Invariants
| Level: | $80$ | $\SL_2$-level: | $80$ | Newform level: | $1$ | ||
| Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
| Genus: | $7 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (of which $4$ are rational) | Cusp widths | $1^{2}\cdot2^{3}\cdot5^{2}\cdot10^{3}\cdot16\cdot80$ | Cusp orbits | $1^{4}\cdot2^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 7$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 7$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 80H7 |
Level structure
| $\GL_2(\Z/80\Z)$-generators: | $\begin{bmatrix}9&38\\58&29\end{bmatrix}$, $\begin{bmatrix}16&67\\63&20\end{bmatrix}$, $\begin{bmatrix}26&31\\5&52\end{bmatrix}$, $\begin{bmatrix}31&28\\30&29\end{bmatrix}$, $\begin{bmatrix}32&21\\45&48\end{bmatrix}$, $\begin{bmatrix}61&0\\52&9\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 80.144.7.bt.2 for the level structure with $-I$) |
| Cyclic 80-isogeny field degree: | $2$ |
| Cyclic 80-torsion field degree: | $32$ |
| Full 80-torsion field degree: | $40960$ |
Rational points
This modular curve has 4 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.144.3-40.bx.1.7 | $40$ | $2$ | $2$ | $3$ | $0$ |
| 80.48.0-80.m.2.1 | $80$ | $6$ | $6$ | $0$ | $?$ |
| 80.144.3-40.bx.1.18 | $80$ | $2$ | $2$ | $3$ | $?$ |