{
  "id": 6290,
  "curve_key": "17102494896:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-356301977",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 70.68747057049045,
  "faltings_height": 3.958862959182361,
  "conductor": "4062435162051472928",
  "bad_primes": [
    "2",
    "73",
    "89",
    "173",
    "317"
  ],
  "discriminant": "2894907359346510360016757312",
  "regulator": "178695.2209904693981450944476744850335189256522270912",
  "points": [
    [
      "-14308",
      "1472702"
    ],
    [
      "-2853",
      "996648"
    ],
    [
      "23141",
      "2036408"
    ],
    [
      "53573",
      "11604736"
    ],
    [
      "-2059549/121",
      "1416969712/1331"
    ],
    [
      "-1382437/169",
      "3380255956/2197"
    ],
    [
      "-103952/9",
      "43321996/27"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Quartic twist y^2 = x^3 + ax (j = 1728) of rank 7. 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 23:46:59",
  "updated_at": "2026-10-31 23:46:59"
}