Modular curve 328.96.3.be.1

• Label: 328.96.3.be.1
• Level: $328$
• Index: $96$
• Genus: $3$
• Cusps: $12$
• $\Q$-cusps: $4$

Invariants

Level:	$328$		$\SL_2$-level:	$8$		Newform level:	$1$
Index:	$96$		$\PSL_2$-index:	$96$
Genus:	$3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$
Cusps:	$12$ (of which $4$ are rational)		Cusp widths	$8^{12}$		Cusp orbits	$1^{4}\cdot2^{2}\cdot4$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
Analytic rank:	not computed
$\Q$-gonality:	$2 \le \gamma \le 3$
$\overline{\Q}$-gonality:	$2 \le \gamma \le 3$
Rational cusps:	$4$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:

8B3

Level structure

$\GL_2(\Z/328\Z)$-generators:	$\begin{bmatrix}71&256\\100&203\end{bmatrix}$, $\begin{bmatrix}113&72\\196&231\end{bmatrix}$, $\begin{bmatrix}183&100\\240&197\end{bmatrix}$, $\begin{bmatrix}273&84\\300&97\end{bmatrix}$, $\begin{bmatrix}297&100\\324&67\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	328.192.3-328.be.1.1, 328.192.3-328.be.1.2, 328.192.3-328.be.1.3, 328.192.3-328.be.1.4, 328.192.3-328.be.1.5, 328.192.3-328.be.1.6, 328.192.3-328.be.1.7, 328.192.3-328.be.1.8, 328.192.3-328.be.1.9, 328.192.3-328.be.1.10, 328.192.3-328.be.1.11, 328.192.3-328.be.1.12
Cyclic 328-isogeny field degree:	$84$
Cyclic 328-torsion field degree:	$6720$
Full 328-torsion field degree:	$44083200$

Rational points

This modular curve has 4 rational cusps but no known non-cuspidal rational points.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank
8.48.0.c.1	$8$	$2$	$2$	$0$	$0$
328.48.1.n.1	$328$	$2$	$2$	$1$	$?$
328.48.2.a.1	$328$	$2$	$2$	$2$	$?$

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

Covering curve	Level	Index	Degree	Genus
328.192.5.z.1	$328$	$2$	$2$	$5$
328.192.5.z.2	$328$	$2$	$2$	$5$
328.192.5.bb.3	$328$	$2$	$2$	$5$
328.192.5.bb.4	$328$	$2$	$2$	$5$