{
  "id": 3688,
  "curve_key": "1176927340081:-1276797456605888425",
  "ainvs": [
    "1",
    "0",
    "0",
    "-24519319585",
    "1477772790757961"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    5
  ],
  "naive_height": 83.38178462744966,
  "faltings_height": 4.561567740590492,
  "conductor": "4117912962",
  "bad_primes": [
    "2",
    "3",
    "23",
    "31",
    "109",
    "8831"
  ],
  "discriminant": "10724981106820835455814863872",
  "regulator": "9407.526032880879290159710704292337965319481184",
  "points": [
    [
      "-19491554662/1985281",
      "115941819971764651/2797260929"
    ],
    [
      "-52219990/289",
      "14938486843/4913"
    ],
    [
      "317940818/3721",
      "570874437383/226981"
    ],
    [
      "12358702698050/135512881",
      "565389700242439451/1577505447721"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -1116/23 of the universal curve with a 5-torsion point, y^2 + (t+1)xy + ty = x^3 + tx^2 (as searched in arXiv:2003.00077, Sec. 12), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:33:20",
  "updated_at": "2026-09-29 19:33:20"
}