Modular curve 88.240.16.h.1

• Label: 88.240.16.h.1
• Level: $88$
• Index: $240$
• Genus: $16$
• Cusps: $10$
• $\Q$-cusps: $0$

Invariants

Level:	$88$		$\SL_2$-level:	$44$		Newform level:	$1$
Index:	$240$		$\PSL_2$-index:	$240$
Genus:	$16 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$
Cusps:	$10$ (none of which are rational)		Cusp widths	$4^{5}\cdot44^{5}$		Cusp orbits	$5^{2}$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
Analytic rank:	not computed
$\Q$-gonality:	$4 \le \gamma \le 30$
$\overline{\Q}$-gonality:	$4 \le \gamma \le 16$
Rational cusps:	$0$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:

44A16

Level structure

$\GL_2(\Z/88\Z)$-generators:	$\begin{bmatrix}54&57\\25&22\end{bmatrix}$, $\begin{bmatrix}55&83\\41&68\end{bmatrix}$, $\begin{bmatrix}75&39\\11&14\end{bmatrix}$, $\begin{bmatrix}87&67\\8&17\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	88.480.16-88.h.1.1, 88.480.16-88.h.1.2, 88.480.16-88.h.1.3, 88.480.16-88.h.1.4, 88.480.16-88.h.1.5, 88.480.16-88.h.1.6, 88.480.16-88.h.1.7, 88.480.16-88.h.1.8, 264.480.16-88.h.1.1, 264.480.16-88.h.1.2, 264.480.16-88.h.1.3, 264.480.16-88.h.1.4, 264.480.16-88.h.1.5, 264.480.16-88.h.1.6, 264.480.16-88.h.1.7, 264.480.16-88.h.1.8
Cyclic 88-isogeny field degree:	$12$
Cyclic 88-torsion field degree:	$480$
Full 88-torsion field degree:	$84480$

Rational points

This modular curve has no $\Q_p$ points for $p=13,17$, and therefore no rational points.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank
44.120.6.b.1	$44$	$2$	$2$	$6$	$5$
88.48.4.b.2	$88$	$5$	$5$	$4$	$?$