{
  "id": 6300,
  "curve_key": "-1643011439520:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "34229404990",
    "0"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 84.38265575262025,
  "faltings_height": 5.100128391026512,
  "conductor": "74985738622043961606400",
  "bad_primes": [
    "2",
    "5",
    "11",
    "29",
    "53",
    "193",
    "1049"
  ],
  "discriminant": "-2566717215768227303409476575936000",
  "regulator": "2888515.48731536691286538129629997444190086377682238340",
  "points": [
    [
      "150626",
      "92591954"
    ],
    [
      "228536",
      "140565964"
    ],
    [
      "334631",
      "221191091"
    ],
    [
      "760815",
      "682958265"
    ],
    [
      "888386",
      "855306686"
    ],
    [
      "1846240/9",
      "3378157640/27"
    ],
    [
      "3224626/9",
      "6516969146/27"
    ],
    [
      "4892536/9",
      "11431410364/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + ax (j = 1728) of rank 8. Rank proven (independent generators plus a matching 2-descent upper bound) in M. Rubinstein's elliptic-curves-by-rank collection, file families/family_Z2.add_2026-10-24.part1.tsv.gz:\r\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-10-31 23:53:19",
  "updated_at": "2026-10-31 23:53:19"
}