Modular curve 120.144.9.jam.2

• Label: 120.144.9.jam.2
• Level: $120$
• Index: $144$
• Genus: $9$
• Cusps: $8$
• $\Q$-cusps: $0$

Invariants

Level:	$120$		$\SL_2$-level:	$30$		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	$6^{4}\cdot30^{4}$		Cusp orbits	$4^{2}$
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:

30K9

Level structure

$\GL_2(\Z/120\Z)$-generators:	$\begin{bmatrix}64&23\\67&100\end{bmatrix}$, $\begin{bmatrix}81&98\\58&51\end{bmatrix}$, $\begin{bmatrix}112&111\\69&104\end{bmatrix}$, $\begin{bmatrix}114&47\\47&9\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	240.288.9-120.jam.2.1, 240.288.9-120.jam.2.2, 240.288.9-120.jam.2.3, 240.288.9-120.jam.2.4, 240.288.9-120.jam.2.5, 240.288.9-120.jam.2.6, 240.288.9-120.jam.2.7, 240.288.9-120.jam.2.8, 240.288.9-120.jam.2.9, 240.288.9-120.jam.2.10, 240.288.9-120.jam.2.11, 240.288.9-120.jam.2.12, 240.288.9-120.jam.2.13, 240.288.9-120.jam.2.14, 240.288.9-120.jam.2.15, 240.288.9-120.jam.2.16
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 $p=11$, and therefore no rational points.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank
60.72.1.fo.2	$60$	$2$	$2$	$1$	$1$
120.72.3.fxc.1	$120$	$2$	$2$	$3$	$?$
120.72.3.gpg.2	$120$	$2$	$2$	$3$	$?$
120.72.5.jb.2	$120$	$2$	$2$	$5$	$?$
120.72.5.ku.1	$120$	$2$	$2$	$5$	$?$
120.72.5.me.1	$120$	$2$	$2$	$5$	$?$
120.72.5.cji.1	$120$	$2$	$2$	$5$	$?$