Modular curve 184.48.0.q.1

• Label: 184.48.0.q.1
• Level: $184$
• Index: $48$
• Genus: $0$
• Cusps: $10$
• $\Q$-cusps: $0$

Invariants

Level:	$184$		$\SL_2$-level:	$8$
Index:	$48$		$\PSL_2$-index:	$48$
Genus:	$0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$
Cusps:	$10$ (none of which are rational)		Cusp widths	$2^{4}\cdot4^{2}\cdot8^{4}$		Cusp orbits	$2^{5}$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
$\Q$-gonality:	$1 \le \gamma \le 2$
$\overline{\Q}$-gonality:	$1$
Rational cusps:	$0$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:

8O0

Level structure

$\GL_2(\Z/184\Z)$-generators:	$\begin{bmatrix}37&36\\146&169\end{bmatrix}$, $\begin{bmatrix}85&28\\42&119\end{bmatrix}$, $\begin{bmatrix}107&148\\50&59\end{bmatrix}$, $\begin{bmatrix}135&24\\168&153\end{bmatrix}$, $\begin{bmatrix}171&84\\128&119\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	184.96.0-184.q.1.1, 184.96.0-184.q.1.2, 184.96.0-184.q.1.3, 184.96.0-184.q.1.4, 184.96.0-184.q.1.5, 184.96.0-184.q.1.6, 184.96.0-184.q.1.7, 184.96.0-184.q.1.8, 184.96.0-184.q.1.9, 184.96.0-184.q.1.10, 184.96.0-184.q.1.11, 184.96.0-184.q.1.12, 184.96.0-184.q.1.13, 184.96.0-184.q.1.14, 184.96.0-184.q.1.15, 184.96.0-184.q.1.16
Cyclic 184-isogeny field degree:	$48$
Cyclic 184-torsion field degree:	$4224$
Full 184-torsion field degree:	$8549376$

Models

This modular curve is isomorphic to $\mathbb{P}^1$.

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
8.24.0.e.1	$8$	$2$	$2$	$0$	$0$
184.24.0.h.2	$184$	$2$	$2$	$0$	$?$
184.24.0.l.1	$184$	$2$	$2$	$0$	$?$

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

Covering curve	Level	Index	Degree	Genus
184.96.1.g.2	$184$	$2$	$2$	$1$
184.96.1.j.2	$184$	$2$	$2$	$1$
184.96.1.w.1	$184$	$2$	$2$	$1$
184.96.1.z.2	$184$	$2$	$2$	$1$
184.96.1.bc.1	$184$	$2$	$2$	$1$
184.96.1.bd.1	$184$	$2$	$2$	$1$
184.96.1.bg.2	$184$	$2$	$2$	$1$
184.96.1.bh.2	$184$	$2$	$2$	$1$