{
  "id": 3303,
  "curve_key": "17783041:-74990982689",
  "ainvs": [
    "1",
    "1",
    "1",
    "-370480",
    "86640752"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    4
  ],
  "naive_height": 50.081267424887635,
  "faltings_height": 1.5004094422108414,
  "conductor": "273585",
  "bad_primes": [
    "3",
    "5",
    "13",
    "23",
    "61"
  ],
  "discriminant": "17783025",
  "regulator": "29.4301384082516934286119690527890314272531",
  "points": [
    [
      "576",
      "7759"
    ],
    [
      "1192",
      "36016"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 273585c1 = LMFDB 273585.c4: https://www.lmfdb.org/EllipticCurve/Q/273585/c/4\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 273585, minimal discriminant 17783025, torsion ℤ/4ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:54:30",
  "updated_at": "2026-09-26 20:54:30"
}