{
  "id": 3715,
  "curve_key": "128872186933528282201:-1429078124975764630338128238301",
  "ainvs": [
    "1",
    "0",
    "1",
    "-2684837227781839213",
    "1654025607387102256872495156"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    6
  ],
  "naive_height": 138.91605836437154,
  "faltings_height": 9.479243164917424,
  "conductor": "169544208072571930",
  "bad_primes": [
    "2",
    "5",
    "13",
    "17",
    "31",
    "73",
    "1609",
    "1699",
    "12401"
  ],
  "discriminant": "56742026048583851334135583943924588786582150899414062500",
  "regulator": "781771.35761373214987212794781968623651621329718360",
  "points": [
    [
      "13954857175",
      "1637591576321412"
    ],
    [
      "-2801199722691425/2053489",
      "155101909598953581456144/2942649737"
    ],
    [
      "-83834917710200/137641",
      "2826330296615650158132/51064811"
    ],
    [
      "9815257612300/841",
      "30461968473530239143/24389"
    ],
    [
      "26282754809300/259081",
      "4903625179966746304848/131872229"
    ],
    [
      "7816008668421825/9467929",
      "13461014964193448416596/29132817533"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -125551/56575 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 01:48:37",
  "updated_at": "2026-09-30 01:48:37"
}