Invariants
| Level: | $208$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
| Cusps: | $24$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{12}\cdot16^{4}$ | Cusp orbits | $2^{2}\cdot4^{5}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16O5 |
Level structure
| $\GL_2(\Z/208\Z)$-generators: | $\begin{bmatrix}25&24\\56&63\end{bmatrix}$, $\begin{bmatrix}57&52\\144&29\end{bmatrix}$, $\begin{bmatrix}127&4\\116&185\end{bmatrix}$, $\begin{bmatrix}135&144\\40&157\end{bmatrix}$, $\begin{bmatrix}177&112\\152&85\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | 208.384.5-208.f.1.1, 208.384.5-208.f.1.2, 208.384.5-208.f.1.3, 208.384.5-208.f.1.4, 208.384.5-208.f.1.5, 208.384.5-208.f.1.6, 208.384.5-208.f.1.7, 208.384.5-208.f.1.8, 208.384.5-208.f.1.9, 208.384.5-208.f.1.10, 208.384.5-208.f.1.11, 208.384.5-208.f.1.12, 208.384.5-208.f.1.13, 208.384.5-208.f.1.14, 208.384.5-208.f.1.15, 208.384.5-208.f.1.16 |
| Cyclic 208-isogeny field degree: | $56$ |
| Cyclic 208-torsion field degree: | $2688$ |
| Full 208-torsion field degree: | $3354624$ |
Rational points
This modular curve has no real points and no $\Q_p$ points for $p=3$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 16.96.2.a.1 | $16$ | $2$ | $2$ | $2$ | $0$ |
| 104.96.1.x.1 | $104$ | $2$ | $2$ | $1$ | $?$ |
| 208.96.2.c.1 | $208$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 208.384.13.b.1 | $208$ | $2$ | $2$ | $13$ |
| 208.384.13.d.2 | $208$ | $2$ | $2$ | $13$ |
| 208.384.13.i.2 | $208$ | $2$ | $2$ | $13$ |
| 208.384.13.k.2 | $208$ | $2$ | $2$ | $13$ |
| 208.384.13.cw.2 | $208$ | $2$ | $2$ | $13$ |
| 208.384.13.cy.2 | $208$ | $2$ | $2$ | $13$ |
| 208.384.13.dd.1 | $208$ | $2$ | $2$ | $13$ |
| 208.384.13.df.2 | $208$ | $2$ | $2$ | $13$ |