{
  "id": 2712,
  "curve_key": "5089:-370513",
  "ainvs": [
    "1",
    "0",
    "0",
    "-106",
    "420"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6
  ],
  "naive_height": 25.645287621644034,
  "faltings_height": 0.033342373799352364,
  "conductor": "310",
  "bad_primes": [
    "2",
    "5",
    "31"
  ],
  "discriminant": "-3174400",
  "regulator": "0.9776191070965400572788433675257063742869",
  "points": [
    [
      "6",
      "0"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 310b1 = LMFDB 310.a3: https://www.lmfdb.org/EllipticCurve/Q/310/a/3\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 310, minimal discriminant -3174400, torsion ℤ/6ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:18:52",
  "updated_at": "2026-09-26 20:18:52"
}