Properties

Label 184.48.0.n.2
Level $184$
Index $48$
Genus $0$
Cusps $10$
$\Q$-cusps $2$

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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: $10$ (of which $2$ are rational) Cusp widths $4^{8}\cdot8^{2}$ Cusp orbits $1^{2}\cdot2^{2}\cdot4$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
$\Q$-gonality: $1$
$\overline{\Q}$-gonality: $1$
Rational cusps: $2$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 8N0

Level structure

$\GL_2(\Z/184\Z)$-generators: $\begin{bmatrix}91&88\\124&175\end{bmatrix}$, $\begin{bmatrix}95&102\\156&43\end{bmatrix}$, $\begin{bmatrix}103&142\\60&181\end{bmatrix}$, $\begin{bmatrix}157&32\\136&121\end{bmatrix}$, $\begin{bmatrix}159&58\\160&67\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 184.96.0-184.n.2.1, 184.96.0-184.n.2.2, 184.96.0-184.n.2.3, 184.96.0-184.n.2.4, 184.96.0-184.n.2.5, 184.96.0-184.n.2.6, 184.96.0-184.n.2.7, 184.96.0-184.n.2.8, 184.96.0-184.n.2.9, 184.96.0-184.n.2.10, 184.96.0-184.n.2.11, 184.96.0-184.n.2.12, 184.96.0-184.n.2.13, 184.96.0-184.n.2.14, 184.96.0-184.n.2.15, 184.96.0-184.n.2.16
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 infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.

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.e.1 $184$ $2$ $2$ $0$ $?$
184.24.0.i.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.u.2 $184$ $2$ $2$ $1$
184.96.1.z.2 $184$ $2$ $2$ $1$
184.96.1.bm.1 $184$ $2$ $2$ $1$
184.96.1.bo.1 $184$ $2$ $2$ $1$
184.96.1.bx.1 $184$ $2$ $2$ $1$
184.96.1.bz.2 $184$ $2$ $2$ $1$
184.96.1.cg.1 $184$ $2$ $2$ $1$
184.96.1.ch.1 $184$ $2$ $2$ $1$