{
  "id": 2749,
  "curve_key": "2972393073:-161835666001065",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-61924856",
    "187325279826"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2,
    2
  ],
  "naive_height": 65.43789964141448,
  "faltings_height": 3.237566491231155,
  "conductor": "2042704917",
  "bad_primes": [
    "3",
    "11",
    "31",
    "37",
    "17989"
  ],
  "discriminant": "40896077747150509489089",
  "regulator": "156.5276683242142980618951557109489556792343123",
  "points": [
    [
      "157503/4",
      "-61501361/8"
    ],
    [
      "115877/16",
      "21815631/64"
    ],
    [
      "21117584/4489",
      "-3771646821/300763"
    ],
    [
      "583828/9",
      "-443827897/27"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1510 via the rational 2-torsion point x=-2203. 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 20:20:36",
  "updated_at": "2026-09-26 20:20:36"
}