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: | $\begin{bmatrix}1&96\\136&85\end{bmatrix}$, $\begin{bmatrix}133&24\\152&93\end{bmatrix}$, $\begin{bmatrix}151&16\\41&89\end{bmatrix}$, $\begin{bmatrix}153&160\\170&181\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 208.96.1.bg.1 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.j.1.9 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
104.96.0-104.bf.1.7 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
208.96.0-16.j.1.2 | $208$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
208.96.0-104.bf.1.1 | $208$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
208.96.0-208.bk.2.6 | $208$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
208.96.0-208.bk.2.12 | $208$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
208.96.0-208.bl.2.7 | $208$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
208.96.0-208.bl.2.12 | $208$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
208.96.1-208.h.1.11 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
208.96.1-208.h.1.12 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
208.96.1-208.by.2.7 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
208.96.1-208.by.2.14 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
208.96.1-208.bz.2.6 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
208.96.1-208.bz.2.12 | $208$ | $2$ | $2$ | $1$ | $?$ | 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.2.6 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |
208.384.5-208.lm.1.6 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |
208.384.5-208.ln.2.6 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |
208.384.5-208.lq.2.6 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |