{
  "id": 2682,
  "curve_key": "148761498434881:-1814306112174789450721",
  "ainvs": [
    "1",
    "0",
    "0",
    "-3099197884060",
    "2099891075269145600"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    4,
    2
  ],
  "naive_height": 97.90009637330797,
  "faltings_height": 5.837290735101585,
  "conductor": "2615851410",
  "bad_primes": [
    "2",
    "3",
    "5",
    "19",
    "23",
    "61",
    "3271"
  ],
  "discriminant": "221542081226883833711672772506250000",
  "regulator": "60.661125031086576150044314826802954701685397",
  "points": [
    [
      "57658430/49",
      "98230126520/343"
    ],
    [
      "57350000/49",
      "-94668867880/343"
    ],
    [
      "942993770/841",
      "-4548389505290/24389"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1567 via the rational 2-torsion point x=-505032. 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 20:17:33",
  "updated_at": "2026-09-26 20:17:33"
}