{
  "id": 2911,
  "curve_key": "-336:-6912",
  "ainvs": [
    "0",
    "0",
    "0",
    "7",
    "8"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2
  ],
  "naive_height": 17.682028620967785,
  "faltings_height": -0.4131407816316344,
  "conductor": "4960",
  "bad_primes": [
    "2",
    "5",
    "31"
  ],
  "discriminant": "-49600",
  "regulator": "1.73332520770755389589851185967708555601069",
  "points": [
    [
      "1",
      "4"
    ],
    [
      "7",
      "20"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 4960b1 = LMFDB 4960.b2: https://www.lmfdb.org/EllipticCurve/Q/4960/b/2\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 4960, minimal discriminant -49600, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:28:00",
  "updated_at": "2026-09-26 20:28:00"
}