Invariants
| Level: | $208$ | $\SL_2$-level: | $208$ | Newform level: | $1$ | ||
| Index: | $336$ | $\PSL_2$-index: | $168$ | ||||
| Genus: | $11 = 1 + \frac{ 168 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (all of which are rational) | Cusp widths | $1^{2}\cdot2\cdot8\cdot13^{2}\cdot26\cdot104$ | Cusp orbits | $1^{8}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 11$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 11$ | ||||||
| Rational cusps: | $8$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 104D11 |
Level structure
| $\GL_2(\Z/208\Z)$-generators: | $\begin{bmatrix}50&39\\185&112\end{bmatrix}$, $\begin{bmatrix}65&196\\198&167\end{bmatrix}$, $\begin{bmatrix}76&95\\79&92\end{bmatrix}$, $\begin{bmatrix}101&60\\122&143\end{bmatrix}$, $\begin{bmatrix}144&37\\35&146\end{bmatrix}$, $\begin{bmatrix}150&89\\201&38\end{bmatrix}$, $\begin{bmatrix}184&137\\127&194\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 104.168.11.bx.1 for the level structure with $-I$) |
| Cyclic 208-isogeny field degree: | $2$ |
| Cyclic 208-torsion field degree: | $96$ |
| Full 208-torsion field degree: | $1916928$ |
Rational points
This modular curve has 8 rational cusps but no known non-cuspidal rational points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 16.24.0-8.n.1.8 | $16$ | $14$ | $14$ | $0$ | $0$ |
| $X_0(13)$ | $13$ | $24$ | $12$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 16.24.0-8.n.1.8 | $16$ | $14$ | $14$ | $0$ | $0$ |