Modular curve 168.192.5.bw.2

• Label: 168.192.5.bw.2
• Level: $168$
• Index: $192$
• Genus: $5$
• Cusps: $24$
• $\Q$-cusps: $0$

Invariants

Level:	$168$		$\SL_2$-level:	$8$		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	$8^{24}$		Cusp orbits	$2^{2}\cdot4^{3}\cdot8$
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:

8A5

Level structure

$\GL_2(\Z/168\Z)$-generators:	$\begin{bmatrix}13&150\\52&119\end{bmatrix}$, $\begin{bmatrix}29&28\\144&13\end{bmatrix}$, $\begin{bmatrix}65&76\\152&93\end{bmatrix}$, $\begin{bmatrix}107&152\\12&71\end{bmatrix}$, $\begin{bmatrix}131&122\\140&81\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	168.384.5-168.bw.2.1, 168.384.5-168.bw.2.2, 168.384.5-168.bw.2.3, 168.384.5-168.bw.2.4, 168.384.5-168.bw.2.5, 168.384.5-168.bw.2.6, 168.384.5-168.bw.2.7, 168.384.5-168.bw.2.8, 168.384.5-168.bw.2.9, 168.384.5-168.bw.2.10, 168.384.5-168.bw.2.11, 168.384.5-168.bw.2.12, 168.384.5-168.bw.2.13, 168.384.5-168.bw.2.14, 168.384.5-168.bw.2.15, 168.384.5-168.bw.2.16
Cyclic 168-isogeny field degree:	$64$
Cyclic 168-torsion field degree:	$3072$
Full 168-torsion field degree:	$774144$

Rational points

This modular curve has no $\Q_p$ points for $p=29$, and therefore no rational points.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank
24.96.1.h.1	$24$	$2$	$2$	$1$	$0$
56.96.1.n.2	$56$	$2$	$2$	$1$	$1$
168.96.1.h.2	$168$	$2$	$2$	$1$	$?$
168.96.3.l.1	$168$	$2$	$2$	$3$	$?$
168.96.3.bo.3	$168$	$2$	$2$	$3$	$?$
168.96.3.br.1	$168$	$2$	$2$	$3$	$?$
168.96.3.bx.2	$168$	$2$	$2$	$3$	$?$