{
  "id": 4653,
  "curve_key": "4408224736:-643320210355840",
  "ainvs": [
    "0",
    "1",
    "0",
    "-91838015",
    "744552964129"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 68.19532742108142,
  "faltings_height": 3.7310658589751373,
  "conductor": "520723049109239936",
  "bad_primes": [
    "2",
    "41",
    "71",
    "73",
    "79",
    "97",
    "617",
    "4049"
  ],
  "discriminant": "-189929575751217276702830848",
  "regulator": "200048.571678413458083599937879975034442165849294420527",
  "points": [
    [
      "-4239",
      "1028446"
    ],
    [
      "-8288",
      "967711"
    ],
    [
      "282729/25",
      "134191958/125"
    ],
    [
      "5329",
      "637582"
    ],
    [
      "17896",
      "2198371"
    ],
    [
      "20055",
      "2639948"
    ],
    [
      "98185/16",
      "41085203/64"
    ],
    [
      "407239/9",
      "-255054608/27"
    ]
  ],
  "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. Eight supplied rational points checked exactly on the displayed model. Rational torsion Z/2Z. Source-attributed existing curve.",
  "created_at": "2026-10-20 17:36:03",
  "updated_at": "2026-10-20 17:36:03"
}