Modular curve 88.48.0.s.2

• Label: 88.48.0.s.2
• Level: $88$
• Index: $48$
• Genus: $0$
• Cusps: $10$
• $\Q$-cusps: $0$

Invariants

Level:	$88$		$\SL_2$-level:	$8$
Index:	$48$		$\PSL_2$-index:	$48$
Genus:	$0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$
Cusps:	$10$ (none of which are rational)		Cusp widths	$2^{4}\cdot4^{2}\cdot8^{4}$		Cusp orbits	$2^{3}\cdot4$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
$\Q$-gonality:	$1 \le \gamma \le 2$
$\overline{\Q}$-gonality:	$1$
Rational cusps:	$0$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:

8O0

Level structure

$\GL_2(\Z/88\Z)$-generators:	$\begin{bmatrix}1&0\\70&59\end{bmatrix}$, $\begin{bmatrix}15&64\\8&77\end{bmatrix}$, $\begin{bmatrix}81&56\\56&19\end{bmatrix}$, $\begin{bmatrix}85&76\\30&11\end{bmatrix}$, $\begin{bmatrix}87&52\\48&71\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	88.96.0-88.s.2.1, 88.96.0-88.s.2.2, 88.96.0-88.s.2.3, 88.96.0-88.s.2.4, 88.96.0-88.s.2.5, 88.96.0-88.s.2.6, 88.96.0-88.s.2.7, 88.96.0-88.s.2.8, 88.96.0-88.s.2.9, 88.96.0-88.s.2.10, 88.96.0-88.s.2.11, 88.96.0-88.s.2.12, 88.96.0-88.s.2.13, 88.96.0-88.s.2.14, 88.96.0-88.s.2.15, 88.96.0-88.s.2.16, 264.96.0-88.s.2.1, 264.96.0-88.s.2.2, 264.96.0-88.s.2.3, 264.96.0-88.s.2.4, 264.96.0-88.s.2.5, 264.96.0-88.s.2.6, 264.96.0-88.s.2.7, 264.96.0-88.s.2.8, 264.96.0-88.s.2.9, 264.96.0-88.s.2.10, 264.96.0-88.s.2.11, 264.96.0-88.s.2.12, 264.96.0-88.s.2.13, 264.96.0-88.s.2.14, 264.96.0-88.s.2.15, 264.96.0-88.s.2.16
Cyclic 88-isogeny field degree:	$24$
Cyclic 88-torsion field degree:	$960$
Full 88-torsion field degree:	$422400$

Models

This modular curve is isomorphic to $\mathbb{P}^1$.

Rational points

This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank
8.24.0.d.1	$8$	$2$	$2$	$0$	$0$
88.24.0.h.2	$88$	$2$	$2$	$0$	$?$
88.24.0.m.1	$88$	$2$	$2$	$0$	$?$

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

Covering curve	Level	Index	Degree	Genus
88.96.1.b.1	$88$	$2$	$2$	$1$
88.96.1.c.1	$88$	$2$	$2$	$1$
88.96.1.h.2	$88$	$2$	$2$	$1$
88.96.1.i.2	$88$	$2$	$2$	$1$
88.96.1.bi.2	$88$	$2$	$2$	$1$
88.96.1.bj.2	$88$	$2$	$2$	$1$
88.96.1.bk.1	$88$	$2$	$2$	$1$
88.96.1.bl.1	$88$	$2$	$2$	$1$
264.96.1.is.1	$264$	$2$	$2$	$1$
264.96.1.it.1	$264$	$2$	$2$	$1$
264.96.1.iw.1	$264$	$2$	$2$	$1$
264.96.1.ix.1	$264$	$2$	$2$	$1$
264.96.1.jy.1	$264$	$2$	$2$	$1$
264.96.1.jz.1	$264$	$2$	$2$	$1$
264.96.1.kc.2	$264$	$2$	$2$	$1$
264.96.1.kd.1	$264$	$2$	$2$	$1$
264.144.8.nj.2	$264$	$3$	$3$	$8$
264.192.7.ho.2	$264$	$4$	$4$	$7$