{
  "id": 3691,
  "curve_key": "216482155696:-101882226037119256",
  "ainvs": [
    "0",
    "1",
    "1",
    "-4510044910",
    "117917739750214"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    5
  ],
  "naive_height": 78.32518778876396,
  "faltings_height": 4.397701394474938,
  "conductor": "10994568585",
  "bad_primes": [
    "3",
    "5",
    "7",
    "11",
    "13",
    "732239"
  ],
  "discriminant": "-135795635709244219536049096875",
  "regulator": "305.8910313754455621270446339143097730910264338",
  "points": [
    [
      "40166",
      "1252597"
    ],
    [
      "113536",
      "32701762"
    ],
    [
      "131411",
      "42362512"
    ],
    [
      "7070441/256",
      "15556063477/4096"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -91/495 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 19:33:50",
  "updated_at": "2026-09-29 19:33:50"
}