{
  "id": 1193,
  "curve_key": "117639585:-1275937096689",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-2450825",
    "1477391753"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    6
  ],
  "naive_height": 55.74940843179655,
  "faltings_height": 2.234446595080927,
  "conductor": "2327418",
  "bad_primes": [
    "2",
    "3",
    "31",
    "43",
    "97"
  ],
  "discriminant": "4170909418426368",
  "regulator": "29.278919428549781670610254101077596423864261",
  "points": [
    [
      "-1797",
      "9628"
    ],
    [
      "-1409",
      "46876"
    ],
    [
      "-89",
      "41212"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Found by a rational-parameter search of the Kubert-Tate family for torsion 6, at t=4/93. In y^2+(1-c)xy-by=x^3-bx^2 the parameters are defined by c=t;b=t*(t+1); Converted to the global minimal model; PARI/GP ellrank returned bounds [3,3]. The 3 supplied points and the torsion subgroup are independently certified by the site.",
  "created_at": "2026-09-23 21:43:28",
  "updated_at": "2026-09-23 21:43:28"
}