{
  "id": 2836,
  "curve_key": "1109017268491849:-37222805367547106292037",
  "ainvs": [
    "1",
    "0",
    "1",
    "-23104526426914",
    "43081948731506022632"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    6
  ],
  "naive_height": 103.9424171476638,
  "faltings_height": 6.51623777809222,
  "conductor": "12059599736130",
  "bad_primes": [
    "2",
    "3",
    "5",
    "23",
    "41",
    "61",
    "107",
    "241",
    "271"
  ],
  "discriminant": "-12462670641263425938977862888259236959940",
  "regulator": "3846.13778673917998284144625375509405683742645022",
  "points": [
    [
      "-20884313/4",
      "37018344097/8"
    ],
    [
      "520302982/169",
      "-2340127574452/2197"
    ],
    [
      "276989040/121",
      "1967155391141/1331"
    ],
    [
      "4562261515/729",
      "-235926356232601/19683"
    ],
    [
      "99583556725/2401",
      "-31225686589128361/117649"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous to curve#1247 via the rational 2-torsion point x=2777581. 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 20:24:37",
  "updated_at": "2026-09-26 20:24:37"
}