{
  "id": 2684,
  "curve_key": "5673025:2497477375",
  "ainvs": [
    "1",
    "1",
    "1",
    "-118188",
    "-2939844"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2,
    2
  ],
  "naive_height": 46.65369912941523,
  "faltings_height": 1.953939982669294,
  "conductor": "608475",
  "bad_primes": [
    "3",
    "5",
    "7",
    "19",
    "61"
  ],
  "discriminant": "102047903187890625",
  "regulator": "12.328537419931489130596568595223112460534475",
  "points": [
    [
      "-221",
      "3638"
    ],
    [
      "-329",
      "848"
    ],
    [
      "416",
      "-4692"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1528 via the rational 2-torsion point x=165. 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 20:17:37",
  "updated_at": "2026-09-26 20:17:37"
}