Invariants
| Level: | $208$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (none of which are rational) | Cusp widths | $2^{8}\cdot4^{4}\cdot16^{4}$ | Cusp orbits | $2^{6}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16M1 |
Level structure
| $\GL_2(\Z/208\Z)$-generators: | $\begin{bmatrix}125&72\\206&61\end{bmatrix}$, $\begin{bmatrix}133&184\\21&195\end{bmatrix}$, $\begin{bmatrix}173&40\\169&135\end{bmatrix}$, $\begin{bmatrix}185&32\\77&143\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 208.96.1.bf.1 for the level structure with $-I$) |
| Cyclic 208-isogeny field degree: | $28$ |
| Cyclic 208-torsion field degree: | $672$ |
| Full 208-torsion field degree: | $3354624$ |
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 |
|---|---|---|---|---|---|---|
| 16.96.0-16.j.1.2 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 208.96.0-16.j.1.4 | $208$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 104.96.0-104.bf.2.2 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 208.96.0-104.bf.2.8 | $208$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 208.96.0-208.bs.2.6 | $208$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 208.96.0-208.bs.2.9 | $208$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 208.96.0-208.bt.2.6 | $208$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 208.96.0-208.bt.2.9 | $208$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 208.96.1-208.g.1.5 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 208.96.1-208.g.1.6 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 208.96.1-208.bq.2.6 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 208.96.1-208.bq.2.9 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 208.96.1-208.br.1.4 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 208.96.1-208.br.1.9 | $208$ | $2$ | $2$ | $1$ | $?$ | 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 |
|---|---|---|---|---|---|---|
| 208.384.5-208.lk.1.1 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 208.384.5-208.ll.1.3 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 208.384.5-208.lo.2.3 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 208.384.5-208.lp.2.1 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |