{
  "id": 3287,
  "curve_key": "12721:-1434761",
  "ainvs": [
    "1",
    "1",
    "1",
    "-265",
    "1550"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    4
  ],
  "naive_height": 28.353028350468634,
  "faltings_height": -0.025854078185461486,
  "conductor": "1155",
  "bad_primes": [
    "3",
    "5",
    "7",
    "11"
  ],
  "discriminant": "12705",
  "regulator": "3.400361211524176451702109824738060668811",
  "points": [
    [
      "34",
      "165"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 1155e1 = LMFDB 1155.e4: https://www.lmfdb.org/EllipticCurve/Q/1155/e/4\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 1155, minimal discriminant 12705, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:51:55",
  "updated_at": "2026-09-26 20:51:55"
}