Modular curve 120.60.4.bw.1

• Label: 120.60.4.bw.1
• Level: $120$
• Index: $60$
• Genus: $4$
• Cusps: $4$
• $\Q$-cusps: $2$

Invariants

Level:	$120$		$\SL_2$-level:	$40$		Newform level:	$1$
Index:	$60$		$\PSL_2$-index:	$60$
Genus:	$4 = 1 + \frac{ 60 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$
Cusps:	$4$ (of which $2$ are rational)		Cusp widths	$5^{2}\cdot10\cdot40$		Cusp orbits	$1^{2}\cdot2$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
Analytic rank:	not computed
$\Q$-gonality:	$2 \le \gamma \le 4$
$\overline{\Q}$-gonality:	$2 \le \gamma \le 4$
Rational cusps:	$2$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:

40B4

Level structure

$\GL_2(\Z/120\Z)$-generators:	$\begin{bmatrix}5&44\\2&7\end{bmatrix}$, $\begin{bmatrix}6&11\\73&84\end{bmatrix}$, $\begin{bmatrix}21&38\\34&81\end{bmatrix}$, $\begin{bmatrix}22&107\\61&108\end{bmatrix}$, $\begin{bmatrix}31&50\\28&69\end{bmatrix}$, $\begin{bmatrix}72&23\\11&48\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	120.120.4-120.bw.1.1, 120.120.4-120.bw.1.2, 120.120.4-120.bw.1.3, 120.120.4-120.bw.1.4, 120.120.4-120.bw.1.5, 120.120.4-120.bw.1.6, 120.120.4-120.bw.1.7, 120.120.4-120.bw.1.8, 120.120.4-120.bw.1.9, 120.120.4-120.bw.1.10, 120.120.4-120.bw.1.11, 120.120.4-120.bw.1.12, 120.120.4-120.bw.1.13, 120.120.4-120.bw.1.14, 120.120.4-120.bw.1.15, 120.120.4-120.bw.1.16, 120.120.4-120.bw.1.17, 120.120.4-120.bw.1.18, 120.120.4-120.bw.1.19, 120.120.4-120.bw.1.20, 120.120.4-120.bw.1.21, 120.120.4-120.bw.1.22, 120.120.4-120.bw.1.23, 120.120.4-120.bw.1.24, 120.120.4-120.bw.1.25, 120.120.4-120.bw.1.26, 120.120.4-120.bw.1.27, 120.120.4-120.bw.1.28, 120.120.4-120.bw.1.29, 120.120.4-120.bw.1.30, 120.120.4-120.bw.1.31, 120.120.4-120.bw.1.32
Cyclic 120-isogeny field degree:	$48$
Cyclic 120-torsion field degree:	$1536$
Full 120-torsion field degree:	$589824$

Rational points

This modular curve has 2 rational cusps but no known non-cuspidal 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
$X_{S_4}(5)$	$5$	$12$	$12$	$0$	$0$
24.12.0.y.1	$24$	$5$	$5$	$0$	$0$

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank
20.30.2.c.1	$20$	$2$	$2$	$2$	$0$
24.12.0.y.1	$24$	$5$	$5$	$0$	$0$

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

Covering curve	Level	Index	Degree	Genus
120.120.8.bk.1	$120$	$2$	$2$	$8$
120.120.8.bm.1	$120$	$2$	$2$	$8$
120.120.8.bz.1	$120$	$2$	$2$	$8$
120.120.8.cb.1	$120$	$2$	$2$	$8$
120.120.8.de.1	$120$	$2$	$2$	$8$
120.120.8.dh.1	$120$	$2$	$2$	$8$
120.120.8.dr.1	$120$	$2$	$2$	$8$
120.120.8.ds.1	$120$	$2$	$2$	$8$
120.120.8.ek.1	$120$	$2$	$2$	$8$
120.120.8.em.1	$120$	$2$	$2$	$8$
120.120.8.eo.1	$120$	$2$	$2$	$8$
120.120.8.eq.1	$120$	$2$	$2$	$8$
120.120.8.fi.1	$120$	$2$	$2$	$8$
120.120.8.fk.1	$120$	$2$	$2$	$8$
120.120.8.fm.1	$120$	$2$	$2$	$8$
120.120.8.fo.1	$120$	$2$	$2$	$8$
120.180.10.cu.1	$120$	$3$	$3$	$10$
120.180.14.fe.1	$120$	$3$	$3$	$14$
120.240.13.bzc.1	$120$	$4$	$4$	$13$
120.240.17.brc.1	$120$	$4$	$4$	$17$