Modular curve 120.120.5.iq.1

• Label: 120.120.5.iq.1
• Level: $120$
• Index: $120$
• Genus: $5$
• Cusps: $12$
• $\Q$-cusps: $2$

Invariants

Level:	$120$		$\SL_2$-level:	$10$		Newform level:	$1$
Index:	$120$		$\PSL_2$-index:	$120$
Genus:	$5 = 1 + \frac{ 120 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$
Cusps:	$12$ (of which $2$ are rational)		Cusp widths	$10^{12}$		Cusp orbits	$1^{2}\cdot2\cdot4^{2}$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
Analytic rank:	not computed
$\Q$-gonality:	$2 \le \gamma \le 5$
$\overline{\Q}$-gonality:	$2 \le \gamma \le 5$
Rational cusps:	$2$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:

10A5

Level structure

$\GL_2(\Z/120\Z)$-generators:	$\begin{bmatrix}20&29\\97&98\end{bmatrix}$, $\begin{bmatrix}21&25\\70&91\end{bmatrix}$, $\begin{bmatrix}40&59\\27&53\end{bmatrix}$, $\begin{bmatrix}66&67\\1&60\end{bmatrix}$, $\begin{bmatrix}113&102\\21&37\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	120.240.5-120.iq.1.1, 120.240.5-120.iq.1.2, 120.240.5-120.iq.1.3, 120.240.5-120.iq.1.4, 120.240.5-120.iq.1.5, 120.240.5-120.iq.1.6, 120.240.5-120.iq.1.7, 120.240.5-120.iq.1.8, 120.240.5-120.iq.1.9, 120.240.5-120.iq.1.10, 120.240.5-120.iq.1.11, 120.240.5-120.iq.1.12, 120.240.5-120.iq.1.13, 120.240.5-120.iq.1.14, 120.240.5-120.iq.1.15, 120.240.5-120.iq.1.16
Cyclic 120-isogeny field degree:	$48$
Cyclic 120-torsion field degree:	$768$
Full 120-torsion field degree:	$294912$

Rational points

This modular curve has 2 rational cusps but no known non-cuspidal rational points.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank
5.60.0.a.1	$5$	$2$	$2$	$0$	$0$
120.24.1.jr.1	$120$	$5$	$5$	$1$	$?$
120.24.1.jr.2	$120$	$5$	$5$	$1$	$?$
120.60.2.e.1	$120$	$2$	$2$	$2$	$?$
120.60.3.dr.1	$120$	$2$	$2$	$3$	$?$

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

Covering curve	Level	Index	Degree	Genus
120.360.13.ga.1	$120$	$3$	$3$	$13$