{
  "id": 1156,
  "curve_key": "1888:-216800",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-39",
    "264"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    4
  ],
  "naive_height": 24.573461097095258,
  "faltings_height": 0.09972674117846664,
  "conductor": "5304",
  "bad_primes": [
    "2",
    "3",
    "13",
    "17"
  ],
  "discriminant": "-23305776",
  "regulator": "3.96846021424446964617745345128244670643630",
  "points": [
    [
      "1",
      "15"
    ],
    [
      "8",
      "20"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 5304k1, rank exactly 2 according to Cremona's tables. Witness generators from https://github.com/JohnCremona/ecdata/blob/master/allgens/allgens.00000-09999 . Found by screening the local allgens tables for missing torsion size records; torsion and independence independently verified by the site.",
  "created_at": "2026-09-23 21:37:50",
  "updated_at": "2026-09-23 21:37:50"
}