Modular curve 120.144.9.dzc.1

• Label: 120.144.9.dzc.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	$2^{4}$
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:	$\begin{bmatrix}23&0\\24&23\end{bmatrix}$, $\begin{bmatrix}37&48\\12&25\end{bmatrix}$, $\begin{bmatrix}51&67\\52&53\end{bmatrix}$, $\begin{bmatrix}79&20\\56&107\end{bmatrix}$, $\begin{bmatrix}107&52\\48&7\end{bmatrix}$, $\begin{bmatrix}119&116\\104&19\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	120.288.9-120.dzc.1.1, 120.288.9-120.dzc.1.2, 120.288.9-120.dzc.1.3, 120.288.9-120.dzc.1.4, 120.288.9-120.dzc.1.5, 120.288.9-120.dzc.1.6, 120.288.9-120.dzc.1.7, 120.288.9-120.dzc.1.8, 120.288.9-120.dzc.1.9, 120.288.9-120.dzc.1.10, 120.288.9-120.dzc.1.11, 120.288.9-120.dzc.1.12, 120.288.9-120.dzc.1.13, 120.288.9-120.dzc.1.14, 120.288.9-120.dzc.1.15, 120.288.9-120.dzc.1.16, 240.288.9-120.dzc.1.1, 240.288.9-120.dzc.1.2, 240.288.9-120.dzc.1.3, 240.288.9-120.dzc.1.4, 240.288.9-120.dzc.1.5, 240.288.9-120.dzc.1.6, 240.288.9-120.dzc.1.7, 240.288.9-120.dzc.1.8, 240.288.9-120.dzc.1.9, 240.288.9-120.dzc.1.10, 240.288.9-120.dzc.1.11, 240.288.9-120.dzc.1.12, 240.288.9-120.dzc.1.13, 240.288.9-120.dzc.1.14, 240.288.9-120.dzc.1.15, 240.288.9-120.dzc.1.16
Cyclic 120-isogeny field degree:	$48$
Cyclic 120-torsion field degree:	$1536$
Full 120-torsion field degree:	$245760$

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
$X_{\mathrm{ns}}^+(3)$	$3$	$48$	$48$	$0$	$0$
40.48.1.ea.1	$40$	$3$	$3$	$1$	$0$

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank
12.72.4.p.1	$12$	$2$	$2$	$4$	$0$
40.48.1.ea.1	$40$	$3$	$3$	$1$	$0$
120.72.2.wi.1	$120$	$2$	$2$	$2$	$?$
120.72.2.wj.1	$120$	$2$	$2$	$2$	$?$
120.72.4.hx.1	$120$	$2$	$2$	$4$	$?$
120.72.5.bx.1	$120$	$2$	$2$	$5$	$?$
120.72.5.bsg.1	$120$	$2$	$2$	$5$	$?$
120.72.5.bsh.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.urk.1	$120$	$2$	$2$	$17$
120.288.17.urs.1	$120$	$2$	$2$	$17$
120.288.17.utw.1	$120$	$2$	$2$	$17$
120.288.17.uue.1	$120$	$2$	$2$	$17$
120.288.17.vfs.1	$120$	$2$	$2$	$17$
120.288.17.vge.1	$120$	$2$	$2$	$17$
120.288.17.viq.1	$120$	$2$	$2$	$17$
120.288.17.viy.1	$120$	$2$	$2$	$17$
120.288.17.whg.1	$120$	$2$	$2$	$17$
120.288.17.who.1	$120$	$2$	$2$	$17$
120.288.17.wjs.1	$120$	$2$	$2$	$17$
120.288.17.wka.1	$120$	$2$	$2$	$17$
120.288.17.wrc.1	$120$	$2$	$2$	$17$
120.288.17.wrk.1	$120$	$2$	$2$	$17$
120.288.17.wto.1	$120$	$2$	$2$	$17$
120.288.17.wtw.1	$120$	$2$	$2$	$17$
240.288.19.eww.1	$240$	$2$	$2$	$19$
240.288.19.exy.1	$240$	$2$	$2$	$19$
240.288.19.eyg.1	$240$	$2$	$2$	$19$
240.288.19.eza.1	$240$	$2$	$2$	$19$
240.288.19.gkk.1	$240$	$2$	$2$	$19$
240.288.19.gkw.1	$240$	$2$	$2$	$19$
240.288.19.glu.1	$240$	$2$	$2$	$19$
240.288.19.gly.1	$240$	$2$	$2$	$19$
240.288.19.hqf.1	$240$	$2$	$2$	$19$
240.288.19.hqj.1	$240$	$2$	$2$	$19$
240.288.19.hrh.1	$240$	$2$	$2$	$19$
240.288.19.hrt.1	$240$	$2$	$2$	$19$
240.288.19.igl.1	$240$	$2$	$2$	$19$
240.288.19.ihf.1	$240$	$2$	$2$	$19$
240.288.19.ihn.1	$240$	$2$	$2$	$19$
240.288.19.iip.1	$240$	$2$	$2$	$19$