Modular curve 120.144.9.bbc.1

• Label: 120.144.9.bbc.1
• Level: $120$
• Index: $144$
• Genus: $9$
• Cusps: $8$
• $\Q$-cusps: $0$

Invariants

Level:	$120$		$\SL_2$-level:	$24$		Newform level:	$1$
Index:	$144$		$\PSL_2$-index:	$144$
Genus:	$9 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$
Cusps:	$8$ (none of which are rational)		Cusp widths	$12^{4}\cdot24^{4}$		Cusp orbits	$2^{2}\cdot4$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
Analytic rank:	not computed
$\Q$-gonality:	$3 \le \gamma \le 16$
$\overline{\Q}$-gonality:	$3 \le \gamma \le 9$
Rational cusps:	$0$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:

24C9

Level structure

$\GL_2(\Z/120\Z)$-generators:	$\begin{bmatrix}9&70\\52&37\end{bmatrix}$, $\begin{bmatrix}23&60\\26&49\end{bmatrix}$, $\begin{bmatrix}53&96\\14&67\end{bmatrix}$, $\begin{bmatrix}79&94\\52&59\end{bmatrix}$, $\begin{bmatrix}79&106\\90&101\end{bmatrix}$, $\begin{bmatrix}83&32\\38&73\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	120.288.9-120.bbc.1.1, 120.288.9-120.bbc.1.2, 120.288.9-120.bbc.1.3, 120.288.9-120.bbc.1.4, 120.288.9-120.bbc.1.5, 120.288.9-120.bbc.1.6, 120.288.9-120.bbc.1.7, 120.288.9-120.bbc.1.8, 120.288.9-120.bbc.1.9, 120.288.9-120.bbc.1.10, 120.288.9-120.bbc.1.11, 120.288.9-120.bbc.1.12, 120.288.9-120.bbc.1.13, 120.288.9-120.bbc.1.14, 120.288.9-120.bbc.1.15, 120.288.9-120.bbc.1.16, 240.288.9-120.bbc.1.1, 240.288.9-120.bbc.1.2, 240.288.9-120.bbc.1.3, 240.288.9-120.bbc.1.4, 240.288.9-120.bbc.1.5, 240.288.9-120.bbc.1.6, 240.288.9-120.bbc.1.7, 240.288.9-120.bbc.1.8, 240.288.9-120.bbc.1.9, 240.288.9-120.bbc.1.10, 240.288.9-120.bbc.1.11, 240.288.9-120.bbc.1.12, 240.288.9-120.bbc.1.13, 240.288.9-120.bbc.1.14, 240.288.9-120.bbc.1.15, 240.288.9-120.bbc.1.16
Cyclic 120-isogeny field degree:	$96$
Cyclic 120-torsion field degree:	$3072$
Full 120-torsion field degree:	$245760$

Rational points

This modular curve has no real points, 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
$X_{\mathrm{ns}}^+(3)$	$3$	$48$	$48$	$0$	$0$
40.48.1.bk.1	$40$	$3$	$3$	$1$	$0$

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank
24.72.4.ce.1	$24$	$2$	$2$	$4$	$1$
40.48.1.bk.1	$40$	$3$	$3$	$1$	$0$
60.72.4.a.1	$60$	$2$	$2$	$4$	$0$
120.72.2.sg.1	$120$	$2$	$2$	$2$	$?$
120.72.2.wy.1	$120$	$2$	$2$	$2$	$?$
120.72.5.b.1	$120$	$2$	$2$	$5$	$?$
120.72.5.boe.1	$120$	$2$	$2$	$5$	$?$
120.72.5.bsw.1	$120$	$2$	$2$	$5$	$?$

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

Covering curve	Level	Index	Degree	Genus
120.288.17.ihq.1	$120$	$2$	$2$	$17$
120.288.17.ihr.1	$120$	$2$	$2$	$17$
120.288.17.ihy.1	$120$	$2$	$2$	$17$
120.288.17.ihz.1	$120$	$2$	$2$	$17$
120.288.17.jcg.1	$120$	$2$	$2$	$17$
120.288.17.jch.1	$120$	$2$	$2$	$17$
120.288.17.jco.1	$120$	$2$	$2$	$17$
120.288.17.jcp.1	$120$	$2$	$2$	$17$
120.288.17.kgc.1	$120$	$2$	$2$	$17$
120.288.17.kgd.1	$120$	$2$	$2$	$17$
120.288.17.kgk.1	$120$	$2$	$2$	$17$
120.288.17.kgl.1	$120$	$2$	$2$	$17$
120.288.17.kju.1	$120$	$2$	$2$	$17$
120.288.17.kjv.1	$120$	$2$	$2$	$17$
120.288.17.kkc.1	$120$	$2$	$2$	$17$
120.288.17.kkd.1	$120$	$2$	$2$	$17$
240.288.19.to.1	$240$	$2$	$2$	$19$
240.288.19.to.2	$240$	$2$	$2$	$19$
240.288.19.bcg.1	$240$	$2$	$2$	$19$
240.288.19.bcg.2	$240$	$2$	$2$	$19$
240.288.19.blw.1	$240$	$2$	$2$	$19$
240.288.19.blw.2	$240$	$2$	$2$	$19$
240.288.19.bpi.1	$240$	$2$	$2$	$19$
240.288.19.bpi.2	$240$	$2$	$2$	$19$
240.288.19.byg.1	$240$	$2$	$2$	$19$
240.288.19.byg.2	$240$	$2$	$2$	$19$
240.288.19.bzu.1	$240$	$2$	$2$	$19$
240.288.19.bzu.2	$240$	$2$	$2$	$19$
240.288.19.cbi.1	$240$	$2$	$2$	$19$
240.288.19.cbi.2	$240$	$2$	$2$	$19$
240.288.19.cbu.1	$240$	$2$	$2$	$19$
240.288.19.cbu.2	$240$	$2$	$2$	$19$