{
  "id": 2937,
  "curve_key": "167631429706952862825801:-262997967823251493517935556340853701",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-3492321452228184642204",
    "304395796092599346008815791925428"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    6
  ],
  "naive_height": 163.11490874808726,
  "faltings_height": 11.648664703694475,
  "conductor": "301672788158929193370",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "47",
    "61",
    "73",
    "83",
    "2707",
    "41227"
  ],
  "discriminant": "-37301758245181885632846565419139376044852621619348415150495061312500",
  "regulator": "155899.9336216451167649460184613556390350529008851708",
  "points": [
    [
      "244773328996390993/729",
      "-121100558700847029096685168/19683"
    ],
    [
      "9315580206613/9",
      "-28390031655710197147/27"
    ],
    [
      "-9563366220467/144",
      "-26959598547870097483/1728"
    ],
    [
      "14723311170229512/6241",
      "-1785982145887780735795254/493039"
    ],
    [
      "4261842078115512/11881",
      "-275352099136282551082074/1295029"
    ],
    [
      "85352208922",
      "-25062150548086096"
    ],
    [
      "14083899996037272/121",
      "-1671415260911051954693826/1331"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1263 via the rational 2-torsion point x=42142183992. 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 20:29:09",
  "updated_at": "2026-09-26 20:29:09"
}