{
  "id": 2526,
  "curve_key": "29968:5156416",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-624",
    "-5760"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2
  ],
  "naive_height": 30.92365627405161,
  "faltings_height": 0.42077897367091244,
  "conductor": "336",
  "bad_primes": [
    "2",
    "3",
    "7"
  ],
  "discriminant": "188116992",
  "regulator": "1.492598417389027417818875207263106353784",
  "points": [
    [
      "66",
      "-486"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#2076 via the rational 2-torsion point x=8. 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 20:07:06",
  "updated_at": "2026-09-26 20:07:06"
}