{
  "id": 3712,
  "curve_key": "926760491805947449:-898837989363429011748970093",
  "ainvs": [
    "1",
    "0",
    "1",
    "-19307510245957239",
    "1040321745339454020879686"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    6
  ],
  "naive_height": 124.1262900760691,
  "faltings_height": 8.196040339940978,
  "conductor": "79182482567274710",
  "bad_primes": [
    "2",
    "5",
    "13",
    "17",
    "23",
    "31",
    "37",
    "103",
    "113",
    "116689"
  ],
  "discriminant": "-6903378250880291137646188042617871992304351407100",
  "regulator": "260463.85344491051502691726790239293322824620586005",
  "points": [
    [
      "289094507/4",
      "1197511386379/8"
    ],
    [
      "80408068",
      "87806756173"
    ],
    [
      "2398296433",
      "117256288642278"
    ],
    [
      "56837482/49",
      "346060724320744/343"
    ],
    [
      "145782519467/1849",
      "7180884275205466/79507"
    ],
    [
      "93500791458568/1256641",
      "176227970218951431293/1408694561"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -27223/14911 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 01:48:01",
  "updated_at": "2026-09-30 01:48:01"
}