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 | $2^{4}\cdot4^{2}$ | ||
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: | $\begin{bmatrix}67&168\\64&43\end{bmatrix}$, $\begin{bmatrix}85&136\\200&143\end{bmatrix}$, $\begin{bmatrix}137&0\\191&15\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 208.96.1.y.2 for the level structure with $-I$) |
Cyclic 208-isogeny field degree: | $28$ |
Cyclic 208-torsion field degree: | $1344$ |
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.e.1.8 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
104.96.0-104.be.2.5 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
208.96.0-16.e.1.6 | $208$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
208.96.0-104.be.2.6 | $208$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
208.96.0-208.bs.1.6 | $208$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
208.96.0-208.bs.1.12 | $208$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
208.96.0-208.bt.2.2 | $208$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
208.96.0-208.bt.2.16 | $208$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
208.96.1-208.f.1.8 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
208.96.1-208.f.1.15 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
208.96.1-208.by.2.6 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
208.96.1-208.by.2.12 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
208.96.1-208.bz.1.9 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
208.96.1-208.bz.1.16 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |