{
  "id": 2868,
  "curve_key": "10363366618604359257747156713353372579201:-746780123911747695965716525786346849739649423742212693108801",
  "ainvs": [
    "1",
    "0",
    "0",
    "-215903471220924151203065764861528595400",
    "864328847120078351794179948910231841265079500777989160000"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    4,
    2
  ],
  "naive_height": 276.4172873219873,
  "faltings_height": 21.06191432026679,
  "conductor": "3720844854479034579834388830",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "19",
    "23",
    "43",
    "71",
    "97",
    "263",
    "337",
    "2063",
    "2957",
    "9479"
  ],
  "discriminant": "321376428424457778492877576634598596788604608494086573176396465756458283654487594306919350701858141280016000000000000",
  "regulator": "2397438.6293156798641730739724053253866523178340155",
  "points": [
    [
      "797973359997676388302800/229441",
      "1370502119902560682800777417564179400/109902239"
    ],
    [
      "91083063688989370663487760/4566769",
      "-654089009863248144840748763509810515720/9759185353"
    ],
    [
      "12736005904002286800",
      "-13432631178313904311764275400"
    ],
    [
      "13528242951714550800",
      "-20478852418660990325996675400"
    ],
    [
      "3098092920736259365399245450/18003049",
      "-171826373366721687940399878058491459675300/76386936907"
    ],
    [
      "2628862212560550941711998344162300/83939513746201",
      "-121160844676201841622349398429844901673414379857900/769041317955145378051"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1903 via the rational 2-torsion point x=131121445710117831551/4. 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 20:26:03",
  "updated_at": "2026-09-26 20:26:03"
}