{
  "id": 2657,
  "curve_key": "1086572176:-35805211408576",
  "ainvs": [
    "0",
    "1",
    "0",
    "-22636920",
    "41433671268"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    4,
    2
  ],
  "naive_height": 62.41888135582476,
  "faltings_height": 2.935640124540626,
  "conductor": "895440",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "41"
  ],
  "discriminant": "484042276123136640000",
  "regulator": "2.31815437609645692241288104254896899003638",
  "points": [
    [
      "4551",
      "-180810"
    ],
    [
      "19986",
      "-2751840"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1472 via the rational 2-torsion point x=-5413. 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 20:16:01",
  "updated_at": "2026-09-26 20:16:01"
}