{
  "id": 2885,
  "curve_key": "9136:745984",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-190",
    "-800"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2,
    2
  ],
  "naive_height": 27.359933795687375,
  "faltings_height": 0.27276855414623674,
  "conductor": "43680",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13"
  ],
  "discriminant": "119246400",
  "regulator": "3.10511747103844780266198062247745345681630",
  "points": [
    [
      "-8",
      "12"
    ],
    [
      "-9",
      "10"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 43680f1 = LMFDB 43680.o3: https://www.lmfdb.org/EllipticCurve/Q/43680/o/3\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 43680, minimal discriminant 119246400, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:26:51",
  "updated_at": "2026-09-26 20:26:51"
}