{
  "id": 6319,
  "curve_key": "-4952239767744:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "103171661828",
    "0"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 87.69258320551145,
  "faltings_height": 5.375955678767444,
  "conductor": "21288783608702384603168",
  "bad_primes": [
    "2",
    "17",
    "73",
    "113",
    "193",
    "953"
  ],
  "discriminant": "-70284773862608380869607771951075328",
  "regulator": "26944358155.7566041367948866524108492307940030847470825",
  "points": [
    [
      "11294588176/120409",
      "-4281992113223688/41781923"
    ],
    [
      "25780798096/3481",
      "-4143359289389352/205379"
    ],
    [
      "13424896",
      "-49202896032"
    ],
    [
      "25792681201/484",
      "-4142405637057513/10648"
    ],
    [
      "153664/169",
      "-21279171984/2197"
    ],
    [
      "2142722150416/61324561",
      "-29003609835316413048/480232637191"
    ],
    [
      "174378902569/4875264",
      "-657962962789378859/10764582912"
    ],
    [
      "57307165632553326736/2549655447656769",
      "-6214795759245376436580112900888/128742590285046479100897"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + ax (j = 1728) of rank 8: the rational 2-isogenous partner (a -> -4a) of y^2 = x^3 - 25792915457x, from M. Rubinstein's elliptic-curves-by-rank collection (families/family_Z2.add_2026-10-24.part1.tsv.gz). The eight generators were transported through the 2-isogeny (x, y) -> (y^2/x^2, y(a - x^2)/x^2) and checked exactly on this model; rank is preserved under isogeny.\r\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-11-01 00:08:19",
  "updated_at": "2026-11-01 00:08:19"
}