{
  "id": 2685,
  "curve_key": "89640108735073:-759444566623399877905",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1867502265314",
    "878986611300042564"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    4,
    2
  ],
  "naive_height": 96.38047193364028,
  "faltings_height": 6.0080629180602445,
  "conductor": "2434962642",
  "bad_primes": [
    "2",
    "3",
    "7",
    "31",
    "67",
    "103",
    "271"
  ],
  "discriminant": "83063377742955889354772628074406084864",
  "regulator": "141.10696100860225752479929841433587960420589",
  "points": [
    [
      "1219468",
      "-644893274"
    ],
    [
      "34463699236/19321",
      "-4823996476116422/2685619"
    ],
    [
      "3561525196/1849",
      "-167389003036046/79507"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1566 via the rational 2-torsion point x=-4557345/4. 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 20:17:41",
  "updated_at": "2026-09-26 20:17:41"
}