Rational Preperiodic Points
Dimension 1, degree 2 polynomials over ℚ
Functions over ℚ: 12 distinct graph structures Export to Sage
| Label | Function | Field of Definition | Cardinality | Periodic Cycles | Preperiodic Components | Longest Tail | Graph | Citations |
|---|---|---|---|---|---|---|---|---|
| 1.5b15356e.43983826.1 | (x2 − 21/16·y2 : y2) | 1.1.1.1 | 9 | 2, 1, 1, 1 | 4, 2, 2, 1 | 1 | view | WR1994, Poonen1998, Doyle2014, Doyle2018, Doyle2020 |
| 1.7009e2bc.27fbdf16.1 | (x2 − 29/16·y2 : y2) | 1.1.1.1 | 9 | 3, 1 | 8, 1 | 2 | view | WR1994, Poonen1998, Hutz2013, Doyle2014, Doyle2018, Doyle2020, DoHy2025, Hutz2026 |
| 1.de450653.9e174cad.1 | (x2 − 10/9·y2 : y2) | 1.1.1.1 | 7 | 1, 1, 1 | 4, 2, 1 | 2 | view | Poonen1998, Doyle2014, Doyle2018, Doyle2020 |
| 1.05f9cf28.88243c92.1 | (x2 − 13/9·y2 : y2) | 1.1.1.1 | 7 | 2, 1 | 6, 1 | 2 | view | Poonen1998, Doyle2014, Doyle2018, Doyle2020 |
| 1.e5f33c31.5bededd8.1 | (x2 − 301/144·y2 : y2) | 1.1.1.1 | 7 | 3, 1 | 6, 1 | 1 | view | WR1994, Poonen1998, Doyle2014, Doyle2018, Doyle2020 |
| 1.a6935bbd.880302df.1 | (x2 − 2y2 : y2) | 1.1.1.1 | 6 | 1, 1, 1 | 3, 2, 1 | 2 | view | WR1994, Poonen1998, Ingram2012, Doyle2014, Lukas2014, Doyle2018, Doyle2020 |
| 1.13a1af67.7eb43a7f.1 | (x2 − 3/4·y2 : y2) | 1.1.1.1 | 5 | 1, 1, 1 | 2, 2, 1 | 1 | view | Poonen1998, Doyle2014, Doyle2018 |
| 1.751d2996.7bc729ec.1 | (x2 − 7/4·y2 : y2) | 1.1.1.1 | 5 | 2, 1 | 4, 1 | 1 | view | Poonen1998 |
| 1.b5876aa4.6951d87f.1 | (x2 − y2 : y2) | 1.1.1.1 | 4 | 2, 1 | 3, 1 | 1 | view | Poonen1998, Ingram2012, Doyle2014, Lukas2014, CV2017, Doyle2018, Doyle2020, DoHi2025 |
| 1.a68cf1ff.024ac6d7.1 | (x2 : y2) | 1.1.1.1 | 4 | 1, 1, 1 | 2, 1, 1 | 1 | view | Morton1992, FN1997, Poonen1998, Manes2008, Ingram2012, Doyle2014, Lukas2014, Doyle2018, Doyle2020 |
| 1.8f2b16a9.99353b99.1 | (x2 + 1/4·y2 : y2) | 1.1.1.1 | 3 | 1, 1 | 2, 1 | 1 | view | Poonen1998, Doyle2014, Doyle2018, Doyle2020 |
| 1.1a2a6bbf.1ed2bf82.1 | (x2 + y2 : y2) | 1.1.1.1 | 1 | 1 | 1 | 0 | view | Morton1992, Poonen1998, Doyle2014, Doyle2018, DoHi2025 |