{
  "id": 999,
  "curve_key": "-464:-8216",
  "ainvs": [
    "0",
    "-1",
    "1",
    "10",
    "6"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    5
  ],
  "naive_height": 18.419653656678765,
  "faltings_height": -0.35618203740767507,
  "conductor": "155",
  "bad_primes": [
    "5",
    "31"
  ],
  "discriminant": "-96875",
  "regulator": "1.514887282206749682835235426532428402510",
  "points": [
    [
      "2",
      "5"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 155a1 = LMFDB 155.a2: https://www.lmfdb.org/EllipticCurve/Q/155/a/2\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 155, minimal discriminant -96875, torsion ℤ/5ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-23 15:13:16",
  "updated_at": "2026-09-23 15:13:16"
}