Modular curve 112.96.2.b.1

• Label: 112.96.2.b.1
• Level: $112$
• Index: $96$
• Genus: $2$
• Cusps: $14$
• $\Q$-cusps: $2$

Invariants

Level:	$112$		$\SL_2$-level:	$16$		Newform level:	$1$
Index:	$96$		$\PSL_2$-index:	$96$
Genus:	$2 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 14 }{2}$
Cusps:	$14$ (of which $2$ are rational)		Cusp widths	$4^{8}\cdot8^{4}\cdot16^{2}$		Cusp orbits	$1^{2}\cdot2^{4}\cdot4$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
Analytic rank:	not computed
$\Q$-gonality:	$2$
$\overline{\Q}$-gonality:	$2$
Rational cusps:	$2$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:

16I2

Level structure

$\GL_2(\Z/112\Z)$-generators:	$\begin{bmatrix}1&8\\84&1\end{bmatrix}$, $\begin{bmatrix}15&72\\0&15\end{bmatrix}$, $\begin{bmatrix}39&60\\76&43\end{bmatrix}$, $\begin{bmatrix}49&32\\8&45\end{bmatrix}$, $\begin{bmatrix}79&100\\100&17\end{bmatrix}$, $\begin{bmatrix}111&60\\12&63\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	112.192.2-112.b.1.1, 112.192.2-112.b.1.2, 112.192.2-112.b.1.3, 112.192.2-112.b.1.4, 112.192.2-112.b.1.5, 112.192.2-112.b.1.6, 112.192.2-112.b.1.7, 112.192.2-112.b.1.8, 112.192.2-112.b.1.9, 112.192.2-112.b.1.10, 112.192.2-112.b.1.11, 112.192.2-112.b.1.12, 112.192.2-112.b.1.13, 112.192.2-112.b.1.14, 112.192.2-112.b.1.15, 112.192.2-112.b.1.16, 112.192.2-112.b.1.17, 112.192.2-112.b.1.18, 112.192.2-112.b.1.19, 112.192.2-112.b.1.20, 112.192.2-112.b.1.21, 112.192.2-112.b.1.22, 112.192.2-112.b.1.23, 112.192.2-112.b.1.24, 112.192.2-112.b.1.25, 112.192.2-112.b.1.26, 112.192.2-112.b.1.27, 112.192.2-112.b.1.28, 112.192.2-112.b.1.29, 112.192.2-112.b.1.30, 112.192.2-112.b.1.31, 112.192.2-112.b.1.32
Cyclic 112-isogeny field degree:	$32$
Cyclic 112-torsion field degree:	$768$
Full 112-torsion field degree:	$516096$

Rational points

This modular curve has 2 rational cusps but no known non-cuspidal rational points.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank
8.48.0.c.1	$8$	$2$	$2$	$0$	$0$

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

Covering curve	Level	Index	Degree	Genus
112.192.5.c.1	$112$	$2$	$2$	$5$
112.192.5.c.2	$112$	$2$	$2$	$5$
112.192.5.g.1	$112$	$2$	$2$	$5$
112.192.5.g.2	$112$	$2$	$2$	$5$
112.192.5.j.1	$112$	$2$	$2$	$5$
112.192.5.j.2	$112$	$2$	$2$	$5$
112.192.5.l.1	$112$	$2$	$2$	$5$
112.192.5.l.2	$112$	$2$	$2$	$5$
112.192.5.bn.1	$112$	$2$	$2$	$5$
112.192.5.bn.4	$112$	$2$	$2$	$5$
112.192.5.bs.1	$112$	$2$	$2$	$5$
112.192.5.bs.2	$112$	$2$	$2$	$5$
112.192.5.cq.1	$112$	$2$	$2$	$5$
112.192.5.cq.2	$112$	$2$	$2$	$5$
112.192.5.cu.1	$112$	$2$	$2$	$5$
112.192.5.cu.2	$112$	$2$	$2$	$5$
112.192.7.b.1	$112$	$2$	$2$	$7$
112.192.7.d.1	$112$	$2$	$2$	$7$
112.192.7.g.1	$112$	$2$	$2$	$7$
112.192.7.h.1	$112$	$2$	$2$	$7$
112.192.7.p.1	$112$	$2$	$2$	$7$
112.192.7.t.1	$112$	$2$	$2$	$7$
112.192.7.x.1	$112$	$2$	$2$	$7$
112.192.7.z.1	$112$	$2$	$2$	$7$