Invariants
Level: | $184$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $2^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 48$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8G1 |
Level structure
$\GL_2(\Z/184\Z)$-generators: | $\begin{bmatrix}29&26\\144&35\end{bmatrix}$, $\begin{bmatrix}29&32\\24&43\end{bmatrix}$, $\begin{bmatrix}81&106\\52&57\end{bmatrix}$, $\begin{bmatrix}107&14\\180&125\end{bmatrix}$, $\begin{bmatrix}123&38\\72&81\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 184.96.1-184.bg.1.1, 184.96.1-184.bg.1.2, 184.96.1-184.bg.1.3, 184.96.1-184.bg.1.4, 184.96.1-184.bg.1.5, 184.96.1-184.bg.1.6, 184.96.1-184.bg.1.7, 184.96.1-184.bg.1.8, 184.96.1-184.bg.1.9, 184.96.1-184.bg.1.10, 184.96.1-184.bg.1.11, 184.96.1-184.bg.1.12, 184.96.1-184.bg.1.13, 184.96.1-184.bg.1.14, 184.96.1-184.bg.1.15, 184.96.1-184.bg.1.16 |
Cyclic 184-isogeny field degree: | $48$ |
Cyclic 184-torsion field degree: | $4224$ |
Full 184-torsion field degree: | $8549376$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
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 | Kernel decomposition |
---|---|---|---|---|---|---|
8.24.0.d.1 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
184.24.0.h.1 | $184$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
184.24.1.d.1 | $184$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
184.96.1.a.1 | $184$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
184.96.1.g.1 | $184$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
184.96.1.bj.1 | $184$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
184.96.1.bl.1 | $184$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
184.96.1.bs.1 | $184$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
184.96.1.bu.1 | $184$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
184.96.1.ce.1 | $184$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
184.96.1.cf.2 | $184$ | $2$ | $2$ | $1$ | $?$ | dimension zero |