{
  "id": 3390,
  "curve_key": "882452640441601:-26214230279939981514625",
  "ainvs": [
    "1",
    "0",
    "0",
    "-18384430009200",
    "30340542773450255616"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    10
  ],
  "naive_height": 103.24117871422196,
  "faltings_height": 6.013769662758995,
  "conductor": "165875358",
  "bad_primes": [
    "2",
    "3",
    "11",
    "17",
    "19",
    "31",
    "251"
  ],
  "discriminant": "366370200490110686235606505300992",
  "regulator": "28.5294083830662455669754628147203087853793",
  "points": [
    [
      "1492251771/676",
      "12585031032543/17576"
    ],
    [
      "129815541048/52441",
      "-14070017529384/12008989"
    ]
  ],
  "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 = 18/19; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 165875358, torsion ℤ/10ℤ.",
  "created_at": "2026-09-26 21:19:26",
  "updated_at": "2026-09-26 21:19:26"
}