Invariants
| Level: | $160$ | $\SL_2$-level: | $32$ | Newform level: | $1$ | ||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $3 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (all of which are rational) | Cusp widths | $4^{2}\cdot8\cdot32$ | Cusp orbits | $1^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 3$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 32A3 |
Level structure
| $\GL_2(\Z/160\Z)$-generators: | $\begin{bmatrix}7&16\\122&53\end{bmatrix}$, $\begin{bmatrix}64&19\\21&118\end{bmatrix}$, $\begin{bmatrix}88&97\\69&84\end{bmatrix}$, $\begin{bmatrix}100&27\\17&38\end{bmatrix}$, $\begin{bmatrix}123&122\\98&115\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 160.48.3.a.1 for the level structure with $-I$) |
| Cyclic 160-isogeny field degree: | $24$ |
| Cyclic 160-torsion field degree: | $768$ |
| Full 160-torsion field degree: | $1966080$ |
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 |
|---|---|---|---|---|---|
| 16.48.1-16.b.1.6 | $16$ | $2$ | $2$ | $1$ | $0$ |
| 160.48.1-16.b.1.3 | $160$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.