{
  "id": 2699,
  "curve_key": "86101934967841:-751501253444762323889",
  "ainvs": [
    "1",
    "1",
    "1",
    "-1793790311830",
    "869792370000289427"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    4,
    2
  ],
  "naive_height": 96.25965900181139,
  "faltings_height": 5.969540549295393,
  "conductor": "990867570",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "31",
    "101",
    "137"
  ],
  "discriminant": "42573079286403505742002551202160640000",
  "regulator": "26.612770981016028357684802045476606997964827",
  "points": [
    [
      "71837369/25",
      "-551339192013/125"
    ],
    [
      "352816097",
      "-6627214437969"
    ],
    [
      "8068757",
      "-22625072049"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1572 via the rational 2-torsion point x=12289779/4. 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 20:18:18",
  "updated_at": "2026-09-26 20:18:18"
}