{
  "id": 1127,
  "curve_key": "433:-8585",
  "ainvs": [
    "1",
    "1",
    "1",
    "-9",
    "6"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2
  ],
  "naive_height": 18.21221318400747,
  "faltings_height": -0.5456579707062845,
  "conductor": "1443",
  "bad_primes": [
    "3",
    "13",
    "37"
  ],
  "discriminant": "4329",
  "regulator": "0.790463101484975738716171228728583121090222",
  "points": [
    [
      "2",
      "0"
    ],
    [
      "4",
      "5"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 1443c1, rank exactly 2 according to Cremona's tables. Witness generators from https://github.com/JohnCremona/ecdata/blob/master/allgens/allgens.00000-09999 . Found by screening the local allgens tables for missing torsion size records; torsion and independence independently verified by the site.",
  "created_at": "2026-09-23 21:36:52",
  "updated_at": "2026-09-23 21:36:52"
}