Invariants
| Level: | $328$ | $\SL_2$-level: | $328$ | Newform level: | $1$ | ||
| Index: | $504$ | $\PSL_2$-index: | $252$ | ||||
| Genus: | $19 = 1 + \frac{ 252 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (all of which are rational) | Cusp widths | $1^{2}\cdot4\cdot41^{2}\cdot164$ | Cusp orbits | $1^{6}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $6 \le \gamma \le 19$ | ||||||
| $\overline{\Q}$-gonality: | $6 \le \gamma \le 19$ | ||||||
| Rational cusps: | $6$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 164B19 |
Level structure
| $\GL_2(\Z/328\Z)$-generators: | $\begin{bmatrix}56&287\\303&204\end{bmatrix}$, $\begin{bmatrix}60&253\\25&288\end{bmatrix}$, $\begin{bmatrix}120&149\\293&304\end{bmatrix}$, $\begin{bmatrix}142&223\\139&226\end{bmatrix}$, $\begin{bmatrix}287&260\\6&49\end{bmatrix}$, $\begin{bmatrix}316&179\\297&34\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 164.252.19.c.1 for the level structure with $-I$) |
| Cyclic 328-isogeny field degree: | $2$ |
| Cyclic 328-torsion field degree: | $160$ |
| Full 328-torsion field degree: | $8396800$ |
Rational points
This modular curve has 6 rational cusps but no known non-cuspidal rational points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.12.0-4.c.1.5 | $8$ | $42$ | $42$ | $0$ | $0$ |
| $X_0(41)$ | $41$ | $12$ | $6$ | $3$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.12.0-4.c.1.5 | $8$ | $42$ | $42$ | $0$ | $0$ |