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: | $\begin{bmatrix}7&132\\180&71\end{bmatrix}$, $\begin{bmatrix}25&48\\86&37\end{bmatrix}$, $\begin{bmatrix}67&120\\18&21\end{bmatrix}$, $\begin{bmatrix}113&0\\136&127\end{bmatrix}$, $\begin{bmatrix}171&148\\124&171\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 184.24.0.h.2 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.1.7 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 184.24.0-4.b.1.2 | $184$ | $2$ | $2$ | $0$ | $?$ |
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.1.18 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.b.1.14 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.d.1.11 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.e.1.11 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.g.2.10 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.i.1.15 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.k.2.12 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.m.2.12 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.o.1.10 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.q.1.10 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.s.2.13 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.u.2.9 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.w.1.12 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.x.2.12 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.z.2.10 | $184$ | $2$ | $2$ | $0$ |
| 184.96.0-184.ba.2.14 | $184$ | $2$ | $2$ | $0$ |
| 184.96.1-184.m.1.9 | $184$ | $2$ | $2$ | $1$ |
| 184.96.1-184.q.2.1 | $184$ | $2$ | $2$ | $1$ |
| 184.96.1-184.w.1.1 | $184$ | $2$ | $2$ | $1$ |
| 184.96.1-184.x.1.5 | $184$ | $2$ | $2$ | $1$ |
| 184.96.1-184.bc.2.3 | $184$ | $2$ | $2$ | $1$ |
| 184.96.1-184.be.1.13 | $184$ | $2$ | $2$ | $1$ |
| 184.96.1-184.bg.2.6 | $184$ | $2$ | $2$ | $1$ |
| 184.96.1-184.bi.2.2 | $184$ | $2$ | $2$ | $1$ |