Invariants
Level: | $208$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (of which $4$ are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot16^{2}$ | Cusp orbits | $1^{4}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16E1 |
Level structure
$\GL_2(\Z/208\Z)$-generators: | $\begin{bmatrix}9&192\\22&109\end{bmatrix}$, $\begin{bmatrix}13&132\\202&187\end{bmatrix}$, $\begin{bmatrix}93&184\\108&133\end{bmatrix}$, $\begin{bmatrix}133&60\\106&107\end{bmatrix}$, $\begin{bmatrix}169&12\\22&195\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 208.48.1.a.1 for the level structure with $-I$) |
Cyclic 208-isogeny field degree: | $28$ |
Cyclic 208-torsion field degree: | $2688$ |
Full 208-torsion field degree: | $6709248$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
8.48.0-8.i.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
208.48.0-8.i.1.8 | $208$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
208.48.0-208.r.1.8 | $208$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
208.48.0-208.r.1.9 | $208$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
208.48.1-208.c.1.8 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
208.48.1-208.c.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 |
---|---|---|---|---|---|---|
208.192.1-208.e.1.2 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
208.192.1-208.e.2.3 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
208.192.1-208.n.1.3 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
208.192.1-208.n.2.2 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
208.192.3-208.cb.2.1 | $208$ | $2$ | $2$ | $3$ | $?$ | not computed |
208.192.3-208.cd.1.3 | $208$ | $2$ | $2$ | $3$ | $?$ | not computed |
208.192.3-208.cd.2.10 | $208$ | $2$ | $2$ | $3$ | $?$ | not computed |
208.192.3-208.cg.1.12 | $208$ | $2$ | $2$ | $3$ | $?$ | not computed |
208.192.3-208.cg.2.4 | $208$ | $2$ | $2$ | $3$ | $?$ | not computed |
208.192.3-208.ch.1.3 | $208$ | $2$ | $2$ | $3$ | $?$ | not computed |
208.192.3-208.de.2.5 | $208$ | $2$ | $2$ | $3$ | $?$ | not computed |
208.192.3-208.dh.1.6 | $208$ | $2$ | $2$ | $3$ | $?$ | not computed |
208.192.3-208.dh.2.2 | $208$ | $2$ | $2$ | $3$ | $?$ | not computed |
208.192.3-208.dj.1.12 | $208$ | $2$ | $2$ | $3$ | $?$ | not computed |
208.192.3-208.dj.2.5 | $208$ | $2$ | $2$ | $3$ | $?$ | not computed |
208.192.3-208.dk.2.1 | $208$ | $2$ | $2$ | $3$ | $?$ | not computed |