Invariants
Level: | $328$ | $\SL_2$-level: | $8$ | ||||
Index: | $96$ | $\PSL_2$-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 | $4^{8}\cdot8^{2}$ | 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: | 8N0 |
Level structure
$\GL_2(\Z/328\Z)$-generators: | $\begin{bmatrix}15&280\\180&259\end{bmatrix}$, $\begin{bmatrix}49&156\\112&173\end{bmatrix}$, $\begin{bmatrix}187&104\\296&233\end{bmatrix}$, $\begin{bmatrix}219&130\\208&223\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 328.48.0.i.1 for the level structure with $-I$) |
Cyclic 328-isogeny field degree: | $84$ |
Cyclic 328-torsion field degree: | $6720$ |
Full 328-torsion field degree: | $44083200$ |
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 |
---|---|---|---|---|---|
8.48.0-8.d.1.13 | $8$ | $2$ | $2$ | $0$ | $0$ |
328.48.0-164.c.1.11 | $328$ | $2$ | $2$ | $0$ | $?$ |
328.48.0-164.c.1.13 | $328$ | $2$ | $2$ | $0$ | $?$ |
328.48.0-8.d.1.11 | $328$ | $2$ | $2$ | $0$ | $?$ |
328.48.0-328.h.2.8 | $328$ | $2$ | $2$ | $0$ | $?$ |
328.48.0-328.h.2.26 | $328$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
328.192.1-328.c.1.4 | $328$ | $2$ | $2$ | $1$ |
328.192.1-328.i.2.6 | $328$ | $2$ | $2$ | $1$ |
328.192.1-328.ba.2.4 | $328$ | $2$ | $2$ | $1$ |
328.192.1-328.bc.1.4 | $328$ | $2$ | $2$ | $1$ |
328.192.1-328.bs.2.6 | $328$ | $2$ | $2$ | $1$ |
328.192.1-328.bu.1.4 | $328$ | $2$ | $2$ | $1$ |
328.192.1-328.ca.1.4 | $328$ | $2$ | $2$ | $1$ |
328.192.1-328.cb.2.7 | $328$ | $2$ | $2$ | $1$ |