{
  "id": 1157,
  "curve_key": "33025:-5998625",
  "ainvs": [
    "1",
    "1",
    "1",
    "-688",
    "6656"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    4
  ],
  "naive_height": 31.21506038817158,
  "faltings_height": 0.349222430221688,
  "conductor": "2175",
  "bad_primes": [
    "3",
    "5",
    "29"
  ],
  "discriminant": "20390625",
  "regulator": "1.92989989018885637930651116130325729428639",
  "points": [
    [
      "14",
      "-3"
    ],
    [
      "11",
      "18"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 2175c1, 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 21:37:52",
  "updated_at": "2026-09-23 21:37:52"
}