{
  "id": 2919,
  "curve_key": "-4182378224:-5932031196422080",
  "ainvs": [
    "0",
    "1",
    "0",
    "87132880",
    "6865805892004"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2
  ],
  "naive_height": 72.63828615635657,
  "faltings_height": 4.111303340163126,
  "conductor": "48324055603376",
  "bad_primes": [
    "2",
    "7",
    "29",
    "37",
    "71",
    "109",
    "223",
    "233"
  ],
  "discriminant": "-20406338818348890733884587008",
  "regulator": "1834.374918007137707898876096545034697833746457176740",
  "points": [
    [
      "-16113",
      "1130794"
    ],
    [
      "32481/64",
      "1345903601/512"
    ],
    [
      "3189274/81",
      "6157307492/729"
    ],
    [
      "249706/9",
      "149459156/27"
    ],
    [
      "778318/9",
      "-694256752/27"
    ],
    [
      "106986",
      "-35224444"
    ],
    [
      "2535135/49",
      "-4198990214/343"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1330 via the rational 2-torsion point x=34963. 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 20:28:22",
  "updated_at": "2026-09-26 20:28:22"
}