Invariants
| Level: | $96$ | $\SL_2$-level: | $32$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
| Cusps: | $24$ (none of which are rational) | Cusp widths | $2^{8}\cdot4^{12}\cdot32^{4}$ | Cusp orbits | $2^{4}\cdot4^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 32N5 |
Level structure
| $\GL_2(\Z/96\Z)$-generators: | $\begin{bmatrix}31&16\\43&9\end{bmatrix}$, $\begin{bmatrix}39&32\\61&57\end{bmatrix}$, $\begin{bmatrix}49&56\\22&45\end{bmatrix}$, $\begin{bmatrix}95&88\\21&53\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 96.192.5.bs.2 for the level structure with $-I$) |
| Cyclic 96-isogeny field degree: | $16$ |
| Cyclic 96-torsion field degree: | $128$ |
| Full 96-torsion field degree: | $49152$ |
Rational points
This modular curve has no $\Q_p$ points for $p=31$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 16.192.1-16.l.2.2 | $16$ | $2$ | $2$ | $1$ | $0$ |
| 96.192.1-16.l.2.4 | $96$ | $2$ | $2$ | $1$ | $?$ |
| 96.192.2-96.d.1.1 | $96$ | $2$ | $2$ | $2$ | $?$ |
| 96.192.2-96.d.1.29 | $96$ | $2$ | $2$ | $2$ | $?$ |
| 96.192.2-96.f.1.5 | $96$ | $2$ | $2$ | $2$ | $?$ |
| 96.192.2-96.f.1.29 | $96$ | $2$ | $2$ | $2$ | $?$ |