Invariants
| Level: | $80$ | $\SL_2$-level: | $80$ | Newform level: | $200$ | ||
| 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 | $5^{4}\cdot10^{2}\cdot20^{2}\cdot40^{4}$ | Cusp orbits | $2^{2}\cdot4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 28$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 15$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 40L15 |
Level structure
| $\GL_2(\Z/80\Z)$-generators: | $\begin{bmatrix}0&1\\79&66\end{bmatrix}$, $\begin{bmatrix}6&69\\45&14\end{bmatrix}$, $\begin{bmatrix}56&47\\73&38\end{bmatrix}$, $\begin{bmatrix}62&5\\27&48\end{bmatrix}$, $\begin{bmatrix}63&6\\54&47\end{bmatrix}$, $\begin{bmatrix}76&21\\49&72\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 40.240.15.gs.2 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 $p=3$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 80.240.7-40.cj.1.1 | $80$ | $2$ | $2$ | $7$ | $?$ |
| 80.240.7-40.cj.1.19 | $80$ | $2$ | $2$ | $7$ | $?$ |