Invariants
Level: | $328$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (of which $2$ are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8F1 |
Level structure
$\GL_2(\Z/328\Z)$-generators: | $\begin{bmatrix}53&320\\4&81\end{bmatrix}$, $\begin{bmatrix}169&48\\198&241\end{bmatrix}$, $\begin{bmatrix}221&44\\192&23\end{bmatrix}$, $\begin{bmatrix}261&292\\118&147\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 328.48.1.bu.1 for the level structure with $-I$) |
Cyclic 328-isogeny field degree: | $42$ |
Cyclic 328-torsion field degree: | $6720$ |
Full 328-torsion field degree: | $44083200$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
8.48.0-8.i.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
164.48.0-164.c.1.3 | $164$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
328.48.0-164.c.1.10 | $328$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
328.48.0-8.i.1.7 | $328$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
328.48.1-328.c.1.3 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
328.48.1-328.c.1.19 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
328.192.1-328.ca.1.3 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
328.192.1-328.ca.2.7 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
328.192.1-328.cb.1.1 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
328.192.1-328.cb.2.2 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
328.192.1-328.cc.1.2 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
328.192.1-328.cc.2.4 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
328.192.1-328.cd.1.1 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
328.192.1-328.cd.2.3 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |