Modular curve 264.24.0.do.1

• Label: 264.24.0.do.1
• Level: $264$
• Index: $24$
• Genus: $0$
• Cusps: $6$
• $\Q$-cusps: $0$

Invariants

Level:	$264$		$\SL_2$-level:	$8$
Index:	$24$		$\PSL_2$-index:	$24$
Genus:	$0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$
Cusps:	$6$ (none of which are rational)		Cusp widths	$2^{4}\cdot8^{2}$		Cusp orbits	$2^{3}$
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:

8G0

Level structure

$\GL_2(\Z/264\Z)$-generators:	$\begin{bmatrix}43&224\\100&201\end{bmatrix}$, $\begin{bmatrix}109&176\\246&1\end{bmatrix}$, $\begin{bmatrix}181&120\\16&115\end{bmatrix}$, $\begin{bmatrix}197&228\\224&247\end{bmatrix}$, $\begin{bmatrix}251&16\\205&159\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	264.48.0-264.do.1.1, 264.48.0-264.do.1.2, 264.48.0-264.do.1.3, 264.48.0-264.do.1.4, 264.48.0-264.do.1.5, 264.48.0-264.do.1.6, 264.48.0-264.do.1.7, 264.48.0-264.do.1.8, 264.48.0-264.do.1.9, 264.48.0-264.do.1.10, 264.48.0-264.do.1.11, 264.48.0-264.do.1.12, 264.48.0-264.do.1.13, 264.48.0-264.do.1.14, 264.48.0-264.do.1.15, 264.48.0-264.do.1.16
Cyclic 264-isogeny field degree:	$96$
Cyclic 264-torsion field degree:	$7680$
Full 264-torsion field degree:	$40550400$

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
24.12.0.ba.1	$24$	$2$	$2$	$0$	$0$
88.12.0.y.1	$88$	$2$	$2$	$0$	$?$
264.12.0.s.1	$264$	$2$	$2$	$0$	$?$

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

Covering curve	Level	Index	Degree	Genus
264.72.4.mk.1	$264$	$3$	$3$	$4$
264.96.3.nm.1	$264$	$4$	$4$	$3$
264.288.19.bcd.1	$264$	$12$	$12$	$19$