{
  "id": 3689,
  "curve_key": "46948870321:-148773497567275369",
  "ainvs": [
    "1",
    "0",
    "0",
    "-978101465",
    "172191466601817"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    5
  ],
  "naive_height": 79.0824027873996,
  "faltings_height": 4.648040429115433,
  "conductor": "4317455370",
  "bad_primes": [
    "2",
    "3",
    "5",
    "139",
    "1035361"
  ],
  "discriminant": "-12748882549946802125976562500000",
  "regulator": "393.6762163569255855409194524812951873433580458",
  "points": [
    [
      "-44936",
      "11221003"
    ],
    [
      "-13676",
      "13534963"
    ],
    [
      "14562574",
      "55564744963"
    ],
    [
      "11922454/121",
      "42701633753/1331"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -417/250 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 19:33:30",
  "updated_at": "2026-09-29 19:33:30"
}