Invariants
| Level: | $96$ | $\SL_2$-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: | 32C3 |
Level structure
| $\GL_2(\Z/96\Z)$-generators: | $\begin{bmatrix}3&94\\40&45\end{bmatrix}$, $\begin{bmatrix}50&43\\75&74\end{bmatrix}$, $\begin{bmatrix}52&9\\77&64\end{bmatrix}$, $\begin{bmatrix}67&70\\92&57\end{bmatrix}$, $\begin{bmatrix}94&75\\9&4\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 96.48.3.c.1 for the level structure with $-I$) |
| Cyclic 96-isogeny field degree: | $16$ |
| Cyclic 96-torsion field degree: | $256$ |
| Full 96-torsion field degree: | $196608$ |
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.1.2 | $16$ | $2$ | $2$ | $1$ | $0$ |
| 96.48.1-16.b.1.7 | $96$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 96.192.5-96.c.2.1 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.f.1.2 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.i.2.1 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.k.1.2 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.ba.1.16 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.ba.2.14 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.bb.1.16 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.bb.2.14 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.bi.2.2 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.bj.2.1 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.bm.2.2 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.bn.2.1 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.bu.1.27 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.bu.2.19 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.bv.1.14 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.bv.2.10 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.cr.1.7 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.cr.2.15 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.cu.1.7 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.cu.2.15 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.dd.1.3 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.dd.2.7 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.dg.1.3 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.dg.2.7 | $96$ | $2$ | $2$ | $5$ |
| 96.288.11-96.j.1.1 | $96$ | $3$ | $3$ | $11$ |
| 96.384.13-96.ka.1.7 | $96$ | $4$ | $4$ | $13$ |