Modular curve 280.192.5.gz.1

• Label: 280.192.5.gz.1
• Level: $280$
• Index: $192$
• Genus: $5$
• Cusps: $24$
• $\Q$-cusps: $0$

Invariants

Level:	$280$		$\SL_2$-level:	$8$		Newform level:	$1$
Index:	$192$		$\PSL_2$-index:	$192$
Genus:	$5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$
Cusps:	$24$ (none of which are rational)		Cusp widths	$8^{24}$		Cusp orbits	$2^{4}\cdot4^{2}\cdot8$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
Analytic rank:	not computed
$\Q$-gonality:	$3 \le \gamma \le 8$
$\overline{\Q}$-gonality:	$3 \le \gamma \le 5$
Rational cusps:	$0$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:

8A5

Level structure

$\GL_2(\Z/280\Z)$-generators:	$\begin{bmatrix}63&20\\64&151\end{bmatrix}$, $\begin{bmatrix}79&184\\56&139\end{bmatrix}$, $\begin{bmatrix}115&196\\92&179\end{bmatrix}$, $\begin{bmatrix}163&202\\52&101\end{bmatrix}$, $\begin{bmatrix}277&174\\92&91\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	280.384.5-280.gz.1.1, 280.384.5-280.gz.1.2, 280.384.5-280.gz.1.3, 280.384.5-280.gz.1.4, 280.384.5-280.gz.1.5, 280.384.5-280.gz.1.6, 280.384.5-280.gz.1.7, 280.384.5-280.gz.1.8, 280.384.5-280.gz.1.9, 280.384.5-280.gz.1.10, 280.384.5-280.gz.1.11, 280.384.5-280.gz.1.12, 280.384.5-280.gz.1.13, 280.384.5-280.gz.1.14, 280.384.5-280.gz.1.15, 280.384.5-280.gz.1.16
Cyclic 280-isogeny field degree:	$96$
Cyclic 280-torsion field degree:	$4608$
Full 280-torsion field degree:	$7741440$

Rational points

This modular curve has no $\Q_p$ points for $p=29$, and therefore no rational points.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank
40.96.3.be.1	$40$	$2$	$2$	$3$	$0$
56.96.1.w.2	$56$	$2$	$2$	$1$	$1$
280.96.1.bl.2	$280$	$2$	$2$	$1$	$?$
280.96.1.cy.1	$280$	$2$	$2$	$1$	$?$
280.96.3.bj.1	$280$	$2$	$2$	$3$	$?$
280.96.3.bl.2	$280$	$2$	$2$	$3$	$?$
280.96.3.bu.1	$280$	$2$	$2$	$3$	$?$