{
  "id": 2738,
  "curve_key": "2607651088141361751073:-43936239773858227518175051157425",
  "ainvs": [
    "1",
    "0",
    "0",
    "-54326064336278369814",
    "50852129363364295006901630244"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    4,
    2
  ],
  "naive_height": 147.93821040830235,
  "faltings_height": 10.389454063369092,
  "conductor": "2102768214757266",
  "bad_primes": [
    "2",
    "3",
    "7",
    "17",
    "19",
    "37",
    "41",
    "59",
    "137",
    "12641"
  ],
  "discriminant": "9144229140796918280110011172769317296641959623894777201041664",
  "regulator": "1029.903922724717077216793449717812597499327161",
  "points": [
    [
      "43276210236990/2809",
      "-252241862173101259164/148877"
    ],
    [
      "34880172465150/169",
      "-205869760380962074314/2197"
    ],
    [
      "14284953644580/121",
      "-53886201358243351698/1331"
    ],
    [
      "27921549987/4",
      "-867582877290057/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1636 via the rational 2-torsion point x=62402710175/4. 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 20:20:06",
  "updated_at": "2026-09-26 20:20:06"
}