{
  "id": 2845,
  "curve_key": "37800976:-232409714624",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-787520",
    "269255232"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    4
  ],
  "naive_height": 52.34353644108691,
  "faltings_height": 1.9169629854990526,
  "conductor": "305040",
  "bad_primes": [
    "2",
    "3",
    "5",
    "31",
    "41"
  ],
  "discriminant": "34895795097600",
  "regulator": "7.8592842061040382364912764268833134072809573",
  "points": [
    [
      "512",
      "24"
    ],
    [
      "514",
      "50"
    ],
    [
      "488",
      "960"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 305040s3 = LMFDB 305040.s1: https://www.lmfdb.org/EllipticCurve/Q/305040/s/1\n\nMordell–Weil rank exactly 3 (Cremona's tables). Conductor 305040, minimal discriminant 34895795097600, torsion ℤ/4ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:25:02",
  "updated_at": "2026-09-26 20:25:02"
}