Modular curve 264.192.5.ks.3

• Label: 264.192.5.ks.3
• Level: $264$
• Index: $192$
• Genus: $5$
• Cusps: $24$
• $\Q$-cusps: $0$

Invariants

Level:	$264$		$\SL_2$-level:	$12$		Newform level:	$1$
Index:	$192$		$\PSL_2$-index:	$192$
Genus:	$5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$
Cusps:	$24$ (none of which are rational)		Cusp widths	$4^{12}\cdot12^{12}$		Cusp orbits	$2^{2}\cdot4^{5}$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
Analytic rank:	not computed
$\Q$-gonality:	$2 \le \gamma \le 8$
$\overline{\Q}$-gonality:	$2 \le \gamma \le 5$
Rational cusps:	$0$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:

12E5

Level structure

$\GL_2(\Z/264\Z)$-generators:	$\begin{bmatrix}11&30\\186&161\end{bmatrix}$, $\begin{bmatrix}59&94\\78&55\end{bmatrix}$, $\begin{bmatrix}83&82\\56&255\end{bmatrix}$, $\begin{bmatrix}113&34\\30&7\end{bmatrix}$, $\begin{bmatrix}155&108\\230&151\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	264.384.5-264.ks.3.1, 264.384.5-264.ks.3.2, 264.384.5-264.ks.3.3, 264.384.5-264.ks.3.4, 264.384.5-264.ks.3.5, 264.384.5-264.ks.3.6, 264.384.5-264.ks.3.7, 264.384.5-264.ks.3.8, 264.384.5-264.ks.3.9, 264.384.5-264.ks.3.10, 264.384.5-264.ks.3.11, 264.384.5-264.ks.3.12, 264.384.5-264.ks.3.13, 264.384.5-264.ks.3.14, 264.384.5-264.ks.3.15, 264.384.5-264.ks.3.16
Cyclic 264-isogeny field degree:	$48$
Cyclic 264-torsion field degree:	$1920$
Full 264-torsion field degree:	$5068800$

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
24.96.1.cp.2	$24$	$2$	$2$	$1$	$1$
132.96.1.f.3	$132$	$2$	$2$	$1$	$?$
264.96.1.lu.1	$264$	$2$	$2$	$1$	$?$
264.96.3.do.1	$264$	$2$	$2$	$3$	$?$
264.96.3.ek.1	$264$	$2$	$2$	$3$	$?$
264.96.3.eq.2	$264$	$2$	$2$	$3$	$?$
264.96.3.es.2	$264$	$2$	$2$	$3$	$?$