{
  "id": 3690,
  "curve_key": "1030992011041:-1049719865542103089",
  "ainvs": [
    "1",
    "0",
    "0",
    "-21479000230",
    "1214951758164452"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    5
  ],
  "naive_height": 82.99011001548881,
  "faltings_height": 4.727391369986232,
  "conductor": "9065661330",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "1445879"
  ],
  "discriminant": "-3486389335571941515722649600000",
  "regulator": "36.83529351284906917186031745349027854706209898",
  "points": [
    [
      "-131732",
      "41999626"
    ],
    [
      "48844",
      "16779178"
    ],
    [
      "64652",
      "9792650"
    ],
    [
      "180932",
      "56933930"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -95/792 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 19:33:41",
  "updated_at": "2026-09-29 19:33:41"
}