{
  "id": 2680,
  "curve_key": "87791025:809028192375",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-1828980",
    "-935917978"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2,
    2
  ],
  "naive_height": 54.871409497271124,
  "faltings_height": 2.459898524889008,
  "conductor": "684475",
  "bad_primes": [
    "5",
    "11",
    "19",
    "131"
  ],
  "discriminant": "12790507315828515625",
  "regulator": "14.319064998139118729160737691390388925151563",
  "points": [
    [
      "552499/36",
      "-410670605/216"
    ],
    [
      "71506/9",
      "-18930335/27"
    ],
    [
      "4903",
      "-331000"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1530 via the rational 2-torsion point x=349. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.",
  "created_at": "2026-09-26 20:17:26",
  "updated_at": "2026-09-26 20:17:26"
}