{
  "id": 2764,
  "curve_key": "882702382252677697168:-26225285935723788504062770137280",
  "ainvs": [
    "0",
    "1",
    "0",
    "-18389632963597452024",
    "30353340197254136817762388836"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    4,
    2
  ],
  "naive_height": 144.6885592942206,
  "faltings_height": 9.65201744465408,
  "conductor": "438112332979152",
  "bad_primes": [
    "2",
    "3",
    "13",
    "17",
    "19",
    "149",
    "349",
    "41801"
  ],
  "discriminant": "2228790781967417240163263242768273751820201544704082944",
  "regulator": "2808.555385421914444623504229722913193016542948",
  "points": [
    [
      "2103044027734/9",
      "-3049298346895979516/27"
    ],
    [
      "2314651465496338761/892575376",
      "271751111072246103981126093/26666581933376"
    ],
    [
      "63962188287042/19321",
      "-203746309023873461760/2685619"
    ],
    [
      "25305513887706/10201",
      "-306406108953164688/1030301"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1637 via the rational 2-torsion point x=-4944951205. 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 20:21:23",
  "updated_at": "2026-09-26 20:21:23"
}