Modular curve 80.192.7.cj.1

• Label: 80.192.7.cj.1
• Level: $80$
• Index: $192$
• Genus: $7$
• Cusps: $20$
• $\Q$-cusps: $0$

Invariants

Level:	$80$		$\SL_2$-level:	$16$		Newform level:	$1$
Index:	$192$		$\PSL_2$-index:	$192$
Genus:	$7 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 20 }{2}$
Cusps:	$20$ (none of which are rational)		Cusp widths	$8^{16}\cdot16^{4}$		Cusp orbits	$2^{4}\cdot4^{3}$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
Analytic rank:	not computed
$\Q$-gonality:	$2 \le \gamma \le 12$
$\overline{\Q}$-gonality:	$2 \le \gamma \le 7$
Rational cusps:	$0$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:

16B7

Level structure

$\GL_2(\Z/80\Z)$-generators:	$\begin{bmatrix}1&36\\48&75\end{bmatrix}$, $\begin{bmatrix}9&0\\68&63\end{bmatrix}$, $\begin{bmatrix}33&16\\56&39\end{bmatrix}$, $\begin{bmatrix}63&24\\36&27\end{bmatrix}$, $\begin{bmatrix}73&68\\0&41\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	80.384.7-80.cj.1.1, 80.384.7-80.cj.1.2, 80.384.7-80.cj.1.3, 80.384.7-80.cj.1.4, 80.384.7-80.cj.1.5, 80.384.7-80.cj.1.6, 80.384.7-80.cj.1.7, 80.384.7-80.cj.1.8, 80.384.7-80.cj.1.9, 80.384.7-80.cj.1.10, 80.384.7-80.cj.1.11, 80.384.7-80.cj.1.12, 80.384.7-80.cj.1.13, 80.384.7-80.cj.1.14, 80.384.7-80.cj.1.15, 80.384.7-80.cj.1.16, 240.384.7-80.cj.1.1, 240.384.7-80.cj.1.2, 240.384.7-80.cj.1.3, 240.384.7-80.cj.1.4, 240.384.7-80.cj.1.5, 240.384.7-80.cj.1.6, 240.384.7-80.cj.1.7, 240.384.7-80.cj.1.8, 240.384.7-80.cj.1.9, 240.384.7-80.cj.1.10, 240.384.7-80.cj.1.11, 240.384.7-80.cj.1.12, 240.384.7-80.cj.1.13, 240.384.7-80.cj.1.14, 240.384.7-80.cj.1.15, 240.384.7-80.cj.1.16
Cyclic 80-isogeny field degree:	$24$
Cyclic 80-torsion field degree:	$384$
Full 80-torsion field degree:	$61440$

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
16.96.2.c.1	$16$	$2$	$2$	$2$	$0$
40.96.3.be.1	$40$	$2$	$2$	$3$	$0$
80.96.2.f.1	$80$	$2$	$2$	$2$	$?$

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

Covering curve	Level	Index	Degree	Genus
80.384.13.ep.1	$80$	$2$	$2$	$13$
80.384.13.ep.2	$80$	$2$	$2$	$13$
80.384.13.fk.1	$80$	$2$	$2$	$13$
80.384.13.fk.2	$80$	$2$	$2$	$13$
80.384.13.ms.1	$80$	$2$	$2$	$13$
80.384.13.ms.2	$80$	$2$	$2$	$13$
80.384.13.nc.1	$80$	$2$	$2$	$13$
80.384.13.nc.2	$80$	$2$	$2$	$13$
240.384.13.bdy.1	$240$	$2$	$2$	$13$
240.384.13.bdy.2	$240$	$2$	$2$	$13$
240.384.13.beh.1	$240$	$2$	$2$	$13$
240.384.13.beh.2	$240$	$2$	$2$	$13$
240.384.13.cjc.1	$240$	$2$	$2$	$13$
240.384.13.cjc.2	$240$	$2$	$2$	$13$
240.384.13.cjl.1	$240$	$2$	$2$	$13$
240.384.13.cjl.2	$240$	$2$	$2$	$13$