{
  "id": 4559,
  "curve_key": "10771936:-21249065600",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-224415",
    "24668631"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 48.57736437469981,
  "faltings_height": 2.0895966253620717,
  "conductor": "838923722112",
  "bad_primes": [
    "2",
    "3",
    "7",
    "31",
    "47",
    "71",
    "431"
  ],
  "discriminant": "462033884258295552",
  "regulator": "722.33064930542585374738402968451994007927340827372",
  "points": [
    [
      "-441",
      "6138"
    ],
    [
      "-306",
      "8037"
    ],
    [
      "2070",
      "91791"
    ],
    [
      "775",
      "17766"
    ],
    [
      "-450",
      "5859"
    ],
    [
      "1574",
      "59737"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "From Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z2.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Six supplied rational points checked exactly and certified independent modulo torsion. Rational torsion C2. Source-attributed existing curve.",
  "created_at": "2026-10-18 01:57:11",
  "updated_at": "2026-10-18 01:57:11"
}