Invariants
| Level: | $208$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
| Cusps: | $24$ (of which $4$ are rational) | Cusp widths | $4^{16}\cdot16^{8}$ | Cusp orbits | $1^{4}\cdot2^{2}\cdot4^{2}\cdot8$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 5$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 5$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16M5 |
Level structure
| $\GL_2(\Z/208\Z)$-generators: | $\begin{bmatrix}25&192\\17&71\end{bmatrix}$, $\begin{bmatrix}97&16\\118&185\end{bmatrix}$, $\begin{bmatrix}161&48\\95&39\end{bmatrix}$, $\begin{bmatrix}177&64\\44&173\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 208.192.5.lq.1 for the level structure with $-I$) |
| Cyclic 208-isogeny field degree: | $14$ |
| Cyclic 208-torsion field degree: | $672$ |
| Full 208-torsion field degree: | $1677312$ |
Rational points
This modular curve has 4 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 16.192.1-16.m.1.2 | $16$ | $2$ | $2$ | $1$ | $0$ |
| 104.192.1-104.cm.1.1 | $104$ | $2$ | $2$ | $1$ | $?$ |
| 208.192.1-16.m.1.6 | $208$ | $2$ | $2$ | $1$ | $?$ |
| 208.192.1-208.bg.2.1 | $208$ | $2$ | $2$ | $1$ | $?$ |
| 208.192.1-208.bg.2.10 | $208$ | $2$ | $2$ | $1$ | $?$ |
| 208.192.1-104.cm.1.8 | $208$ | $2$ | $2$ | $1$ | $?$ |
| 208.192.3-208.gl.1.1 | $208$ | $2$ | $2$ | $3$ | $?$ |
| 208.192.3-208.gl.1.2 | $208$ | $2$ | $2$ | $3$ | $?$ |
| 208.192.3-208.hd.2.3 | $208$ | $2$ | $2$ | $3$ | $?$ |
| 208.192.3-208.hd.2.13 | $208$ | $2$ | $2$ | $3$ | $?$ |
| 208.192.3-208.he.1.2 | $208$ | $2$ | $2$ | $3$ | $?$ |
| 208.192.3-208.he.1.3 | $208$ | $2$ | $2$ | $3$ | $?$ |
| 208.192.3-208.hf.1.1 | $208$ | $2$ | $2$ | $3$ | $?$ |
| 208.192.3-208.hf.1.2 | $208$ | $2$ | $2$ | $3$ | $?$ |