030806069,
  "conductor": "149033482159618868502058245714126232025398782901544198400",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "23",
    "31",
    "67",
    "89",
    "307",
    "317",
    "337",
    "1223",
    "2153",
    "10657"
  ],
  "discriminant": "227423734243558474578935295974382094902182242945420454495532728769709616120283456000",
  "regulator": "261619711909133.8778330587756240329843771003187412606364843860086",
  "points": [
    [
      "40502815695250",
      "68095917826495656950"
    ],
    [
      "-6327619304591/4",
      "392735126147523810937/8"
    ],
    [
      "-2211553703101972190/76729",
      "3008656553586590275897391890/21253933"
    ],
    [
      "-5321527835161031/144",
      "133004860544159607469843/1728"
    ],
    [
      "-3636467276537160/1369",
      "-3217457963157928795943820/50653"
    ],
    [
      "947544741895153935/3721",
      "-911440746861495549168800265/226981"
    ],
    [
      "115337107736760",
      "-1165455112761905953260"
    ],
    [
      "50289827997240",
      "224598565448552943180"
    ],
    [
      "264325378043686609/4356",
      "103991570672793643083320713/287496"
    ],
    [
      "177617015126165689/324",
      "74665747783962957864740003/5832"
    ],
    [
      "-382291046344334/225",
      "171689748953423691457286/3375"
    ],
    [
      "-301160451110375/16",
      "-9504467293840947827075/64"
    ],
    [
      "-58860725050023936/3721",
      "-32244663522690200213254272/226981"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + a x with a = -1525990877673927911985309090. 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 21:29:39",
  "updated_at": "2026-10-20 21:29:39"
}