{
  "id": 6049,
  "curve_key": "235638001:-3855231597257",
  "ainvs": [
    "1",
    "1",
    "1",
    "-4909125",
    "4460028139"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    5
  ],
  "family": null,
  "families": [],
  "naive_height": 57.960904396497504,
  "faltings_height": 2.7790596455085095,
  "conductor": "57838586",
  "bad_primes": [
    "2",
    "13",
    "29",
    "79",
    "971"
  ],
  "discriminant": "-1029483579976206950816",
  "regulator": "120.52902546765862969912351594602404192745971",
  "points": [
    [
      "979",
      "23872"
    ],
    [
      "3293",
      "153326"
    ],
    [
      "40101571/38809",
      "165631829564/7645373"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained in my own rational-parameter search of the Tate X_1(5) family, following the construction described by David Renshaw on curves #1185 and #1186. The family is y^2+(1-t)*x*y-t*y=x^3-t*x^2, specialized at t=-79/26. Clearing denominators with x=X/26^2 and y=Y/26^3 gives [105,2054,53404,0,0]; the displayed equation is its global minimal model, with discriminant -1029483579976206950816. All three listed rational points were checked exactly and returned as an independent set, with rank bounds [3,3]. The rational torsion subgroup is Z/5Z.",
  "created_at": "2026-10-28 17:07:14",
  "updated_at": "2026-10-28 17:07:14"
}