{
  "id": 1185,
  "curve_key": "12960481:-51184271825",
  "ainvs": [
    "1",
    "1",
    "1",
    "-270010",
    "59128551"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    5
  ],
  "naive_height": 49.31739626176222,
  "faltings_height": 2.0762773207062613,
  "conductor": "3559178",
  "bad_primes": [
    "2",
    "7",
    "37",
    "6871"
  ],
  "discriminant": "-256252875388461728",
  "regulator": "25.328383630871813151698326778280537918378323",
  "points": [
    [
      "-499",
      "8611"
    ],
    [
      "-1293/4",
      "86241/8"
    ],
    [
      "-277",
      "10757"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Found by a rational-parameter search of the Kubert-Tate family for torsion 5, at t=-37/14. 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 21:39:57",
  "updated_at": "2026-09-23 21:39:57"
}