{
  "id": 3018,
  "curve_key": "2761:-52741",
  "ainvs": [
    "1",
    "0",
    "1",
    "-58",
    "56"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6
  ],
  "naive_height": 23.770044635790462,
  "faltings_height": 0.04051397423363333,
  "conductor": "870",
  "bad_primes": [
    "2",
    "3",
    "5",
    "29"
  ],
  "discriminant": "10570500",
  "regulator": "0.9922518400487123482261270061277082571301",
  "points": [
    [
      "0",
      "7"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 870c1 = LMFDB 870.c3: https://www.lmfdb.org/EllipticCurve/Q/870/c/3\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 870, minimal discriminant 10570500, torsion ℤ/6ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:33:31",
  "updated_at": "2026-09-26 20:33:31"
}