Modular curve 240.96.3.sx.1

• Label: 240.96.3.sx.1
• Level: $240$
• Index: $96$
• Genus: $3$
• Cusps: $12$
• $\Q$-cusps: $0$

Invariants

Level:	$240$		$\SL_2$-level:	$16$		Newform level:	$1$
Index:	$96$		$\PSL_2$-index:	$96$
Genus:	$3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$
Cusps:	$12$ (none of which are rational)		Cusp widths	$4^{8}\cdot16^{4}$		Cusp orbits	$2^{4}\cdot4$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
Analytic rank:	not computed
$\Q$-gonality:	$2 \le \gamma \le 4$
$\overline{\Q}$-gonality:	$2 \le \gamma \le 3$
Rational cusps:	$0$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:

16I3

Level structure

$\GL_2(\Z/240\Z)$-generators:	$\begin{bmatrix}79&24\\193&169\end{bmatrix}$, $\begin{bmatrix}139&176\\154&15\end{bmatrix}$, $\begin{bmatrix}149&232\\14&125\end{bmatrix}$, $\begin{bmatrix}167&16\\31&205\end{bmatrix}$, $\begin{bmatrix}223&216\\47&85\end{bmatrix}$, $\begin{bmatrix}233&144\\156&61\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	240.192.3-240.sx.1.1, 240.192.3-240.sx.1.2, 240.192.3-240.sx.1.3, 240.192.3-240.sx.1.4, 240.192.3-240.sx.1.5, 240.192.3-240.sx.1.6, 240.192.3-240.sx.1.7, 240.192.3-240.sx.1.8, 240.192.3-240.sx.1.9, 240.192.3-240.sx.1.10, 240.192.3-240.sx.1.11, 240.192.3-240.sx.1.12, 240.192.3-240.sx.1.13, 240.192.3-240.sx.1.14, 240.192.3-240.sx.1.15, 240.192.3-240.sx.1.16, 240.192.3-240.sx.1.17, 240.192.3-240.sx.1.18, 240.192.3-240.sx.1.19, 240.192.3-240.sx.1.20, 240.192.3-240.sx.1.21, 240.192.3-240.sx.1.22, 240.192.3-240.sx.1.23, 240.192.3-240.sx.1.24
Cyclic 240-isogeny field degree:	$48$
Cyclic 240-torsion field degree:	$3072$
Full 240-torsion field degree:	$5898240$

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
24.48.1.dk.1	$24$	$2$	$2$	$1$	$1$
80.48.2.j.1	$80$	$2$	$2$	$2$	$?$
240.48.0.m.1	$240$	$2$	$2$	$0$	$?$

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

Covering curve	Level	Index	Degree	Genus
240.192.5.bwf.1	$240$	$2$	$2$	$5$
240.192.5.bwf.2	$240$	$2$	$2$	$5$
240.192.5.bwn.1	$240$	$2$	$2$	$5$
240.192.5.bwn.2	$240$	$2$	$2$	$5$
240.192.5.bwq.1	$240$	$2$	$2$	$5$
240.192.5.bwq.2	$240$	$2$	$2$	$5$
240.192.5.bwt.1	$240$	$2$	$2$	$5$
240.192.5.bwt.2	$240$	$2$	$2$	$5$
240.288.19.eos.1	$240$	$3$	$3$	$19$
240.384.21.cvg.1	$240$	$4$	$4$	$21$