Modular curve 120.48.0.r.1

• Label: 120.48.0.r.1
• Level: $120$
• Index: $48$
• Genus: $0$
• Cusps: $10$
• $\Q$-cusps: $0$

Invariants

Level:	$120$		$\SL_2$-level:	$8$
Index:	$48$		$\PSL_2$-index:	$48$
Genus:	$0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$
Cusps:	$10$ (none of which are rational)		Cusp widths	$4^{8}\cdot8^{2}$		Cusp orbits	$2^{3}\cdot4$
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:

8N0

Level structure

$\GL_2(\Z/120\Z)$-generators:	$\begin{bmatrix}29&94\\108&71\end{bmatrix}$, $\begin{bmatrix}65&102\\24&67\end{bmatrix}$, $\begin{bmatrix}71&88\\24&73\end{bmatrix}$, $\begin{bmatrix}73&86\\92&33\end{bmatrix}$, $\begin{bmatrix}89&66\\108&115\end{bmatrix}$, $\begin{bmatrix}103&64\\8&111\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	120.96.0-120.r.1.1, 120.96.0-120.r.1.2, 120.96.0-120.r.1.3, 120.96.0-120.r.1.4, 120.96.0-120.r.1.5, 120.96.0-120.r.1.6, 120.96.0-120.r.1.7, 120.96.0-120.r.1.8, 120.96.0-120.r.1.9, 120.96.0-120.r.1.10, 120.96.0-120.r.1.11, 120.96.0-120.r.1.12, 120.96.0-120.r.1.13, 120.96.0-120.r.1.14, 120.96.0-120.r.1.15, 120.96.0-120.r.1.16, 120.96.0-120.r.1.17, 120.96.0-120.r.1.18, 120.96.0-120.r.1.19, 120.96.0-120.r.1.20, 120.96.0-120.r.1.21, 120.96.0-120.r.1.22, 120.96.0-120.r.1.23, 120.96.0-120.r.1.24, 120.96.0-120.r.1.25, 120.96.0-120.r.1.26, 120.96.0-120.r.1.27, 120.96.0-120.r.1.28, 120.96.0-120.r.1.29, 120.96.0-120.r.1.30, 120.96.0-120.r.1.31, 120.96.0-120.r.1.32
Cyclic 120-isogeny field degree:	$48$
Cyclic 120-torsion field degree:	$1536$
Full 120-torsion field degree:	$737280$

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
20.24.0.c.1	$20$	$2$	$2$	$0$	$0$
24.24.0.h.1	$24$	$2$	$2$	$0$	$0$
120.24.0.t.2	$120$	$2$	$2$	$0$	$?$

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

Covering curve	Level	Index	Degree	Genus
120.96.1.i.2	$120$	$2$	$2$	$1$
120.96.1.bd.2	$120$	$2$	$2$	$1$
120.96.1.dk.2	$120$	$2$	$2$	$1$
120.96.1.dm.2	$120$	$2$	$2$	$1$
120.96.1.ft.2	$120$	$2$	$2$	$1$
120.96.1.fx.2	$120$	$2$	$2$	$1$
120.96.1.gy.2	$120$	$2$	$2$	$1$
120.96.1.hc.2	$120$	$2$	$2$	$1$
120.96.1.ma.2	$120$	$2$	$2$	$1$
120.96.1.me.2	$120$	$2$	$2$	$1$
120.96.1.ng.2	$120$	$2$	$2$	$1$
120.96.1.nk.2	$120$	$2$	$2$	$1$
120.96.1.ok.2	$120$	$2$	$2$	$1$
120.96.1.om.2	$120$	$2$	$2$	$1$
120.96.1.os.2	$120$	$2$	$2$	$1$
120.96.1.ot.2	$120$	$2$	$2$	$1$
120.144.8.bx.2	$120$	$3$	$3$	$8$
120.192.7.cg.1	$120$	$4$	$4$	$7$
120.240.16.bg.1	$120$	$5$	$5$	$16$
120.288.15.vv.2	$120$	$6$	$6$	$15$