Modular curve 264.48.0.g.1

• Label: 264.48.0.g.1
• Level: $264$
• Index: $48$
• Genus: $0$
• Cusps: $10$
• $\Q$-cusps: $0$

Invariants

Level:	$264$		$\SL_2$-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	$4^{8}\cdot8^{2}$		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:

8N0

Level structure

$\GL_2(\Z/264\Z)$-generators:	$\begin{bmatrix}29&36\\216&221\end{bmatrix}$, $\begin{bmatrix}37&168\\104&241\end{bmatrix}$, $\begin{bmatrix}131&148\\212&27\end{bmatrix}$, $\begin{bmatrix}143&174\\172&223\end{bmatrix}$, $\begin{bmatrix}151&28\\228&97\end{bmatrix}$, $\begin{bmatrix}241&204\\148&97\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	264.96.0-264.g.1.1, 264.96.0-264.g.1.2, 264.96.0-264.g.1.3, 264.96.0-264.g.1.4, 264.96.0-264.g.1.5, 264.96.0-264.g.1.6, 264.96.0-264.g.1.7, 264.96.0-264.g.1.8, 264.96.0-264.g.1.9, 264.96.0-264.g.1.10, 264.96.0-264.g.1.11, 264.96.0-264.g.1.12, 264.96.0-264.g.1.13, 264.96.0-264.g.1.14, 264.96.0-264.g.1.15, 264.96.0-264.g.1.16, 264.96.0-264.g.1.17, 264.96.0-264.g.1.18, 264.96.0-264.g.1.19, 264.96.0-264.g.1.20, 264.96.0-264.g.1.21, 264.96.0-264.g.1.22, 264.96.0-264.g.1.23, 264.96.0-264.g.1.24, 264.96.0-264.g.1.25, 264.96.0-264.g.1.26, 264.96.0-264.g.1.27, 264.96.0-264.g.1.28, 264.96.0-264.g.1.29, 264.96.0-264.g.1.30, 264.96.0-264.g.1.31, 264.96.0-264.g.1.32
Cyclic 264-isogeny field degree:	$96$
Cyclic 264-torsion field degree:	$7680$
Full 264-torsion field degree:	$20275200$

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
12.24.0.c.1	$12$	$2$	$2$	$0$	$0$
88.24.0.h.1	$88$	$2$	$2$	$0$	$?$
264.24.0.t.2	$264$	$2$	$2$	$0$	$?$

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

Covering curve	Level	Index	Degree	Genus
264.96.1.q.1	$264$	$2$	$2$	$1$
264.96.1.bc.2	$264$	$2$	$2$	$1$
264.96.1.dc.2	$264$	$2$	$2$	$1$
264.96.1.de.1	$264$	$2$	$2$	$1$
264.96.1.fu.2	$264$	$2$	$2$	$1$
264.96.1.fw.1	$264$	$2$	$2$	$1$
264.96.1.gk.1	$264$	$2$	$2$	$1$
264.96.1.gm.2	$264$	$2$	$2$	$1$
264.96.1.ig.1	$264$	$2$	$2$	$1$
264.96.1.ii.2	$264$	$2$	$2$	$1$
264.96.1.iw.2	$264$	$2$	$2$	$1$
264.96.1.iy.1	$264$	$2$	$2$	$1$
264.96.1.ko.2	$264$	$2$	$2$	$1$
264.96.1.kq.1	$264$	$2$	$2$	$1$
264.96.1.kw.1	$264$	$2$	$2$	$1$
264.96.1.kx.2	$264$	$2$	$2$	$1$
264.144.8.y.1	$264$	$3$	$3$	$8$
264.192.7.u.1	$264$	$4$	$4$	$7$