{
  "id": 6302,
  "curve_key": "-1994923653024:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "41560909438",
    "0"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 84.96488068913158,
  "faltings_height": 5.1486471357357875,
  "conductor": "110547788372072798454016",
  "bad_primes": [
    "2",
    "31",
    "41",
    "2273",
    "7193"
  ],
  "discriminant": "-4594466621102907024890585383403008",
  "regulator": "7933247.21845444961595955708795840874009478230417238751",
  "points": [
    [
      "123039",
      "83523951"
    ],
    [
      "167648",
      "108071704"
    ],
    [
      "1068911",
      "1125047257"
    ],
    [
      "4950594",
      "11024372766"
    ],
    [
      "70463/49",
      "2651734079/343"
    ],
    [
      "152561/4",
      "324037063/8"
    ],
    [
      "72224575/81",
      "629639399935/729"
    ],
    [
      "369789824/1849",
      "10154289895856/79507"
    ]
  ],
  "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 23:54:31",
  "updated_at": "2026-10-31 23:54:31"
}