{
  "id": 1708,
  "curve_key": "156769853553:-1561432885881450921",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-3266038616",
    "1807214804798370"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    4
  ],
  "naive_height": 83.78427118033342,
  "faltings_height": 5.039817997669865,
  "conductor": "104067785215251",
  "bad_primes": [
    "3",
    "11",
    "13",
    "199",
    "367",
    "433",
    "2557"
  ],
  "discriminant": "-1408691989476819092254743109782063",
  "regulator": "14370.391947962429895538577753714591661360141013778",
  "points": [
    [
      "-118849/4",
      "-346570641/8"
    ],
    [
      "14010651/4",
      "-52451120391/8"
    ],
    [
      "-121177",
      "20642760"
    ],
    [
      "-4788039/64",
      "20708159239/512"
    ],
    [
      "23534886/25",
      "114028604694/125"
    ],
    [
      "48371",
      "41956854"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Torsion Z/4. From Michael Rubinstein's github repository:\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-09-25 06:13:38",
  "updated_at": "2026-09-25 06:13:38"
}