{
  "id": 2865,
  "curve_key": "25919613507055423374374903031217380700219201:101562714056178167458104134920218144434509768029713658181099431199",
  "ainvs": [
    "1",
    "1",
    "1",
    "-539991948063654653632810479817028764587900",
    "-117549437565021027150808486136019745497474050697277533028184115"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    4,
    2
  ],
  "naive_height": 299.8907215983888,
  "faltings_height": 23.006512982503583,
  "conductor": "4738696264040550563800319661390",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "29",
    "41",
    "71",
    "113",
    "193",
    "1889",
    "171679",
    "818231"
  ],
  "discriminant": "4107925243910968756555577971267932138331930160031355212466993630352132020561196400611012077776951360146443969310433542006250000",
  "regulator": "58756461.329013825061675423983868403898822493485117",
  "points": [
    [
      "-536374889645973177161923/1369",
      "-294813127701864286112391941117879751/50653"
    ],
    [
      "710424392482594315958683/676",
      "-383319196366071892733652175741354367/17576"
    ],
    [
      "-47478121212002788565577233/85849",
      "-86909036655977036213915599321157458769/25153757"
    ],
    [
      "1906115601627742684914024114439543/1473053125636",
      "-65698404381948908979385410503893129616495628350723/1787835740265659384"
    ],
    [
      "5608265243269457053003",
      "-416231636017207173248588032741417"
    ],
    [
      "7551440082504255508877027190787/6171359364",
      "15737970533326346107424127492587254684910981371/484809648917112"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1897 via the rational 2-torsion point x=290566547041438749261. 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 20:25:56",
  "updated_at": "2026-09-26 20:25:56"
}