{
  "id": 2671,
  "curve_key": "200641:-68250689",
  "ainvs": [
    "1",
    "1",
    "1",
    "-4180",
    "77252"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2,
    2
  ],
  "naive_height": 36.62781756139593,
  "faltings_height": 1.0700704899202103,
  "conductor": "5115",
  "bad_primes": [
    "3",
    "5",
    "11",
    "31"
  ],
  "discriminant": "1978593890625",
  "regulator": "0.603467573678516105120115249599573304206251",
  "points": [
    [
      "62",
      "-279"
    ],
    [
      "227",
      "-3414"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1428 via the rational 2-torsion point x=-11. 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 20:17:00",
  "updated_at": "2026-09-26 20:17:00"
}