{
  "id": 1057,
  "curve_key": "1309201:-1730503801",
  "ainvs": [
    "1",
    "0",
    "0",
    "-27275",
    "2000625"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    10
  ],
  "naive_height": 42.54335683502454,
  "faltings_height": 1.532262699472469,
  "conductor": "6270",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19"
  ],
  "discriminant": "-434411683200000",
  "regulator": "1.353612730082552633797038062301591543169",
  "points": [
    [
      "22",
      "1177"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 6270r1 = LMFDB 6270.r4: https://www.lmfdb.org/EllipticCurve/Q/6270/r/4\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 6270, minimal discriminant -434411683200000, torsion ℤ/10ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-23 15:21:53",
  "updated_at": "2026-09-23 15:21:53"
}