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 $4$ are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $1^{4}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8F1 |
Level structure
$\GL_2(\Z/328\Z)$-generators: | $\begin{bmatrix}21&158\\184&15\end{bmatrix}$, $\begin{bmatrix}77&264\\264&133\end{bmatrix}$, $\begin{bmatrix}133&34\\156&119\end{bmatrix}$, $\begin{bmatrix}237&116\\32&53\end{bmatrix}$, $\begin{bmatrix}313&216\\88&165\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 328.48.1.o.1 for the level structure with $-I$) |
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 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 |
---|---|---|---|---|---|---|
$X_{\mathrm{arith}}(4)$ | $4$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
328.48.0-4.b.1.7 | $328$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
328.48.0-328.k.1.2 | $328$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
328.48.0-328.k.1.5 | $328$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
328.48.1-328.a.1.1 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
328.48.1-328.a.1.6 | $328$ | $2$ | $2$ | $1$ | $?$ | 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.o.1.1 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
328.192.1-328.o.1.7 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
328.192.1-328.o.2.2 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
328.192.1-328.o.2.5 | $328$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
328.192.3-328.m.1.3 | $328$ | $2$ | $2$ | $3$ | $?$ | not computed |
328.192.3-328.m.1.9 | $328$ | $2$ | $2$ | $3$ | $?$ | not computed |
328.192.3-328.o.1.1 | $328$ | $2$ | $2$ | $3$ | $?$ | not computed |
328.192.3-328.o.1.11 | $328$ | $2$ | $2$ | $3$ | $?$ | not computed |
328.192.3-328.v.1.1 | $328$ | $2$ | $2$ | $3$ | $?$ | not computed |
328.192.3-328.v.1.15 | $328$ | $2$ | $2$ | $3$ | $?$ | not computed |
328.192.3-328.w.1.1 | $328$ | $2$ | $2$ | $3$ | $?$ | not computed |
328.192.3-328.w.1.14 | $328$ | $2$ | $2$ | $3$ | $?$ | not computed |
328.192.3-328.bb.1.2 | $328$ | $2$ | $2$ | $3$ | $?$ | not computed |
328.192.3-328.bb.1.9 | $328$ | $2$ | $2$ | $3$ | $?$ | not computed |
328.192.3-328.bf.1.1 | $328$ | $2$ | $2$ | $3$ | $?$ | not computed |
328.192.3-328.bf.1.11 | $328$ | $2$ | $2$ | $3$ | $?$ | not computed |