Invariants
| Level: | $184$ | $\SL_2$-level: | $8$ | ||||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $4$ are rational) | Cusp widths | $2^{4}\cdot8^{2}$ | Cusp orbits | $1^{4}\cdot2$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8G0 |
Level structure
| $\GL_2(\Z/184\Z)$-generators: | $\begin{bmatrix}77&80\\182&13\end{bmatrix}$, $\begin{bmatrix}83&16\\156&115\end{bmatrix}$, $\begin{bmatrix}107&104\\132&29\end{bmatrix}$, $\begin{bmatrix}127&96\\40&133\end{bmatrix}$, $\begin{bmatrix}175&64\\32&89\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 8.24.0.i.1 for the level structure with $-I$) |
| Cyclic 184-isogeny field degree: | $24$ |
| Cyclic 184-torsion field degree: | $2112$ |
| 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, including 122 stored non-cuspidal points.
Maps to other modular curves
$j$-invariant map of degree 24 to the modular curve $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle \frac{x^{24}(x^{8}+240x^{6}y^{2}+2144x^{4}y^{4}+3840x^{2}y^{6}+256y^{8})^{3}}{y^{2}x^{26}(x-2y)^{8}(x+2y)^{8}(x^{2}+4y^{2})^{2}}$ |
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 184.24.0-4.b.1.6 | $184$ | $2$ | $2$ | $0$ | $?$ |
| 184.24.0-4.b.1.9 | $184$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 184.96.0-8.j.1.3 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-8.j.2.5 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-8.k.1.5 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-8.k.1.6 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-8.k.2.5 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-8.k.2.7 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-8.l.1.3 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-8.l.2.5 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.z.1.9 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.z.2.9 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.ba.1.9 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.ba.1.13 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.ba.2.9 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.ba.2.13 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.bb.1.9 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.bb.2.9 | $184$ | $2$ | $2$ | $0$ |
| 184.96.1-8.h.1.5 | $184$ | $2$ | $2$ | $1$ |
| 184.96.1-8.h.1.9 | $184$ | $2$ | $2$ | $1$ |
| 184.96.1-8.p.1.1 | $184$ | $2$ | $2$ | $1$ |
| 184.96.1-8.p.1.5 | $184$ | $2$ | $2$ | $1$ |
| 184.96.1-184.bu.1.6 | $184$ | $2$ | $2$ | $1$ |
| 184.96.1-184.bu.1.9 | $184$ | $2$ | $2$ | $1$ |
| 184.96.1-184.bv.1.1 | $184$ | $2$ | $2$ | $1$ |
| 184.96.1-184.bv.1.9 | $184$ | $2$ | $2$ | $1$ |