Invariants
| Level: | $96$ | $\SL_2$-level: | $32$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $2 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 14 }{2}$ | ||||||
| Cusps: | $14$ (of which $2$ are rational) | Cusp widths | $2^{8}\cdot4^{4}\cdot32^{2}$ | Cusp orbits | $1^{2}\cdot2^{4}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 32B2 |
Level structure
| $\GL_2(\Z/96\Z)$-generators: | $\begin{bmatrix}9&16\\53&11\end{bmatrix}$, $\begin{bmatrix}41&0\\66&1\end{bmatrix}$, $\begin{bmatrix}69&8\\14&65\end{bmatrix}$, $\begin{bmatrix}81&64\\11&91\end{bmatrix}$, $\begin{bmatrix}83&56\\25&89\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 96.96.2.f.1 for the level structure with $-I$) |
| Cyclic 96-isogeny field degree: | $16$ |
| Cyclic 96-torsion field degree: | $256$ |
| Full 96-torsion field degree: | $98304$ |
Rational points
This modular curve has 2 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 |
|---|---|---|---|---|---|
| 16.96.0-16.j.1.3 | $16$ | $2$ | $2$ | $0$ | $0$ |
| 96.96.0-16.j.1.1 | $96$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 96.384.5-96.bl.1.11 | $96$ | $2$ | $2$ | $5$ |
| 96.384.5-96.bl.2.7 | $96$ | $2$ | $2$ | $5$ |
| 96.384.5-96.bn.1.8 | $96$ | $2$ | $2$ | $5$ |
| 96.384.5-96.bn.2.14 | $96$ | $2$ | $2$ | $5$ |
| 96.384.5-96.bp.1.15 | $96$ | $2$ | $2$ | $5$ |
| 96.384.5-96.bp.2.11 | $96$ | $2$ | $2$ | $5$ |
| 96.384.5-96.bs.1.8 | $96$ | $2$ | $2$ | $5$ |
| 96.384.5-96.bs.2.12 | $96$ | $2$ | $2$ | $5$ |
| 96.384.5-96.cp.1.4 | $96$ | $2$ | $2$ | $5$ |
| 96.384.5-96.cp.2.10 | $96$ | $2$ | $2$ | $5$ |
| 96.384.5-96.cq.1.6 | $96$ | $2$ | $2$ | $5$ |
| 96.384.5-96.cq.2.13 | $96$ | $2$ | $2$ | $5$ |
| 96.384.5-96.cu.1.4 | $96$ | $2$ | $2$ | $5$ |
| 96.384.5-96.cu.2.12 | $96$ | $2$ | $2$ | $5$ |
| 96.384.5-96.cw.1.3 | $96$ | $2$ | $2$ | $5$ |
| 96.384.5-96.cw.2.10 | $96$ | $2$ | $2$ | $5$ |
| 96.384.7-96.cc.1.4 | $96$ | $2$ | $2$ | $7$ |
| 96.384.7-96.ce.1.4 | $96$ | $2$ | $2$ | $7$ |
| 96.384.7-96.cg.1.8 | $96$ | $2$ | $2$ | $7$ |
| 96.384.7-96.ci.1.8 | $96$ | $2$ | $2$ | $7$ |
| 96.384.7-96.cw.1.12 | $96$ | $2$ | $2$ | $7$ |
| 96.384.7-96.cx.1.4 | $96$ | $2$ | $2$ | $7$ |
| 96.384.7-96.cz.1.14 | $96$ | $2$ | $2$ | $7$ |
| 96.384.7-96.db.1.16 | $96$ | $2$ | $2$ | $7$ |