{
  "id": 2688,
  "curve_key": "59643002082946081:6154806518071676277990479",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1242562543394710",
    "-7123618758722429863900"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    4,
    2
  ],
  "naive_height": 115.88145966082968,
  "faltings_height": 7.71317179730937,
  "conductor": "1720479810",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "23",
    "29",
    "71",
    "173"
  ],
  "discriminant": "100859765205280114234994585095514900505600000000",
  "regulator": "48.311933776923277646459345887265590158802570",
  "points": [
    [
      "211680569420/121",
      "97370596606518190/1331"
    ],
    [
      "134237270",
      "-1498394882260"
    ],
    [
      "1062339020",
      "-34606753633510"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1565 via the rational 2-torsion point x=2949068. 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 20:17:48",
  "updated_at": "2026-09-26 20:17:48"
}