{
  "id": 4568,
  "curve_key": "16534873:-66647777885",
  "ainvs": [
    "1",
    "1",
    "0",
    "-344476",
    "76995100"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 49.862946671073544,
  "faltings_height": 2.014637131040361,
  "conductor": "845072108562",
  "bad_primes": [
    "2",
    "3",
    "11",
    "19",
    "43",
    "2113",
    "7417"
  ],
  "discriminant": "45567978237880164",
  "regulator": "392.24891414110502866784617650096669323053848426057",
  "points": [
    [
      "-263",
      "12358"
    ],
    [
      "-453",
      "12073"
    ],
    [
      "-109",
      "10697"
    ],
    [
      "402",
      "-2120"
    ],
    [
      "-582",
      "9278"
    ],
    [
      "-668",
      "3430"
    ]
  ],
  "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 02:04:52",
  "updated_at": "2026-10-18 02:04:52"
}