Invariants
Level: | $328$ | $\SL_2$-level: | $8$ | ||||
Index: | $48$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot8^{4}$ | Cusp orbits | $2^{3}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8O0 |
Level structure
$\GL_2(\Z/328\Z)$-generators: | $\begin{bmatrix}27&192\\164&85\end{bmatrix}$, $\begin{bmatrix}95&220\\10&17\end{bmatrix}$, $\begin{bmatrix}113&192\\54&153\end{bmatrix}$, $\begin{bmatrix}261&72\\258&307\end{bmatrix}$, $\begin{bmatrix}315&272\\92&183\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 328.96.0-328.q.1.1, 328.96.0-328.q.1.2, 328.96.0-328.q.1.3, 328.96.0-328.q.1.4, 328.96.0-328.q.1.5, 328.96.0-328.q.1.6, 328.96.0-328.q.1.7, 328.96.0-328.q.1.8, 328.96.0-328.q.1.9, 328.96.0-328.q.1.10, 328.96.0-328.q.1.11, 328.96.0-328.q.1.12, 328.96.0-328.q.1.13, 328.96.0-328.q.1.14, 328.96.0-328.q.1.15, 328.96.0-328.q.1.16 |
Cyclic 328-isogeny field degree: | $84$ |
Cyclic 328-torsion field degree: | $13440$ |
Full 328-torsion field degree: | $88166400$ |
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 |
---|---|---|---|---|---|
8.24.0.d.1 | $8$ | $2$ | $2$ | $0$ | $0$ |
328.24.0.h.1 | $328$ | $2$ | $2$ | $0$ | $?$ |
328.24.0.l.1 | $328$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
328.96.1.a.1 | $328$ | $2$ | $2$ | $1$ |
328.96.1.d.1 | $328$ | $2$ | $2$ | $1$ |
328.96.1.g.1 | $328$ | $2$ | $2$ | $1$ |
328.96.1.j.1 | $328$ | $2$ | $2$ | $1$ |
328.96.1.ba.1 | $328$ | $2$ | $2$ | $1$ |
328.96.1.bb.1 | $328$ | $2$ | $2$ | $1$ |
328.96.1.bc.1 | $328$ | $2$ | $2$ | $1$ |
328.96.1.bd.1 | $328$ | $2$ | $2$ | $1$ |