Invariants
| Level: | $220$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
| Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
| Genus: | $5 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{4}\cdot10^{4}\cdot20^{4}$ | Cusp orbits | $2^{4}\cdot4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 20I5 |
Level structure
| $\GL_2(\Z/220\Z)$-generators: | $\begin{bmatrix}67&90\\139&159\end{bmatrix}$, $\begin{bmatrix}81&170\\62&11\end{bmatrix}$, $\begin{bmatrix}169&100\\95&29\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 220.144.5.ce.1 for the level structure with $-I$) |
| Cyclic 220-isogeny field degree: | $24$ |
| Cyclic 220-torsion field degree: | $960$ |
| Full 220-torsion field degree: | $2112000$ |
Rational points
This modular curve has no real points and no $\Q_p$ points for $p=19$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 20.144.1-20.d.2.7 | $20$ | $2$ | $2$ | $1$ | $0$ |
| 110.144.1-110.c.1.2 | $110$ | $2$ | $2$ | $1$ | $?$ |
| 220.144.1-110.c.1.9 | $220$ | $2$ | $2$ | $1$ | $?$ |
| 220.144.1-20.d.2.2 | $220$ | $2$ | $2$ | $1$ | $?$ |
| 220.144.3-220.cv.2.1 | $220$ | $2$ | $2$ | $3$ | $?$ |
| 220.144.3-220.cv.2.12 | $220$ | $2$ | $2$ | $3$ | $?$ |