{
  "id": 2649,
  "curve_key": "4059260641:-237288290920561",
  "ainvs": [
    "1",
    "0",
    "0",
    "-84567930",
    "274632178275"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    4,
    2
  ],
  "naive_height": 66.37280005754482,
  "faltings_height": 3.495263334652843,
  "conductor": "1330665",
  "bad_primes": [
    "3",
    "5",
    "7",
    "19",
    "23",
    "29"
  ],
  "discriminant": "6123337821629582375390625",
  "regulator": "6.50721014549991701983124181992138048478267",
  "points": [
    [
      "29955/4",
      "-2010945/8"
    ],
    [
      "1583385",
      "-1993173255"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1467 via the rational 2-torsion point x=-32081/4. 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 20:15:24",
  "updated_at": "2026-09-26 20:15:24"
}