{
  "id": 3377,
  "curve_key": "343943037336001:-6378664837537983577249",
  "ainvs": [
    "1",
    "0",
    "0",
    "-7165479944500",
    "7382713335212300432"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    10
  ],
  "naive_height": 100.41449151135306,
  "faltings_height": 5.778138326078295,
  "conductor": "38882910",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "29",
    "239"
  ],
  "discriminant": "21601664351167071024001843200000",
  "regulator": "49.8571577528434605862897955637929118003680",
  "points": [
    [
      "12199144",
      "41652462988"
    ],
    [
      "38898344/25",
      "2720933212/125"
    ]
  ],
  "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 = 1/17; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 38882910, torsion ℤ/10ℤ.",
  "created_at": "2026-09-26 21:17:12",
  "updated_at": "2026-09-26 21:17:12"
}