Invariants
Level: | $208$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot16^{2}$ | Cusp orbits | $2^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 48$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16G1 |
Level structure
$\GL_2(\Z/208\Z)$-generators: | $\begin{bmatrix}45&144\\18&207\end{bmatrix}$, $\begin{bmatrix}95&128\\40&95\end{bmatrix}$, $\begin{bmatrix}175&204\\158&57\end{bmatrix}$, $\begin{bmatrix}183&44\\150&81\end{bmatrix}$, $\begin{bmatrix}202&115\\89&40\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 208.96.1-208.cc.1.1, 208.96.1-208.cc.1.2, 208.96.1-208.cc.1.3, 208.96.1-208.cc.1.4, 208.96.1-208.cc.1.5, 208.96.1-208.cc.1.6, 208.96.1-208.cc.1.7, 208.96.1-208.cc.1.8, 208.96.1-208.cc.1.9, 208.96.1-208.cc.1.10, 208.96.1-208.cc.1.11, 208.96.1-208.cc.1.12, 208.96.1-208.cc.1.13, 208.96.1-208.cc.1.14, 208.96.1-208.cc.1.15, 208.96.1-208.cc.1.16 |
Cyclic 208-isogeny field degree: | $28$ |
Cyclic 208-torsion field degree: | $2688$ |
Full 208-torsion field degree: | $13418496$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
8.24.0.ba.1 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
208.24.0.n.2 | $208$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
208.24.1.b.1 | $208$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
208.96.1.g.1 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
208.96.1.ba.2 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
208.96.1.bn.1 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
208.96.1.bx.1 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
208.96.1.dm.2 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
208.96.1.ea.1 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
208.96.1.ee.1 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
208.96.1.eo.1 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |