{
  "id": 2815,
  "curve_key": "83690381826361:-8992404396718292452141",
  "ainvs": [
    "1",
    "0",
    "1",
    "-1743549621383",
    "10407875313868888556"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    6
  ],
  "naive_height": 101.10133443591938,
  "faltings_height": 6.482942185561658,
  "conductor": "42652114744890",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "29",
    "31",
    "37",
    "43",
    "8353"
  ],
  "discriminant": "-46456691379466975569936848910769041656250",
  "regulator": "3261.47201084168621545801537945114298304527707562",
  "points": [
    [
      "1042926",
      "3117790159"
    ],
    [
      "141987715/36",
      "1739486036797/216"
    ],
    [
      "-2439810",
      "373262767"
    ],
    [
      "12919114140/1681",
      "1463303900975432/68921"
    ],
    [
      "-1654910/9",
      "-88408645891/27"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1669 via the rational 2-torsion point x=1224183. 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 20:23:40",
  "updated_at": "2026-09-26 20:23:40"
}