Invariants
Level: | $184$ | $\SL_2$-level: | $8$ | ||||
Index: | $48$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot8^{4}$ | Cusp orbits | $2^{3}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $1 \le \gamma \le 2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8O0 |
Level structure
$\GL_2(\Z/184\Z)$-generators: | $\begin{bmatrix}25&76\\44&153\end{bmatrix}$, $\begin{bmatrix}33&60\\116&51\end{bmatrix}$, $\begin{bmatrix}61&176\\66&113\end{bmatrix}$, $\begin{bmatrix}79&176\\82&143\end{bmatrix}$, $\begin{bmatrix}165&52\\104&171\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 184.96.0-184.o.2.1, 184.96.0-184.o.2.2, 184.96.0-184.o.2.3, 184.96.0-184.o.2.4, 184.96.0-184.o.2.5, 184.96.0-184.o.2.6, 184.96.0-184.o.2.7, 184.96.0-184.o.2.8, 184.96.0-184.o.2.9, 184.96.0-184.o.2.10, 184.96.0-184.o.2.11, 184.96.0-184.o.2.12, 184.96.0-184.o.2.13, 184.96.0-184.o.2.14, 184.96.0-184.o.2.15, 184.96.0-184.o.2.16 |
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 real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
8.24.0.d.1 | $8$ | $2$ | $2$ | $0$ | $0$ |
184.24.0.h.1 | $184$ | $2$ | $2$ | $0$ | $?$ |
184.24.0.l.1 | $184$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
184.96.1.a.1 | $184$ | $2$ | $2$ | $1$ |
184.96.1.d.1 | $184$ | $2$ | $2$ | $1$ |
184.96.1.g.1 | $184$ | $2$ | $2$ | $1$ |
184.96.1.j.1 | $184$ | $2$ | $2$ | $1$ |
184.96.1.ba.1 | $184$ | $2$ | $2$ | $1$ |
184.96.1.bb.1 | $184$ | $2$ | $2$ | $1$ |
184.96.1.bc.1 | $184$ | $2$ | $2$ | $1$ |
184.96.1.bd.1 | $184$ | $2$ | $2$ | $1$ |