{
  "id": 6283,
  "curve_key": "417515136:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-8698232",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 59.54949406647073,
  "faltings_height": 3.0306982505140514,
  "conductor": "302636959703296",
  "bad_primes": [
    "2",
    "23",
    "41",
    "1153"
  ],
  "discriminant": "42118503796382716362752",
  "regulator": "13201.242266523851198247394522462606519102359705330",
  "points": [
    [
      "-2944",
      "9568"
    ],
    [
      "-943",
      "85813"
    ],
    [
      "-184",
      "39928"
    ],
    [
      "2952",
      "6888"
    ],
    [
      "-67896/25",
      "7491192/125"
    ],
    [
      "-7544/9",
      "2210392/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + ax (j = 1728) of rank 6. 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 23:41:26",
  "updated_at": "2026-10-31 23:41:26"
}