Invariants
| Level: | $80$ | $\SL_2$-level: | $80$ | Newform level: | $1$ | ||
| Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
| Genus: | $15 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (none of which are rational) | Cusp widths | $5^{8}\cdot20^{2}\cdot80^{2}$ | Cusp orbits | $2^{2}\cdot4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $5 \le \gamma \le 28$ | ||||||
| $\overline{\Q}$-gonality: | $5 \le \gamma \le 15$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 80G15 |
Level structure
| $\GL_2(\Z/80\Z)$-generators: | $\begin{bmatrix}29&64\\16&13\end{bmatrix}$, $\begin{bmatrix}56&63\\37&74\end{bmatrix}$, $\begin{bmatrix}57&34\\6&13\end{bmatrix}$, $\begin{bmatrix}62&25\\77&58\end{bmatrix}$, $\begin{bmatrix}77&62\\24&3\end{bmatrix}$, $\begin{bmatrix}79&24\\48&31\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 80.240.15.bg.1 for the level structure with $-I$) |
| Cyclic 80-isogeny field degree: | $12$ |
| Cyclic 80-torsion field degree: | $192$ |
| Full 80-torsion field degree: | $24576$ |
Rational points
This modular curve has no $\Q_p$ points for $p=3,17$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.240.7-40.cj.1.15 | $40$ | $2$ | $2$ | $7$ | $0$ |
| 80.240.7-40.cj.1.1 | $80$ | $2$ | $2$ | $7$ | $?$ |