{
  "id": 1110,
  "curve_key": "-207:-6345",
  "ainvs": [
    "1",
    "-1",
    "1",
    "4",
    "6"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    4
  ],
  "naive_height": 17.510844760296976,
  "faltings_height": -0.46220749835427793,
  "conductor": "117",
  "bad_primes": [
    "3",
    "13"
  ],
  "discriminant": "-28431",
  "regulator": "1.130335626179551006648752509880637923980",
  "points": [
    [
      "-1/4",
      "15/8"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 117a1 (LMFDB 117.a): the smallest-conductor elliptic curve over Q with rank 1 and torsion subgroup Z/4Z, per Cremona's tables (PARI elldata search over conductors up to 600). Generator (-1/4, 15/8); the point (1, 2) has order 4.",
  "created_at": "2026-09-23 20:24:17",
  "updated_at": "2026-09-23 20:24:17"
}