{
  "id": 4573,
  "curve_key": "481690267488:-334311002430348384",
  "ainvs": [
    "0",
    "0",
    "0",
    "-10035213906",
    "386934030590681"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    4
  ],
  "family": null,
  "families": [],
  "naive_height": 80.70170143760832,
  "faltings_height": 4.318075431437412,
  "conductor": "963092401128",
  "bad_primes": [
    "2",
    "3",
    "11",
    "13",
    "17",
    "101",
    "157",
    "347"
  ],
  "discriminant": "338806043462065476645505872",
  "regulator": "966.973525919612629450616906229557802228282936166",
  "points": [
    [
      "57760",
      "-1989"
    ],
    [
      "936809/16",
      "-18963659/64"
    ],
    [
      "2844605/49",
      "28972658/343"
    ],
    [
      "57004",
      "-344511"
    ],
    [
      "-5597884/49",
      "2232462287/343"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "From Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z4.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Five supplied rational points checked exactly and certified independent modulo torsion. Rational torsion C4. Source-attributed existing curve.",
  "created_at": "2026-10-18 02:09:03",
  "updated_at": "2026-10-18 02:09:03"
}