{
  "id": 3394,
  "curve_key": "63165875502047409:-15867202494086963623872873",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-1315955739625988",
    "18364818030478476137831"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    6,
    2
  ],
  "naive_height": 116.05362181695921,
  "faltings_height": 7.420840675887619,
  "conductor": "4397377590",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "23",
    "29",
    "31",
    "139"
  ],
  "discriminant": "149982322605660868944713975913599161472001600",
  "regulator": "404.71006182935076537852967277095169335707894",
  "points": [
    [
      "77759467/4",
      "90891363693/8"
    ],
    [
      "590482719/25",
      "2677719415487/125"
    ],
    [
      "63685413811/2916",
      "1015219901991223/157464"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Found in a rational-parameter search of the Kubert–Tate family for torsion ℤ/2ℤ × ℤ/6ℤ: y^2 + (1-c)xy - by = x^3 - bx^2 with c=(10-2t)/(t^2-9), b=c+c^2, at t = 6/29; converted to the global minimal model. The 3 witness points were found with PARI/GP ellrank. Conductor 4397377590, torsion ℤ/2ℤ × ℤ/6ℤ.",
  "created_at": "2026-09-26 21:20:05",
  "updated_at": "2026-09-26 21:20:05"
}