{
  "id": 3708,
  "curve_key": "41133235973903753785:-263808696367232839591584292333",
  "ainvs": [
    "1",
    "0",
    "1",
    "-856942416122994871",
    "305334139242515029665195210"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    6
  ],
  "naive_height": 135.49004438931084,
  "faltings_height": 8.842203159878462,
  "conductor": "1469940702224254",
  "bad_primes": [
    "2",
    "13",
    "19",
    "23",
    "29",
    "31",
    "37",
    "97",
    "101",
    "397"
  ],
  "discriminant": "38528381200959072443738103528525883999891989498512",
  "regulator": "13903.957632214866783653550860826586375289850738196",
  "points": [
    [
      "-903695570",
      "18486447750880"
    ],
    [
      "-6255741",
      "17626537223820"
    ],
    [
      "530846676",
      "143750098770"
    ],
    [
      "533274211",
      "45632400208"
    ],
    [
      "541376286",
      "277006976433"
    ],
    [
      "154366989276/289",
      "18471216875145/4913"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 80479/2231 of the universal curve with a 6-torsion point, y^2 + txy + (t+2)y = x^3 (as searched in arXiv:2003.00077, Sec. 13), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-30 01:47:17",
  "updated_at": "2026-09-30 01:47:17"
}