Modular curve 280.24.0.o.1

• Label: 280.24.0.o.1
• Level: $280$
• Index: $24$
• Genus: $0$
• Cusps: $6$
• $\Q$-cusps: $0$

Invariants

Level:	$280$		$\SL_2$-level:	$4$
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	$4^{6}$		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:

4G0

Level structure

$\GL_2(\Z/280\Z)$-generators:	$\begin{bmatrix}3&16\\130&263\end{bmatrix}$, $\begin{bmatrix}117&66\\266&111\end{bmatrix}$, $\begin{bmatrix}145&142\\248&1\end{bmatrix}$, $\begin{bmatrix}249&16\\124&235\end{bmatrix}$, $\begin{bmatrix}259&186\\78&175\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	280.48.0-280.o.1.1, 280.48.0-280.o.1.2, 280.48.0-280.o.1.3, 280.48.0-280.o.1.4, 280.48.0-280.o.1.5, 280.48.0-280.o.1.6, 280.48.0-280.o.1.7, 280.48.0-280.o.1.8, 280.48.0-280.o.1.9, 280.48.0-280.o.1.10, 280.48.0-280.o.1.11, 280.48.0-280.o.1.12, 280.48.0-280.o.1.13, 280.48.0-280.o.1.14, 280.48.0-280.o.1.15, 280.48.0-280.o.1.16
Cyclic 280-isogeny field degree:	$192$
Cyclic 280-torsion field degree:	$18432$
Full 280-torsion field degree:	$61931520$

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
28.12.0.a.1	$28$	$2$	$2$	$0$	$0$
40.12.0.b.1	$40$	$2$	$2$	$0$	$0$
280.12.0.b.1	$280$	$2$	$2$	$0$	$?$

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

Covering curve	Level	Index	Degree	Genus
280.120.8.v.1	$280$	$5$	$5$	$8$
280.144.7.x.1	$280$	$6$	$6$	$7$
280.192.11.v.1	$280$	$8$	$8$	$11$
280.240.15.v.1	$280$	$10$	$10$	$15$