{
  "id": 3300,
  "curve_key": "11370336:-38340692064",
  "ainvs": [
    "0",
    "0",
    "0",
    "-236882",
    "44375801"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    4
  ],
  "naive_height": 48.73955525022381,
  "faltings_height": 1.4021781417752663,
  "conductor": "15080",
  "bad_primes": [
    "2",
    "5",
    "13",
    "29"
  ],
  "discriminant": "11370320",
  "regulator": "11.3510900661569063989994055786885455153926",
  "points": [
    [
      "256",
      "715"
    ],
    [
      "2785/9",
      "22672/27"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 15080e1 = LMFDB 15080.j3: https://www.lmfdb.org/EllipticCurve/Q/15080/j/3\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 15080, minimal discriminant 11370320, torsion ℤ/4ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:54:01",
  "updated_at": "2026-09-26 20:54:01"
}