Invariants
| Level: | $184$ | $\SL_2$-level: | $184$ | Newform level: | $1$ | ||
| Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
| Genus: | $10 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (all of which are rational) | Cusp widths | $1^{2}\cdot4\cdot23^{2}\cdot92$ | Cusp orbits | $1^{6}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 10$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 10$ | ||||||
| Rational cusps: | $6$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 92A10 |
Level structure
| $\GL_2(\Z/184\Z)$-generators: | $\begin{bmatrix}52&59\\1&18\end{bmatrix}$, $\begin{bmatrix}61&148\\156&53\end{bmatrix}$, $\begin{bmatrix}82&161\\51&100\end{bmatrix}$, $\begin{bmatrix}93&146\\56&183\end{bmatrix}$, $\begin{bmatrix}115&72\\4&91\end{bmatrix}$, $\begin{bmatrix}165&124\\66&131\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 92.144.10.c.1 for the level structure with $-I$) |
| Cyclic 184-isogeny field degree: | $2$ |
| Cyclic 184-torsion field degree: | $88$ |
| Full 184-torsion field degree: | $1424896$ |
Rational points
This modular curve has 6 rational cusps but no known non-cuspidal rational points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.12.0-4.c.1.5 | $8$ | $24$ | $24$ | $0$ | $0$ |
| $X_0(23)$ | $23$ | $12$ | $6$ | $2$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.12.0-4.c.1.5 | $8$ | $24$ | $24$ | $0$ | $0$ |