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: | 8G1 |
Level structure
$\GL_2(\Z/328\Z)$-generators: | $\begin{bmatrix}187&198\\244&119\end{bmatrix}$, $\begin{bmatrix}207&298\\16&241\end{bmatrix}$, $\begin{bmatrix}259&314\\176&219\end{bmatrix}$, $\begin{bmatrix}311&108\\320&165\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 328.48.1.bi.2 for the level structure with $-I$) |
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 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.e.1.5 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
328.48.0-8.e.1.9 | $328$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
328.48.0-328.h.2.4 | $328$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
328.48.0-328.h.2.18 | $328$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
328.48.1-328.d.1.14 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
328.48.1-328.d.1.20 | $328$ | $2$ | $2$ | $1$ | $?$ | 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.g.2.6 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
328.192.1-328.w.1.3 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
328.192.1-328.bl.1.3 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
328.192.1-328.bp.2.7 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
328.192.1-328.bu.1.2 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
328.192.1-328.by.2.4 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
328.192.1-328.cf.2.8 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
328.192.1-328.ch.1.4 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |