Modular curve 168.24.0.cc.1

• Label: 168.24.0.cc.1
• Level: $168$
• Index: $24$
• Genus: $0$
• Cusps: $6$
• $\Q$-cusps: $0$

Invariants

Level:	$168$		$\SL_2$-level:	$8$
Index:	$24$		$\PSL_2$-index:	$24$
Genus:	$0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$
Cusps:	$6$ (none of which are rational)		Cusp widths	$2^{4}\cdot8^{2}$		Cusp orbits	$2^{3}$
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:

8G0

Level structure

$\GL_2(\Z/168\Z)$-generators:	$\begin{bmatrix}1&72\\57&17\end{bmatrix}$, $\begin{bmatrix}129&52\\16&19\end{bmatrix}$, $\begin{bmatrix}129&164\\13&123\end{bmatrix}$, $\begin{bmatrix}149&140\\86&73\end{bmatrix}$, $\begin{bmatrix}159&100\\7&155\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	168.48.0-168.cc.1.1, 168.48.0-168.cc.1.2, 168.48.0-168.cc.1.3, 168.48.0-168.cc.1.4, 168.48.0-168.cc.1.5, 168.48.0-168.cc.1.6, 168.48.0-168.cc.1.7, 168.48.0-168.cc.1.8, 168.48.0-168.cc.1.9, 168.48.0-168.cc.1.10, 168.48.0-168.cc.1.11, 168.48.0-168.cc.1.12, 168.48.0-168.cc.1.13, 168.48.0-168.cc.1.14, 168.48.0-168.cc.1.15, 168.48.0-168.cc.1.16
Cyclic 168-isogeny field degree:	$64$
Cyclic 168-torsion field degree:	$3072$
Full 168-torsion field degree:	$6193152$

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
12.12.0.h.1	$12$	$2$	$2$	$0$	$0$
56.12.0.ba.1	$56$	$2$	$2$	$0$	$0$
168.12.0.ba.1	$168$	$2$	$2$	$0$	$?$

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

Covering curve	Level	Index	Degree	Genus
168.72.4.im.1	$168$	$3$	$3$	$4$
168.96.3.ke.1	$168$	$4$	$4$	$3$
168.192.11.ie.1	$168$	$8$	$8$	$11$