Modular curve 280.24.0.ei.1

• Label: 280.24.0.ei.1
• Level: $280$
• Index: $24$
• Genus: $0$
• Cusps: $6$
• $\Q$-cusps: $2$

Invariants

Level:	$280$		$\SL_2$-level:	$8$
Index:	$24$		$\PSL_2$-index:	$24$
Genus:	$0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$
Cusps:	$6$ (of which $2$ are rational)		Cusp widths	$1^{2}\cdot2\cdot4\cdot8^{2}$		Cusp orbits	$1^{2}\cdot2^{2}$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
$\Q$-gonality:	$1$
$\overline{\Q}$-gonality:	$1$
Rational cusps:	$2$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:

8I0

Level structure

$\GL_2(\Z/280\Z)$-generators:	$\begin{bmatrix}20&49\\221&200\end{bmatrix}$, $\begin{bmatrix}100&279\\23&228\end{bmatrix}$, $\begin{bmatrix}118&157\\275&256\end{bmatrix}$, $\begin{bmatrix}170&157\\139&252\end{bmatrix}$, $\begin{bmatrix}206&171\\165&12\end{bmatrix}$, $\begin{bmatrix}256&75\\153&178\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	280.48.0-280.ei.1.1, 280.48.0-280.ei.1.2, 280.48.0-280.ei.1.3, 280.48.0-280.ei.1.4, 280.48.0-280.ei.1.5, 280.48.0-280.ei.1.6, 280.48.0-280.ei.1.7, 280.48.0-280.ei.1.8, 280.48.0-280.ei.1.9, 280.48.0-280.ei.1.10, 280.48.0-280.ei.1.11, 280.48.0-280.ei.1.12, 280.48.0-280.ei.1.13, 280.48.0-280.ei.1.14, 280.48.0-280.ei.1.15, 280.48.0-280.ei.1.16, 280.48.0-280.ei.1.17, 280.48.0-280.ei.1.18, 280.48.0-280.ei.1.19, 280.48.0-280.ei.1.20, 280.48.0-280.ei.1.21, 280.48.0-280.ei.1.22, 280.48.0-280.ei.1.23, 280.48.0-280.ei.1.24, 280.48.0-280.ei.1.25, 280.48.0-280.ei.1.26, 280.48.0-280.ei.1.27, 280.48.0-280.ei.1.28, 280.48.0-280.ei.1.29, 280.48.0-280.ei.1.30, 280.48.0-280.ei.1.31, 280.48.0-280.ei.1.32
Cyclic 280-isogeny field degree:	$48$
Cyclic 280-torsion field degree:	$4608$
Full 280-torsion field degree:	$61931520$

Models

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

Rational points

This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank
$X_0(8)$	$8$	$2$	$2$	$0$	$0$

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

Covering curve	Level	Index	Degree	Genus
280.48.0.cx.2	$280$	$2$	$2$	$0$
280.48.0.da.1	$280$	$2$	$2$	$0$
280.48.0.db.1	$280$	$2$	$2$	$0$
280.48.0.dc.1	$280$	$2$	$2$	$0$
280.48.0.de.2	$280$	$2$	$2$	$0$
280.48.0.dh.1	$280$	$2$	$2$	$0$
280.48.0.dj.1	$280$	$2$	$2$	$0$
280.48.0.dk.1	$280$	$2$	$2$	$0$
280.48.0.do.2	$280$	$2$	$2$	$0$
280.48.0.dr.1	$280$	$2$	$2$	$0$
280.48.0.dt.1	$280$	$2$	$2$	$0$
280.48.0.du.1	$280$	$2$	$2$	$0$
280.48.0.dw.2	$280$	$2$	$2$	$0$
280.48.0.ed.1	$280$	$2$	$2$	$0$
280.48.0.eh.1	$280$	$2$	$2$	$0$
280.48.0.ei.1	$280$	$2$	$2$	$0$
280.120.8.gd.2	$280$	$5$	$5$	$8$
280.144.7.ku.1	$280$	$6$	$6$	$7$
280.192.11.my.1	$280$	$8$	$8$	$11$
280.240.15.ob.1	$280$	$10$	$10$	$15$