Invariants
| Level: | $328$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | Cusp orbits | $2^{2}\cdot4^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8K1 |
Level structure
| $\GL_2(\Z/328\Z)$-generators: | $\begin{bmatrix}9&180\\36&139\end{bmatrix}$, $\begin{bmatrix}53&32\\254&171\end{bmatrix}$, $\begin{bmatrix}255&180\\276&139\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 328.96.1.bu.1 for the level structure with $-I$) |
| Cyclic 328-isogeny field degree: | $84$ |
| Cyclic 328-torsion field degree: | $6720$ |
| Full 328-torsion field degree: | $22041600$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | not computed |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 8.96.0-8.h.1.8 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 328.96.0-8.h.1.5 | $328$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 328.96.0-328.i.1.6 | $328$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 328.96.0-328.i.1.10 | $328$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 328.96.0-328.k.2.7 | $328$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 328.96.0-328.k.2.16 | $328$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 328.96.0-328.y.1.4 | $328$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 328.96.0-328.y.1.12 | $328$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 328.96.1-328.bg.2.2 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 328.96.1-328.bg.2.8 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 328.96.1-328.bi.2.6 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 328.96.1-328.bi.2.8 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 328.96.1-328.bs.1.6 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 328.96.1-328.bs.1.7 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |