{
  "id": 2663,
  "curve_key": "109953:-36368865",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-2291",
    "42666"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2,
    2
  ],
  "naive_height": 34.82342484222084,
  "faltings_height": 0.7097666995453049,
  "conductor": "6867",
  "bad_primes": [
    "3",
    "7",
    "109"
  ],
  "discriminant": "3819610809",
  "regulator": "2.36382840710066653316567366613245420760109",
  "points": [
    [
      "57",
      "-337"
    ],
    [
      "914/25",
      "-12648/125"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1429 via the rational 2-torsion point x=-13. 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 20:16:34",
  "updated_at": "2026-09-26 20:16:34"
}