Invariants
Level: | $208$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $192$ | ||||
Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
Cusps: | $24$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{12}\cdot16^{4}$ | Cusp orbits | $2^{6}\cdot4^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16O5 |
Level structure
$\GL_2(\Z/208\Z)$-generators: | $\begin{bmatrix}15&20\\0&95\end{bmatrix}$, $\begin{bmatrix}49&92\\60&47\end{bmatrix}$, $\begin{bmatrix}63&132\\80&171\end{bmatrix}$, $\begin{bmatrix}127&108\\100&201\end{bmatrix}$, $\begin{bmatrix}207&4\\204&23\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 208.384.5-208.fs.1.1, 208.384.5-208.fs.1.2, 208.384.5-208.fs.1.3, 208.384.5-208.fs.1.4, 208.384.5-208.fs.1.5, 208.384.5-208.fs.1.6, 208.384.5-208.fs.1.7, 208.384.5-208.fs.1.8, 208.384.5-208.fs.1.9, 208.384.5-208.fs.1.10, 208.384.5-208.fs.1.11, 208.384.5-208.fs.1.12, 208.384.5-208.fs.1.13, 208.384.5-208.fs.1.14, 208.384.5-208.fs.1.15, 208.384.5-208.fs.1.16 |
Cyclic 208-isogeny field degree: | $56$ |
Cyclic 208-torsion field degree: | $1344$ |
Full 208-torsion field degree: | $3354624$ |
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 |
---|---|---|---|---|---|
16.96.2.d.1 | $16$ | $2$ | $2$ | $2$ | $0$ |
104.96.1.x.1 | $104$ | $2$ | $2$ | $1$ | $?$ |
208.96.2.j.1 | $208$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
208.384.13.kb.1 | $208$ | $2$ | $2$ | $13$ |
208.384.13.kd.1 | $208$ | $2$ | $2$ | $13$ |
208.384.13.kl.1 | $208$ | $2$ | $2$ | $13$ |
208.384.13.kn.1 | $208$ | $2$ | $2$ | $13$ |
208.384.13.nb.1 | $208$ | $2$ | $2$ | $13$ |
208.384.13.nd.1 | $208$ | $2$ | $2$ | $13$ |
208.384.13.nf.1 | $208$ | $2$ | $2$ | $13$ |
208.384.13.nh.1 | $208$ | $2$ | $2$ | $13$ |