{
  "id": 2961,
  "curve_key": "30928:3878720",
  "ainvs": [
    "0",
    "1",
    "0",
    "-644",
    "-4704"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    4,
    2
  ],
  "naive_height": 31.018251604344336,
  "faltings_height": 0.611126582747461,
  "conductor": "2184",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13"
  ],
  "discriminant": "8414025984",
  "regulator": "1.700598484763839251509225858109905838132",
  "points": [
    [
      "31",
      "78"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 2184m2 = LMFDB 2184.j4: https://www.lmfdb.org/EllipticCurve/Q/2184/j/4\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 2184, minimal discriminant 8414025984, torsion ℤ/2ℤ × ℤ/4ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:30:26",
  "updated_at": "2026-09-26 20:30:26"
}