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 | $2^{6}\cdot4$ | ||
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: | $\begin{bmatrix}127&264\\164&279\end{bmatrix}$, $\begin{bmatrix}129&32\\116&149\end{bmatrix}$, $\begin{bmatrix}209&176\\48&307\end{bmatrix}$, $\begin{bmatrix}225&48\\196&315\end{bmatrix}$, $\begin{bmatrix}271&260\\116&9\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 328.192.1-328.w.1.1, 328.192.1-328.w.1.2, 328.192.1-328.w.1.3, 328.192.1-328.w.1.4, 328.192.1-328.w.1.5, 328.192.1-328.w.1.6, 328.192.1-328.w.1.7, 328.192.1-328.w.1.8, 328.192.1-328.w.1.9, 328.192.1-328.w.1.10, 328.192.1-328.w.1.11, 328.192.1-328.w.1.12 |
Cyclic 328-isogeny field degree: | $84$ |
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 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.c.1 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
328.48.0.b.1 | $328$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
328.48.0.s.1 | $328$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
328.48.0.t.1 | $328$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
328.48.1.n.2 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
328.48.1.bi.2 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
328.48.1.bj.2 | $328$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
328.192.5.w.1 | $328$ | $2$ | $2$ | $5$ | $?$ | not computed |
328.192.5.y.1 | $328$ | $2$ | $2$ | $5$ | $?$ | not computed |
328.192.5.z.2 | $328$ | $2$ | $2$ | $5$ | $?$ | not computed |
328.192.5.bb.1 | $328$ | $2$ | $2$ | $5$ | $?$ | not computed |