Invariants
| Level: | $328$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
| Index: | $96$ | $\PSL_2$-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: | $\begin{bmatrix}215&302\\84&277\end{bmatrix}$, $\begin{bmatrix}273&266\\288&151\end{bmatrix}$, $\begin{bmatrix}321&0\\127&171\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 328-isogeny field degree: | $84$ |
| Cyclic 328-torsion field degree: | $13440$ |
| Full 328-torsion field degree: | $44083200$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | not computed |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 8.48.0.q.2 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 328.48.0.bs.2 | $328$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 328.48.1.if.1 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |