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: | $16$ (of which $4$ are rational) | Cusp widths | $2^{8}\cdot4^{4}\cdot16^{4}$ | Cusp orbits | $1^{4}\cdot4^{3}$ | ||
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: | 16M1 |
Level structure
$\GL_2(\Z/208\Z)$-generators: | $\begin{bmatrix}93&72\\189&171\end{bmatrix}$, $\begin{bmatrix}121&0\\114&129\end{bmatrix}$, $\begin{bmatrix}157&176\\23&119\end{bmatrix}$, $\begin{bmatrix}193&80\\159&103\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 208.96.1.bg.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 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 |
---|---|---|---|---|---|---|
16.96.0-16.j.1.9 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
104.96.0-104.bf.2.2 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
208.96.0-16.j.1.5 | $208$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
208.96.0-104.bf.2.2 | $208$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
208.96.0-208.bk.1.4 | $208$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
208.96.0-208.bk.1.14 | $208$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
208.96.0-208.bl.1.4 | $208$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
208.96.0-208.bl.1.15 | $208$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
208.96.1-208.h.1.1 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
208.96.1-208.h.1.16 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
208.96.1-208.by.1.4 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
208.96.1-208.by.1.14 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
208.96.1-208.bz.1.4 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
208.96.1-208.bz.1.14 | $208$ | $2$ | $2$ | $1$ | $?$ | 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.1.8 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |
208.384.5-208.lm.1.6 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |
208.384.5-208.ln.1.7 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |
208.384.5-208.lq.1.10 | $208$ | $2$ | $2$ | $5$ | $?$ | not computed |