Modular curve 180.144.10.bd.1

• Label: 180.144.10.bd.1
• Level: $180$
• Index: $144$
• Genus: $10$
• Cusps: $6$
• $\Q$-cusps: $2$

Invariants

Level:	$180$		$\SL_2$-level:	$36$		Newform level:	$1$
Index:	$144$		$\PSL_2$-index:	$144$
Genus:	$10 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$
Cusps:	$6$ (of which $2$ are rational)		Cusp widths	$12^{3}\cdot36^{3}$		Cusp orbits	$1^{2}\cdot2^{2}$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
Analytic rank:	not computed
$\Q$-gonality:	$3 \le \gamma \le 10$
$\overline{\Q}$-gonality:	$3 \le \gamma \le 10$
Rational cusps:	$2$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:

36J10

Level structure

$\GL_2(\Z/180\Z)$-generators:	$\begin{bmatrix}4&173\\75&92\end{bmatrix}$, $\begin{bmatrix}28&81\\175&56\end{bmatrix}$, $\begin{bmatrix}82&129\\93&82\end{bmatrix}$, $\begin{bmatrix}156&11\\31&20\end{bmatrix}$, $\begin{bmatrix}171&92\\40&89\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	180.288.10-180.bd.1.1, 180.288.10-180.bd.1.2, 180.288.10-180.bd.1.3, 180.288.10-180.bd.1.4, 180.288.10-180.bd.1.5, 180.288.10-180.bd.1.6, 180.288.10-180.bd.1.7, 180.288.10-180.bd.1.8, 180.288.10-180.bd.1.9, 180.288.10-180.bd.1.10, 180.288.10-180.bd.1.11, 180.288.10-180.bd.1.12, 180.288.10-180.bd.1.13, 180.288.10-180.bd.1.14, 180.288.10-180.bd.1.15, 180.288.10-180.bd.1.16
Cyclic 180-isogeny field degree:	$36$
Cyclic 180-torsion field degree:	$1728$
Full 180-torsion field degree:	$1244160$

Rational points

This modular curve has 2 rational cusps but no known non-cuspidal rational points.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank
36.72.5.o.1	$36$	$2$	$2$	$5$	$1$
60.48.2.f.1	$60$	$3$	$3$	$2$	$1$

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

Covering curve	Level	Index	Degree	Genus
180.288.19.ba.1	$180$	$2$	$2$	$19$
180.288.19.cs.1	$180$	$2$	$2$	$19$
180.288.19.dp.1	$180$	$2$	$2$	$19$
180.288.19.ds.1	$180$	$2$	$2$	$19$
180.288.19.ev.1	$180$	$2$	$2$	$19$
180.288.19.ey.1	$180$	$2$	$2$	$19$
180.288.19.fb.1	$180$	$2$	$2$	$19$
180.288.19.fe.1	$180$	$2$	$2$	$19$