{
  "id": 6301,
  "curve_key": "-1838781903264:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "38307956318",
    "0"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 84.72037337768704,
  "faltings_height": 5.128271526448743,
  "conductor": "93919969104754951495936",
  "bad_primes": [
    "2",
    "41",
    "103",
    "1601",
    "2833"
  ],
  "discriminant": "-3597882073852862248000525042523648",
  "regulator": "202608401.219795628700438998508955309235639605864546479",
  "points": [
    [
      "1498657/4",
      "2069905953/8"
    ],
    [
      "2435121/100",
      "30777993831/1000"
    ],
    [
      "2722513/4",
      "4674203529/8"
    ],
    [
      "37174626/361",
      "486787041198/6859"
    ],
    [
      "245402959/1849",
      "6849712778121/79507"
    ],
    [
      "1020517425/73984",
      "463733391128745/20123648"
    ],
    [
      "1042821634/21609",
      "140669432062174/3176523"
    ],
    [
      "42448532962/9",
      "8745688978711982/27"
    ]
  ],
  "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 23:53:56",
  "updated_at": "2026-10-31 23:53:56"
}