Invariants
| Level: | $184$ | $\SL_2$-level: | $8$ | ||||
| Index: | $96$ | $\PSL_2$-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: | $\begin{bmatrix}19&174\\72&21\end{bmatrix}$, $\begin{bmatrix}67&30\\44&149\end{bmatrix}$, $\begin{bmatrix}103&178\\112&73\end{bmatrix}$, $\begin{bmatrix}123&6\\112&17\end{bmatrix}$, $\begin{bmatrix}179&114\\92&49\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 184.48.0.b.2 for the level structure with $-I$) |
| Cyclic 184-isogeny field degree: | $48$ |
| Cyclic 184-torsion field degree: | $2112$ |
| Full 184-torsion field degree: | $4274688$ |
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 |
|---|---|---|---|---|---|
| $X_{\mathrm{arith}}(4)$ | $4$ | $2$ | $2$ | $0$ | $0$ |
| 184.48.0-4.b.1.3 | $184$ | $2$ | $2$ | $0$ | $?$ |
| 184.48.0-184.h.1.1 | $184$ | $2$ | $2$ | $0$ | $?$ |
| 184.48.0-184.h.1.32 | $184$ | $2$ | $2$ | $0$ | $?$ |
| 184.48.0-184.i.2.3 | $184$ | $2$ | $2$ | $0$ | $?$ |
| 184.48.0-184.i.2.30 | $184$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 184.192.1-184.a.1.3 | $184$ | $2$ | $2$ | $1$ |
| 184.192.1-184.b.2.4 | $184$ | $2$ | $2$ | $1$ |
| 184.192.1-184.e.2.2 | $184$ | $2$ | $2$ | $1$ |
| 184.192.1-184.f.1.1 | $184$ | $2$ | $2$ | $1$ |
| 184.192.1-184.l.1.1 | $184$ | $2$ | $2$ | $1$ |
| 184.192.1-184.m.2.2 | $184$ | $2$ | $2$ | $1$ |
| 184.192.1-184.n.1.1 | $184$ | $2$ | $2$ | $1$ |
| 184.192.1-184.o.2.5 | $184$ | $2$ | $2$ | $1$ |
| 184.192.1-184.p.1.2 | $184$ | $2$ | $2$ | $1$ |
| 184.192.1-184.q.2.7 | $184$ | $2$ | $2$ | $1$ |
| 184.192.1-184.w.2.3 | $184$ | $2$ | $2$ | $1$ |
| 184.192.1-184.x.1.1 | $184$ | $2$ | $2$ | $1$ |
| 184.192.3-184.j.2.11 | $184$ | $2$ | $2$ | $3$ |
| 184.192.3-184.k.2.13 | $184$ | $2$ | $2$ | $3$ |
| 184.192.3-184.m.2.13 | $184$ | $2$ | $2$ | $3$ |
| 184.192.3-184.p.1.11 | $184$ | $2$ | $2$ | $3$ |