{
  "id": 3389,
  "curve_key": "54806900275201:-367080606752077928449",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1141810422400",
    "424861718219592032"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    10
  ],
  "naive_height": 94.90451165815878,
  "faltings_height": 5.880117101212227,
  "conductor": "168077130",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "101",
    "251"
  ],
  "discriminant": "17292010058959530010410479652819300000",
  "regulator": "57.4703368547680757432023940354103330263062",
  "points": [
    [
      "-17939611/16",
      "34828792247/64"
    ],
    [
      "325034369/256",
      "4138027701143/4096"
    ]
  ],
  "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 = 13/30; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 168077130, torsion ℤ/10ℤ.",
  "created_at": "2026-09-26 21:19:14",
  "updated_at": "2026-09-26 21:19:14"
}