Modular curve 120.24.0.cq.1

• Label: 120.24.0.cq.1
• Level: $120$
• Index: $24$
• Genus: $0$
• Cusps: $6$
• $\Q$-cusps: $0$

Invariants

Level:	$120$		$\SL_2$-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

$\GL_2(\Z/120\Z)$-generators:	$\begin{bmatrix}15&104\\98&89\end{bmatrix}$, $\begin{bmatrix}31&32\\13&19\end{bmatrix}$, $\begin{bmatrix}33&56\\104&119\end{bmatrix}$, $\begin{bmatrix}45&116\\74&69\end{bmatrix}$, $\begin{bmatrix}99&112\\40&71\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	120.48.0-120.cq.1.1, 120.48.0-120.cq.1.2, 120.48.0-120.cq.1.3, 120.48.0-120.cq.1.4, 120.48.0-120.cq.1.5, 120.48.0-120.cq.1.6, 120.48.0-120.cq.1.7, 120.48.0-120.cq.1.8, 120.48.0-120.cq.1.9, 120.48.0-120.cq.1.10, 120.48.0-120.cq.1.11, 120.48.0-120.cq.1.12, 120.48.0-120.cq.1.13, 120.48.0-120.cq.1.14, 120.48.0-120.cq.1.15, 120.48.0-120.cq.1.16
Cyclic 120-isogeny field degree:	$48$
Cyclic 120-torsion field degree:	$1536$
Full 120-torsion field degree:	$1474560$

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
20.12.0.h.1	$20$	$2$	$2$	$0$	$0$
24.12.0.y.1	$24$	$2$	$2$	$0$	$0$
120.12.0.y.1	$120$	$2$	$2$	$0$	$?$

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

Covering curve	Level	Index	Degree	Genus
120.72.4.ka.1	$120$	$3$	$3$	$4$
120.96.3.oo.1	$120$	$4$	$4$	$3$
120.120.8.eo.1	$120$	$5$	$5$	$8$
120.144.7.dur.1	$120$	$6$	$6$	$7$
120.240.15.kq.1	$120$	$10$	$10$	$15$