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: | 32A3 |
Level structure
| $\GL_2(\Z/96\Z)$-generators: | $\begin{bmatrix}3&10\\8&69\end{bmatrix}$, $\begin{bmatrix}35&66\\72&13\end{bmatrix}$, $\begin{bmatrix}49&20\\66&67\end{bmatrix}$, $\begin{bmatrix}74&9\\45&14\end{bmatrix}$, $\begin{bmatrix}76&55\\29&30\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 96.48.3.a.2 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.1.6 | $96$ | $2$ | $2$ | $1$ | $?$ |
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.d.2.21 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.g.1.10 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.j.1.19 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.l.2.10 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.bp.2.10 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.bq.1.14 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.br.2.10 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.bs.2.14 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.bt.2.10 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.bu.1.27 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.bv.2.10 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.bw.2.14 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.bx.1.10 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.by.2.3 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.bz.1.10 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.ca.2.2 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.cb.1.10 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.cc.2.2 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.cd.1.10 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.ce.2.2 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.cf.2.7 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.cg.1.10 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.ch.1.11 | $96$ | $2$ | $2$ | $5$ |
| 96.192.5-96.ci.2.10 | $96$ | $2$ | $2$ | $5$ |
| 96.288.11-96.c.1.62 | $96$ | $3$ | $3$ | $11$ |
| 96.384.13-96.jv.2.49 | $96$ | $4$ | $4$ | $13$ |