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: | $\begin{bmatrix}16&5\\35&66\end{bmatrix}$, $\begin{bmatrix}19&16\\40&51\end{bmatrix}$, $\begin{bmatrix}23&30\\78&7\end{bmatrix}$, $\begin{bmatrix}46&75\\15&66\end{bmatrix}$, $\begin{bmatrix}51&62\\68&69\end{bmatrix}$, $\begin{bmatrix}62&43\\35&78\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 80.240.15.bk.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 $p=3$, 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.1.14 | $40$ | $2$ | $2$ | $7$ | $0$ |
80.240.7-40.cj.1.1 | $80$ | $2$ | $2$ | $7$ | $?$ |