{
  "id": 2951,
  "curve_key": "3040:-137656",
  "ainvs": [
    "0",
    "1",
    "1",
    "-63",
    "138"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    3
  ],
  "naive_height": 24.0588383832008,
  "faltings_height": 0.007924291085234302,
  "conductor": "6293",
  "bad_primes": [
    "7",
    "29",
    "31"
  ],
  "discriminant": "5292413",
  "regulator": "4.48197772581653863960624379418198564956107",
  "points": [
    [
      "6",
      "3"
    ],
    [
      "-4",
      "18"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 6293f1 = LMFDB 6293.d2: https://www.lmfdb.org/EllipticCurve/Q/6293/d/2\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 6293, minimal discriminant 5292413, torsion ℤ/3ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:29:47",
  "updated_at": "2026-09-26 20:29:47"
}