{
  "id": 4686,
  "curve_key": "18089056:-76534336000",
  "ainvs": [
    "0",
    "1",
    "0",
    "-376855",
    "88455789"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 50.13245301744918,
  "faltings_height": 2.0152289815665103,
  "conductor": "817578526976",
  "bad_primes": [
    "2",
    "17",
    "47",
    "89",
    "97",
    "463"
  ],
  "discriminant": "35582652651049472",
  "regulator": "1358.8077018147067950661820049355933863927392926033",
  "points": [
    [
      "-593",
      "10186"
    ],
    [
      "239",
      "3478"
    ],
    [
      "383",
      "670"
    ],
    [
      "709",
      "13348"
    ],
    [
      "-513",
      "12126"
    ],
    [
      "55061/100",
      "6941759/1000"
    ]
  ],
  "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. I checked the six supplied rational points exactly on this minimal model. The source records rank 6 with independent points and a matching 2-descent upper bound. Rational torsion Z/2Z. Source-attributed existing curve.",
  "created_at": "2026-10-20 20:38:55",
  "updated_at": "2026-10-20 20:38:55"
}