{
  "id": 3375,
  "curve_key": "12006361189201:27468649511266833575",
  "ainvs": [
    "1",
    "0",
    "0",
    "-250132524775",
    "-31792439260195159"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    10
  ],
  "naive_height": 90.34937317309121,
  "faltings_height": 5.563339203772465,
  "conductor": "34172754",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "19",
    "229"
  ],
  "discriminant": "564943741174552065488203015145378592",
  "regulator": "28.5297547150703122628590221330616137893493",
  "points": [
    [
      "606128",
      "197892269"
    ],
    [
      "2837244536/2209",
      "137896926128773/103823"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Found in a rational-parameter search of the Kubert–Tate family for torsion ℤ/10ℤ: y^2 + (1-c)xy - by = x^3 - bx^2 with d=t^2/(t-(t-1)^2), c=td-t, b=cd, at t = 11/28; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 34172754, torsion ℤ/10ℤ.",
  "created_at": "2026-09-26 21:16:51",
  "updated_at": "2026-09-26 21:16:51"
}