Invariants
| Level: | $160$ | $\SL_2$-level: | $32$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $7 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 20 }{2}$ | ||||||
| Cusps: | $20$ (none of which are rational) | Cusp widths | $4^{16}\cdot32^{4}$ | Cusp orbits | $2^{4}\cdot4^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 12$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 7$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 32L7 |
Level structure
| $\GL_2(\Z/160\Z)$-generators: | $\begin{bmatrix}41&48\\145&19\end{bmatrix}$, $\begin{bmatrix}81&16\\8&29\end{bmatrix}$, $\begin{bmatrix}105&112\\106&149\end{bmatrix}$, $\begin{bmatrix}109&8\\108&17\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 160.192.7.da.1 for the level structure with $-I$) |
| Cyclic 160-isogeny field degree: | $24$ |
| Cyclic 160-torsion field degree: | $384$ |
| Full 160-torsion field degree: | $491520$ |
Rational points
This modular curve has no real points and no $\Q_p$ points for $p=3,31$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 32.192.2-32.d.1.4 | $32$ | $2$ | $2$ | $2$ | $0$ |
| 80.192.3-80.gk.1.1 | $80$ | $2$ | $2$ | $3$ | $?$ |
| 160.192.2-32.d.1.16 | $160$ | $2$ | $2$ | $2$ | $?$ |
| 160.192.2-160.j.1.5 | $160$ | $2$ | $2$ | $2$ | $?$ |
| 160.192.2-160.j.1.12 | $160$ | $2$ | $2$ | $2$ | $?$ |
| 160.192.3-80.gk.1.3 | $160$ | $2$ | $2$ | $3$ | $?$ |