{
  "id": 4561,
  "curve_key": "4780739808:-330554043560160",
  "ainvs": [
    "0",
    "0",
    "0",
    "-99598746",
    "382585698565"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    4
  ],
  "family": null,
  "families": [],
  "naive_height": 66.86358342906604,
  "faltings_height": 3.12095198578288,
  "conductor": "2019047112",
  "bad_primes": [
    "2",
    "3",
    "31",
    "43",
    "109",
    "193"
  ],
  "discriminant": "54642513905165770704",
  "regulator": "297.4398533132935649415694794501494257681215321",
  "points": [
    [
      "22913/4",
      "35217/8"
    ],
    [
      "6341",
      "77400"
    ],
    [
      "5618",
      "18837"
    ],
    [
      "16790",
      "1855665"
    ]
  ],
  "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. Four supplied rational points checked exactly and certified independent modulo torsion. Rational torsion C4. Source-attributed existing curve.",
  "created_at": "2026-10-18 01:58:27",
  "updated_at": "2026-10-18 01:58:27"
}