{
  "id": 1139,
  "curve_key": "3409:143623",
  "ainvs": [
    "1",
    "1",
    "1",
    "-71",
    "-196"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2,
    2
  ],
  "naive_height": 24.402522816413708,
  "faltings_height": 0.05838147128260896,
  "conductor": "3315",
  "bad_primes": [
    "3",
    "5",
    "13",
    "17"
  ],
  "discriminant": "10989225",
  "regulator": "1.35634345933378764540912298034212488754749",
  "points": [
    [
      "-4",
      "8"
    ],
    [
      "22",
      "86"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 3315b2, 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 21:37:20",
  "updated_at": "2026-09-23 21:37:20"
}