{
  "id": 3030,
  "curve_key": "-23639182784:-22789440480401920",
  "ainvs": [
    "0",
    "1",
    "0",
    "492482975",
    "26376831383679"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "naive_height": 75.33014737353123,
  "faltings_height": 4.338608678167304,
  "conductor": "31226965890509248",
  "bad_primes": [
    "2",
    "17",
    "23",
    "31",
    "71",
    "577",
    "593",
    "1657"
  ],
  "discriminant": "-308199324015416875950097235968",
  "regulator": "77789.8089789095997941876580978352459398062760997618495",
  "points": [
    [
      "-2423",
      "5016904"
    ],
    [
      "-18998",
      "3188129"
    ],
    [
      "-16406",
      "3725807"
    ],
    [
      "26749",
      "7660948"
    ],
    [
      "-7166",
      "4741283"
    ],
    [
      "3946",
      "-5327441"
    ],
    [
      "5499",
      "-5408448"
    ],
    [
      "12003361/361",
      "-61162176544/6859"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1348 via the rational 2-torsion point x=12163. 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 20:34:03",
  "updated_at": "2026-09-26 20:34:03"
}