{
  "id": 2894,
  "curve_key": "4790339989146053033358241:-4353670675364782673435924695731294961",
  "ainvs": [
    "1",
    "0",
    "0",
    "-99798749773876104861630",
    "5038970689071293013254867611320900"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    6
  ],
  "naive_height": 170.4859308591178,
  "faltings_height": 12.263988323206224,
  "conductor": "75879741797208175256430",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "23",
    "29",
    "31",
    "67",
    "79",
    "233",
    "5828761"
  ],
  "discriminant": "52645367214393440293642741803951273012786168069023227914816000000000000",
  "regulator": "28787.27382925798132094949688444203275046535872375966",
  "points": [
    [
      "1320820240222140/1369",
      "45498789255481341288810/50653"
    ],
    [
      "-27492815280",
      "88101879236616210"
    ],
    [
      "49716526449660",
      "-350543920216810114830"
    ],
    [
      "-233985590340",
      "124819598526685170"
    ],
    [
      "175897573867260/361",
      "-1841638066801206818970/6859"
    ],
    [
      "-255177298020",
      "117853258806596850"
    ],
    [
      "-1225188845380170384406140/4023157419961",
      "684169701653772957284959125872315370/8069572712966794541"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z6old678-149, rational kernel x=-415131437281/4. Source: https://dujella.github.io/tors/z6old678.html. Independent witness points transported by 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 20:27:14",
  "updated_at": "2026-09-26 20:27:14"
}