Invariants
| Level: | $96$ | $\SL_2$-level: | $32$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $5 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (of which $4$ are rational) | Cusp widths | $4^{4}\cdot8^{2}\cdot32^{2}$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 5$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 5$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 32C5 |
Level structure
| $\GL_2(\Z/96\Z)$-generators: | $\begin{bmatrix}3&14\\92&13\end{bmatrix}$, $\begin{bmatrix}47&68\\40&75\end{bmatrix}$, $\begin{bmatrix}51&82\\10&59\end{bmatrix}$, $\begin{bmatrix}62&45\\93&14\end{bmatrix}$, $\begin{bmatrix}67&90\\66&59\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 96.96.5.bu.2 for the level structure with $-I$) |
| Cyclic 96-isogeny field degree: | $16$ |
| Cyclic 96-torsion field degree: | $512$ |
| Full 96-torsion field degree: | $98304$ |
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 |
|---|---|---|---|---|---|
| 32.96.1-16.v.2.2 | $32$ | $2$ | $2$ | $1$ | $0$ |
| 48.96.1-16.v.2.2 | $48$ | $2$ | $2$ | $1$ | $0$ |
| 96.96.3-96.a.1.11 | $96$ | $2$ | $2$ | $3$ | $?$ |
| 96.96.3-96.a.1.29 | $96$ | $2$ | $2$ | $3$ | $?$ |
| 96.96.3-96.c.1.11 | $96$ | $2$ | $2$ | $3$ | $?$ |
| 96.96.3-96.c.1.12 | $96$ | $2$ | $2$ | $3$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 96.384.9-96.bw.3.20 | $96$ | $2$ | $2$ | $9$ |
| 96.384.9-96.cb.2.6 | $96$ | $2$ | $2$ | $9$ |
| 96.384.9-96.cx.4.8 | $96$ | $2$ | $2$ | $9$ |
| 96.384.9-96.ea.2.2 | $96$ | $2$ | $2$ | $9$ |
| 96.384.9-96.ib.1.13 | $96$ | $2$ | $2$ | $9$ |
| 96.384.9-96.ic.1.13 | $96$ | $2$ | $2$ | $9$ |
| 96.384.9-96.id.2.11 | $96$ | $2$ | $2$ | $9$ |
| 96.384.9-96.ie.2.7 | $96$ | $2$ | $2$ | $9$ |
| 96.384.9-96.ij.1.11 | $96$ | $2$ | $2$ | $9$ |
| 96.384.9-96.ik.1.11 | $96$ | $2$ | $2$ | $9$ |
| 96.384.9-96.il.2.11 | $96$ | $2$ | $2$ | $9$ |
| 96.384.9-96.im.2.7 | $96$ | $2$ | $2$ | $9$ |
| 96.384.9-96.ir.2.3 | $96$ | $2$ | $2$ | $9$ |
| 96.384.9-96.is.2.3 | $96$ | $2$ | $2$ | $9$ |
| 96.384.9-96.it.1.3 | $96$ | $2$ | $2$ | $9$ |
| 96.384.9-96.iu.2.3 | $96$ | $2$ | $2$ | $9$ |
| 96.384.9-96.iz.2.5 | $96$ | $2$ | $2$ | $9$ |
| 96.384.9-96.ja.2.5 | $96$ | $2$ | $2$ | $9$ |
| 96.384.9-96.jb.1.9 | $96$ | $2$ | $2$ | $9$ |
| 96.384.9-96.jc.2.9 | $96$ | $2$ | $2$ | $9$ |
| 96.384.9-96.jm.2.8 | $96$ | $2$ | $2$ | $9$ |
| 96.384.9-96.jq.2.16 | $96$ | $2$ | $2$ | $9$ |
| 96.384.9-96.kc.2.6 | $96$ | $2$ | $2$ | $9$ |
| 96.384.9-96.kg.2.4 | $96$ | $2$ | $2$ | $9$ |