Modular curve 184.96.3.x.1

• Label: 184.96.3.x.1
• Level: $184$
• Index: $96$
• Genus: $3$
• Cusps: $12$
• $\Q$-cusps: $4$

Invariants

Level:	$184$		$\SL_2$-level:	$8$		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:	$12$ (of which $4$ are rational)		Cusp widths	$8^{12}$		Cusp orbits	$1^{4}\cdot2^{2}\cdot4$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
Analytic rank:	not computed
$\Q$-gonality:	$2 \le \gamma \le 3$
$\overline{\Q}$-gonality:	$2 \le \gamma \le 3$
Rational cusps:	$4$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:

8B3

Level structure

$\GL_2(\Z/184\Z)$-generators:	$\begin{bmatrix}7&132\\168&7\end{bmatrix}$, $\begin{bmatrix}7&176\\176&47\end{bmatrix}$, $\begin{bmatrix}25&112\\8&47\end{bmatrix}$, $\begin{bmatrix}55&64\\60&13\end{bmatrix}$, $\begin{bmatrix}119&136\\172&25\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	184.192.3-184.x.1.1, 184.192.3-184.x.1.2, 184.192.3-184.x.1.3, 184.192.3-184.x.1.4, 184.192.3-184.x.1.5, 184.192.3-184.x.1.6, 184.192.3-184.x.1.7, 184.192.3-184.x.1.8, 184.192.3-184.x.1.9, 184.192.3-184.x.1.10, 184.192.3-184.x.1.11, 184.192.3-184.x.1.12
Cyclic 184-isogeny field degree:	$48$
Cyclic 184-torsion field degree:	$2112$
Full 184-torsion field degree:	$4274688$

Rational points

This modular curve has 4 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	$8$	$2$	$2$	$0$	$0$
184.48.1.o.1	$184$	$2$	$2$	$1$	$?$
184.48.2.a.1	$184$	$2$	$2$	$2$	$?$

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

Covering curve	Level	Index	Degree	Genus
184.192.5.ba.1	$184$	$2$	$2$	$5$
184.192.5.ba.2	$184$	$2$	$2$	$5$
184.192.5.bb.1	$184$	$2$	$2$	$5$
184.192.5.bb.2	$184$	$2$	$2$	$5$