Invariants
| Level: | $328$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
| Cusps: | $24$ (of which $4$ are rational) | Cusp widths | $8^{24}$ | Cusp orbits | $1^{4}\cdot2^{2}\cdot4^{2}\cdot8$ | ||
| 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: | 8A5 |
Level structure
| $\GL_2(\Z/328\Z)$-generators: | $\begin{bmatrix}23&142\\24&149\end{bmatrix}$, $\begin{bmatrix}31&96\\24&31\end{bmatrix}$, $\begin{bmatrix}103&28\\232&259\end{bmatrix}$, $\begin{bmatrix}251&290\\212&185\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | 328.384.5-328.bb.4.1, 328.384.5-328.bb.4.2, 328.384.5-328.bb.4.3, 328.384.5-328.bb.4.4, 328.384.5-328.bb.4.5, 328.384.5-328.bb.4.6, 328.384.5-328.bb.4.7, 328.384.5-328.bb.4.8 |
| Cyclic 328-isogeny field degree: | $42$ |
| Cyclic 328-torsion field degree: | $6720$ |
| Full 328-torsion field degree: | $22041600$ |
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 |
|---|---|---|---|---|---|
| 8.96.1.g.1 | $8$ | $2$ | $2$ | $1$ | $0$ |
| 328.96.1.n.2 | $328$ | $2$ | $2$ | $1$ | $?$ |
| 328.96.1.x.2 | $328$ | $2$ | $2$ | $1$ | $?$ |
| 328.96.3.w.3 | $328$ | $2$ | $2$ | $3$ | $?$ |
| 328.96.3.x.2 | $328$ | $2$ | $2$ | $3$ | $?$ |
| 328.96.3.z.2 | $328$ | $2$ | $2$ | $3$ | $?$ |
| 328.96.3.be.1 | $328$ | $2$ | $2$ | $3$ | $?$ |