{
  "id": 3718,
  "curve_key": "40558527436141180986601:-8124740263143198374526397789887349",
  "ainvs": [
    "1",
    "0",
    "1",
    "-844969321586274603888",
    "9403634563752732156680770854638"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    6
  ],
  "naive_height": 156.17109901705126,
  "faltings_height": 10.852615543969987,
  "conductor": "1429018850083757362430",
  "bad_primes": [
    "2",
    "5",
    "7",
    "11",
    "13",
    "23",
    "31",
    "53",
    "71",
    "191",
    "5557",
    "50131"
  ],
  "discriminant": "409222182766127427151741480103299105234709103274735181721914000",
  "regulator": "1313051.653034400716020231400087461101784218440566746",
  "points": [
    [
      "15711858744",
      "79142322811930"
    ],
    [
      "15721202273",
      "72749078498383"
    ],
    [
      "17862297757",
      "98559308422587"
    ],
    [
      "19709817837",
      "637369520507095"
    ],
    [
      "867600482577",
      "807678795455033815"
    ],
    [
      "10441016159141/400",
      "18124022008942076479/8000"
    ],
    [
      "57199477133956/169",
      "431055425932987375690/2197"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -497963/232829 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 01:49:15",
  "updated_at": "2026-09-30 01:49:15"
}