{
  "id": 2814,
  "curve_key": "336448:-1294506496",
  "ainvs": [
    "0",
    "1",
    "0",
    "-7009",
    "1495935"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2
  ],
  "naive_height": 41.962790750594,
  "faltings_height": 1.5544023078744396,
  "conductor": "4594624",
  "bad_primes": [
    "2",
    "17",
    "41",
    "103"
  ],
  "discriminant": "-947721109700608",
  "regulator": "10.41641310513578030289719141633201079425364568",
  "points": [
    [
      "154",
      "2023"
    ],
    [
      "-59/9",
      "33524/27"
    ],
    [
      "715",
      "-19040"
    ],
    [
      "12763/81",
      "-1516672/729"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1582 via the rational 2-torsion point x=67. 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 20:23:36",
  "updated_at": "2026-09-26 20:23:36"
}