{
  "id": 2863,
  "curve_key": "81016129600:-22860851944256000",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-1687836033",
    "26459881991937"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    2,
    2
  ],
  "naive_height": 75.35374230797738,
  "faltings_height": 4.138296421877701,
  "conductor": "18648177600",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "37",
    "41",
    "197"
  ],
  "discriminant": "5289346367855366169600000000",
  "regulator": "188.117617641314234045263744304859554107135364806",
  "points": [
    [
      "473553/16",
      "-99779121/64"
    ],
    [
      "1291977/49",
      "-183688128/343"
    ],
    [
      "623473/9",
      "-420004000/27"
    ],
    [
      "3715537/121",
      "-2520024000/1331"
    ],
    [
      "645507",
      "-517596300"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1689 via the rational 2-torsion point x=-43793. 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 20:25:52",
  "updated_at": "2026-09-26 20:25:52"
}