{
  "id": 6320,
  "curve_key": "7028262073200:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-146422126525",
    "0"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 88.74288172628174,
  "faltings_height": 5.463480555498301,
  "conductor": "27442482094211978976800",
  "bad_primes": [
    "2",
    "5",
    "101",
    "181",
    "421",
    "761"
  ],
  "discriminant": "200909329267937667795582481981000000",
  "regulator": "14952198702.7726711019318160276378563519080316222024569",
  "points": [
    [
      "89775625/196",
      "467522887875/2744"
    ],
    [
      "1363455625/2916",
      "-28933175103875/157464"
    ],
    [
      "9878449/16",
      "-24365790057/64"
    ],
    [
      "23887248025/51984",
      "2044096056603325/11852352"
    ],
    [
      "145225777225/379456",
      "-1055043496342725/233744896"
    ],
    [
      "3801509811268225/24068836",
      "234386664629920725368775/118081709416"
    ],
    [
      "1804172808025/712336",
      "2395539094947591075/601211584"
    ],
    [
      "9730987019209/329476",
      "-30352808857483034973/189119224"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + ax (j = 1728) of rank 8: the rational 2-isogenous partner (a -> -4a, reduced by 16) of y^2 = x^3 + 585688506100x, 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 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 00:09:07",
  "updated_at": "2026-11-01 00:09:07"
}