{
  "id": 1069,
  "curve_key": "173119041:-2278116280161",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-3606647",
    "2637610319"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    9
  ],
  "naive_height": 56.90874004899518,
  "faltings_height": 2.4475130041056645,
  "conductor": "35910",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "19"
  ],
  "discriminant": "-810819072000000000",
  "regulator": "1.798177555696920737888940841223136132479",
  "points": [
    [
      "1077",
      "736"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 35910bt3 = LMFDB 35910.by1: https://www.lmfdb.org/EllipticCurve/Q/35910/by/1\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 35910, minimal discriminant -810819072000000000, torsion ℤ/9ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-23 15:24:00",
  "updated_at": "2026-09-23 15:24:00"
}