{
  "id": 2939,
  "curve_key": "19149881929682448:-2260414430632372555500480",
  "ainvs": [
    "0",
    "0",
    "0",
    "-398955873535051",
    "2616220405824505272570"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2,
    2
  ],
  "naive_height": 112.47321883489951,
  "faltings_height": 7.365985802565505,
  "conductor": "177546673115895824",
  "bad_primes": [
    "2",
    "13",
    "17",
    "53",
    "113",
    "1153",
    "1951",
    "3727"
  ],
  "discriminant": "1107136909990583002308401662040736074016292864",
  "regulator": "3812099.177182706321544401632742249283566726791400953",
  "points": [
    [
      "6915045",
      "13714414080"
    ],
    [
      "9351135301/225",
      "-811561673671424/3375"
    ],
    [
      "161522698/9",
      "-949531247522/27"
    ],
    [
      "6068183801871/167281",
      "-12959532329150869410/68417929"
    ],
    [
      "16905639",
      "-26519025390"
    ],
    [
      "73750760464105/3849444",
      "-338196053479647340835/7552609128"
    ],
    [
      "381476071416541/6497401",
      "-7057376513041968116640/16561875149"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#2085 via the rational 2-torsion point x=45357110. 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 20:29:16",
  "updated_at": "2026-09-26 20:29:16"
}