{
  "id": 55,
  "curve_key": "1057:-190801",
  "ainvs": [
    "1",
    "0",
    "0",
    "-22",
    "219"
  ],
  "rank_lower_bound": 5,
  "naive_height": 24.31797255814547,
  "faltings_height": 0.08369007316794763,
  "conductor": "20384311",
  "bad_primes": [
    "3089",
    "6599"
  ],
  "discriminant": "-20384311",
  "regulator": "23.0216507645579847918634719671775842289367147243",
  "points": [
    [
      "-7",
      "10"
    ],
    [
      "-6",
      "15"
    ],
    [
      "-5",
      "17"
    ],
    [
      "-2",
      "17"
    ],
    [
      "-1",
      "16"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Provenance: Elkies-Watkins, \"Elliptic curves of large rank and small conductor\" (arXiv:math/0403374), Table 4 low absolute-discriminant list for r=5: [1,0,0,-22,219], |Delta|=20384311; their I-column records 29 integral x-coordinates. The submitted points certify rank >= 5 here.",
  "created_at": "2026-05-29 00:03:58",
  "updated_at": "2026-07-01 23:01:14"
}