{
  "id": 3274,
  "curve_key": "17783281:-74988857321",
  "ainvs": [
    "1",
    "1",
    "1",
    "-370485",
    "86638290"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    4,
    2
  ],
  "naive_height": 50.08130791262769,
  "faltings_height": 1.846983032490814,
  "conductor": "273585",
  "bad_primes": [
    "3",
    "5",
    "13",
    "23",
    "61"
  ],
  "discriminant": "316235978150625",
  "regulator": "7.35753460206292335715299226319725785681329",
  "points": [
    [
      "93",
      "7233"
    ],
    [
      "348",
      "-102"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 273585c2 = LMFDB 273585.c3: https://www.lmfdb.org/EllipticCurve/Q/273585/c/3\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 273585, minimal discriminant 316235978150625, torsion ℤ/2ℤ × ℤ/4ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:49:49",
  "updated_at": "2026-09-26 20:49:49"
}