{
  "id": 2974,
  "curve_key": "236406001:-3634860422249",
  "ainvs": [
    "1",
    "1",
    "1",
    "-4925125",
    "4204962242"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    4,
    2
  ],
  "naive_height": 57.84318368434441,
  "faltings_height": 2.295376220478086,
  "conductor": "19065",
  "bad_primes": [
    "3",
    "5",
    "31",
    "41"
  ],
  "discriminant": "218311706390625",
  "regulator": "7.20502898543919713669139430746307905350130",
  "points": [
    [
      "1277",
      "-399"
    ],
    [
      "1112",
      "9681"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 19065g2 = LMFDB 19065.c4: https://www.lmfdb.org/EllipticCurve/Q/19065/c/4\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 19065, minimal discriminant 218311706390625, torsion ℤ/2ℤ × ℤ/4ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:31:15",
  "updated_at": "2026-09-26 20:31:15"
}