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 $2$ are rational) | Cusp widths | $2^{2}\cdot4^{3}\cdot8$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
| 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: | 8J0 |
Level structure
| $\GL_2(\Z/184\Z)$-generators: | $\begin{bmatrix}51&92\\172&127\end{bmatrix}$, $\begin{bmatrix}65&0\\88&45\end{bmatrix}$, $\begin{bmatrix}131&80\\142&7\end{bmatrix}$, $\begin{bmatrix}155&108\\66&69\end{bmatrix}$, $\begin{bmatrix}175&28\\68&43\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 184.24.0.h.1 for the level structure with $-I$) |
| 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 |
|---|---|---|---|---|---|
| 8.24.0-4.b.1.9 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 184.24.0-4.b.1.7 | $184$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 184.96.0-184.a.1.4 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.b.2.21 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.d.1.14 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.e.2.16 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.g.1.15 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.i.2.16 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.k.1.16 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.m.1.15 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.o.2.16 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.q.2.14 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.s.1.12 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.u.1.12 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.w.1.14 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.x.1.16 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.z.1.12 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.ba.1.12 | $184$ | $2$ | $2$ | $0$ |
| 184.96.1-184.m.2.6 | $184$ | $2$ | $2$ | $1$ |
| 184.96.1-184.q.1.4 | $184$ | $2$ | $2$ | $1$ |
| 184.96.1-184.w.1.10 | $184$ | $2$ | $2$ | $1$ |
| 184.96.1-184.x.2.10 | $184$ | $2$ | $2$ | $1$ |
| 184.96.1-184.bc.1.10 | $184$ | $2$ | $2$ | $1$ |
| 184.96.1-184.be.2.11 | $184$ | $2$ | $2$ | $1$ |
| 184.96.1-184.bg.1.13 | $184$ | $2$ | $2$ | $1$ |
| 184.96.1-184.bi.1.13 | $184$ | $2$ | $2$ | $1$ |