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Properties

Label 328.48.0.x.1
Level $328$
Index $48$
Genus $0$
Cusps $10$
$\Q$-cusps $0$

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Invariants

Level: $328$ $\SL_2$-level: $8$
Index: $48$ $\PSL_2$-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 $2^{4}\cdot4^{2}\cdot8^{4}$ Cusp orbits $2^{5}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
$\Q$-gonality: $1 \le \gamma \le 2$
$\overline{\Q}$-gonality: $1$
Rational cusps: $0$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 8O0

Level structure

$\GL_2(\Z/328\Z)$-generators: $\begin{bmatrix}135&296\\38&117\end{bmatrix}$, $\begin{bmatrix}143&8\\240&63\end{bmatrix}$, $\begin{bmatrix}153&244\\82&323\end{bmatrix}$, $\begin{bmatrix}201&116\\266&5\end{bmatrix}$, $\begin{bmatrix}249&124\\228&301\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 328.96.0-328.x.1.1, 328.96.0-328.x.1.2, 328.96.0-328.x.1.3, 328.96.0-328.x.1.4, 328.96.0-328.x.1.5, 328.96.0-328.x.1.6, 328.96.0-328.x.1.7, 328.96.0-328.x.1.8, 328.96.0-328.x.1.9, 328.96.0-328.x.1.10, 328.96.0-328.x.1.11, 328.96.0-328.x.1.12, 328.96.0-328.x.1.13, 328.96.0-328.x.1.14, 328.96.0-328.x.1.15, 328.96.0-328.x.1.16
Cyclic 328-isogeny field degree: $84$
Cyclic 328-torsion field degree: $13440$
Full 328-torsion field degree: $88166400$

Models

This modular curve is isomorphic to $\mathbb{P}^1$.

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
8.24.0.e.1 $8$ $2$ $2$ $0$ $0$
328.24.0.i.2 $328$ $2$ $2$ $0$ $?$
328.24.0.m.1 $328$ $2$ $2$ $0$ $?$

This modular curve is minimally covered by the modular curves in the database listed below.

Covering curve Level Index Degree Genus
328.96.1.s.2 $328$ $2$ $2$ $1$
328.96.1.t.2 $328$ $2$ $2$ $1$
328.96.1.x.1 $328$ $2$ $2$ $1$
328.96.1.y.1 $328$ $2$ $2$ $1$
328.96.1.bm.1 $328$ $2$ $2$ $1$
328.96.1.bn.1 $328$ $2$ $2$ $1$
328.96.1.bo.2 $328$ $2$ $2$ $1$
328.96.1.bp.2 $328$ $2$ $2$ $1$