{
  "id": 3357,
  "curve_key": "4823571078481:-10271543384959003225",
  "ainvs": [
    "1",
    "0",
    "0",
    "-100491064135",
    "11888352025002761"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    10
  ],
  "naive_height": 87.61360697196284,
  "faltings_height": 5.216765613492492,
  "conductor": "34172754",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "17",
    "19",
    "229"
  ],
  "discriminant": "3891575873940612631257756769846272",
  "regulator": "7.13243867876757806571475553326540344733731",
  "points": [
    [
      "59444",
      "78231461"
    ],
    [
      "2627702",
      "4228536389"
    ]
  ],
  "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 = 14/17; 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 21:11:25",
  "updated_at": "2026-09-26 21:11:25"
}