{
  "id": 3257,
  "curve_key": "12400:-1381600",
  "ainvs": [
    "0",
    "1",
    "0",
    "-258",
    "1513"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    3
  ],
  "naive_height": 28.277505611629213,
  "faltings_height": 0.11005796177419992,
  "conductor": "12700",
  "bad_primes": [
    "2",
    "5",
    "127"
  ],
  "discriminant": "-1270000",
  "regulator": "1.65505017914477316253509993673317524096517",
  "points": [
    [
      "9",
      "1"
    ],
    [
      "12",
      "17"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 12700i1 = LMFDB 12700.b1: https://www.lmfdb.org/EllipticCurve/Q/12700/b/1\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 12700, minimal discriminant -1270000, torsion ℤ/3ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:47:02",
  "updated_at": "2026-09-26 20:47:02"
}