Modular curve 72.216.10.bl.1

• Label: 72.216.10.bl.1
• Level: $72$
• Index: $216$
• Genus: $10$
• Cusps: $18$
• $\Q$-cusps: $2$

Invariants

Level:	$72$		$\SL_2$-level:	$18$		Newform level:	$1$
Index:	$216$		$\PSL_2$-index:	$216$
Genus:	$10 = 1 + \frac{ 216 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 18 }{2}$
Cusps:	$18$ (of which $2$ are rational)		Cusp widths	$6^{9}\cdot18^{9}$		Cusp orbits	$1^{2}\cdot2^{4}\cdot4^{2}$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
Analytic rank:	not computed
$\Q$-gonality:	$4 \le \gamma \le 10$
$\overline{\Q}$-gonality:	$4 \le \gamma \le 10$
Rational cusps:	$2$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:

18E10

Level structure

$\GL_2(\Z/72\Z)$-generators:	$\begin{bmatrix}5&54\\66&65\end{bmatrix}$, $\begin{bmatrix}37&36\\18&31\end{bmatrix}$, $\begin{bmatrix}53&33\\16&13\end{bmatrix}$, $\begin{bmatrix}61&63\\54&19\end{bmatrix}$, $\begin{bmatrix}71&51\\46&13\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	72.432.10-72.bl.1.1, 72.432.10-72.bl.1.2, 72.432.10-72.bl.1.3, 72.432.10-72.bl.1.4, 72.432.10-72.bl.1.5, 72.432.10-72.bl.1.6, 72.432.10-72.bl.1.7, 72.432.10-72.bl.1.8, 72.432.10-72.bl.1.9, 72.432.10-72.bl.1.10, 72.432.10-72.bl.1.11, 72.432.10-72.bl.1.12, 72.432.10-72.bl.1.13, 72.432.10-72.bl.1.14, 72.432.10-72.bl.1.15, 72.432.10-72.bl.1.16
Cyclic 72-isogeny field degree:	$4$
Cyclic 72-torsion field degree:	$96$
Full 72-torsion field degree:	$27648$

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
18.108.4.c.1	$18$	$2$	$2$	$4$	$0$
24.72.1.bn.1	$24$	$3$	$3$	$1$	$0$
72.72.1.g.1	$72$	$3$	$3$	$1$	$?$
72.72.4.q.1	$72$	$3$	$3$	$4$	$?$
72.72.4.r.1	$72$	$3$	$3$	$4$	$?$
72.72.4.z.1	$72$	$3$	$3$	$4$	$?$