{
  "id": 3296,
  "curve_key": "4677273:-10115504829",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-97443",
    "11732121"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    4
  ],
  "naive_height": 46.07467741726499,
  "faltings_height": 1.4398863542049625,
  "conductor": "5382",
  "bad_primes": [
    "2",
    "3",
    "13",
    "23"
  ],
  "discriminant": "413720292492",
  "regulator": "0.973591903612835960313969206897904279068373",
  "points": [
    [
      "183",
      "-33"
    ],
    [
      "175",
      "39"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 5382g4 = LMFDB 5382.b1: https://www.lmfdb.org/EllipticCurve/Q/5382/b/1\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 5382, minimal discriminant 413720292492, torsion ℤ/4ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:53:23",
  "updated_at": "2026-09-26 20:53:23"
}