Invariants
Level: | $80$ | $\SL_2$-level: | $80$ | Newform level: | $800$ | ||
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: | 40M15 |
Level structure
$\GL_2(\Z/80\Z)$-generators: | $\begin{bmatrix}22&79\\31&38\end{bmatrix}$, $\begin{bmatrix}26&7\\13&4\end{bmatrix}$, $\begin{bmatrix}32&25\\47&58\end{bmatrix}$, $\begin{bmatrix}45&34\\34&5\end{bmatrix}$, $\begin{bmatrix}53&68\\36&37\end{bmatrix}$, $\begin{bmatrix}63&40\\48&47\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 40.240.15.gq.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
The following modular covers realize this modular curve as a fiber product over $X(1)$.
Factor curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
$X_{\mathrm{ns}}^+(5)$ | $5$ | $48$ | $24$ | $0$ | $0$ |
16.48.0-8.ba.1.7 | $16$ | $10$ | $10$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
16.48.0-8.ba.1.7 | $16$ | $10$ | $10$ | $0$ | $0$ |
80.240.7-40.cj.1.1 | $80$ | $2$ | $2$ | $7$ | $?$ |
80.240.7-40.cj.1.23 | $80$ | $2$ | $2$ | $7$ | $?$ |