Modular curve 120.120.8.de.1

• Label: 120.120.8.de.1
• Level: $120$
• Index: $120$
• Genus: $8$
• Cusps: $6$
• $\Q$-cusps: $0$

Invariants

Level:	$120$		$\SL_2$-level:	$40$		Newform level:	$1$
Index:	$120$		$\PSL_2$-index:	$120$
Genus:	$8 = 1 + \frac{ 120 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$
Cusps:	$6$ (none of which are rational)		Cusp widths	$10^{4}\cdot40^{2}$		Cusp orbits	$2^{3}$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
Analytic rank:	not computed
$\Q$-gonality:	$3 \le \gamma \le 14$
$\overline{\Q}$-gonality:	$3 \le \gamma \le 8$
Rational cusps:	$0$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:

40A8

Level structure

$\GL_2(\Z/120\Z)$-generators:	$\begin{bmatrix}3&98\\32&25\end{bmatrix}$, $\begin{bmatrix}39&44\\4&11\end{bmatrix}$, $\begin{bmatrix}47&45\\60&77\end{bmatrix}$, $\begin{bmatrix}93&20\\8&47\end{bmatrix}$, $\begin{bmatrix}115&73\\8&81\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	120.240.8-120.de.1.1, 120.240.8-120.de.1.2, 120.240.8-120.de.1.3, 120.240.8-120.de.1.4, 120.240.8-120.de.1.5, 120.240.8-120.de.1.6, 120.240.8-120.de.1.7, 120.240.8-120.de.1.8, 120.240.8-120.de.1.9, 120.240.8-120.de.1.10, 120.240.8-120.de.1.11, 120.240.8-120.de.1.12, 120.240.8-120.de.1.13, 120.240.8-120.de.1.14, 120.240.8-120.de.1.15, 120.240.8-120.de.1.16
Cyclic 120-isogeny field degree:	$48$
Cyclic 120-torsion field degree:	$1536$
Full 120-torsion field degree:	$294912$

Rational points

This modular curve has no $\Q_p$ points for $p=7$, and therefore no rational points.

Modular covers

The following modular covers realize this modular curve as a fiber product over $X(1)$.

Factor curve	Level	Index	Degree	Genus	Rank
$X_{S_4}(5)$	$5$	$24$	$24$	$0$	$0$
24.24.0.bk.1	$24$	$5$	$5$	$0$	$0$

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank
24.24.0.bk.1	$24$	$5$	$5$	$0$	$0$
40.60.4.bk.1	$40$	$2$	$2$	$4$	$0$
60.60.4.l.1	$60$	$2$	$2$	$4$	$1$
120.60.4.bw.1	$120$	$2$	$2$	$4$	$?$

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

Covering curve	Level	Index	Degree	Genus
120.360.22.hy.1	$120$	$3$	$3$	$22$