{
  "id": 3070,
  "curve_key": "-1916212195184:-2405316708862487360",
  "ainvs": [
    "0",
    "-1",
    "0",
    "39921087400",
    "2783918068969116"
  ],
  "rank_lower_bound": 9,
  "torsion": [
    2
  ],
  "naive_height": 84.84411461519156,
  "faltings_height": 5.1858316475677855,
  "conductor": "1115505417782881151832",
  "bad_primes": [
    "2",
    "3",
    "13",
    "19",
    "23",
    "29",
    "61",
    "89",
    "180241",
    "288313"
  ],
  "discriminant": "-7419924170119692834064048189344768",
  "regulator": "25806625.593764877805131272669363733051811811245901010005",
  "points": [
    [
      "-60762",
      "11571288"
    ],
    [
      "481281",
      "365344686"
    ],
    [
      "1079398",
      "1141700552"
    ],
    [
      "-61154",
      "10671256"
    ],
    [
      "418273",
      "304400198"
    ],
    [
      "766558",
      "695574008"
    ],
    [
      "-22559",
      "-43264966"
    ],
    [
      "-725495/16",
      "-1899117731/64"
    ],
    [
      "223933",
      "151502008"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1364 via the rational 2-torsion point x=31682. 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 20:35:50",
  "updated_at": "2026-09-26 20:35:50"
}