{
  "id": 1186,
  "curve_key": "26496016:-190511398936",
  "ainvs": [
    "0",
    "1",
    "1",
    "-552000",
    "220315304"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    5
  ],
  "naive_height": 51.94595573331478,
  "faltings_height": 2.3512718312613083,
  "conductor": "2266095",
  "bad_primes": [
    "3",
    "5",
    "13",
    "11621"
  ],
  "discriminant": "-10239213052529296875",
  "regulator": "10.481588762531397206393178706812492884475615",
  "points": [
    [
      "-894",
      "292"
    ],
    [
      "-699",
      "16282"
    ],
    [
      "-2211/4",
      "151121/8"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Found by a rational-parameter search of the Kubert-Tate family for torsion 5, at t=-39/25. In y^2+(1-c)xy-by=x^3-bx^2 the parameters are defined by c=t;b=t; 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 21:40:00",
  "updated_at": "2026-09-23 21:40:00"
}