Invariants
| Level: | $208$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (all of which are rational) | Cusp widths | $2^{2}\cdot4\cdot16$ | Cusp orbits | $1^{4}$ | ||
| 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: | 16A1 |
Level structure
| $\GL_2(\Z/208\Z)$-generators: | $\begin{bmatrix}0&157\\15&170\end{bmatrix}$, $\begin{bmatrix}21&192\\24&77\end{bmatrix}$, $\begin{bmatrix}29&198\\92&75\end{bmatrix}$, $\begin{bmatrix}87&136\\32&119\end{bmatrix}$, $\begin{bmatrix}97&80\\60&173\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 208.24.1.a.1 for the level structure with $-I$) |
| Cyclic 208-isogeny field degree: | $28$ |
| Cyclic 208-torsion field degree: | $1344$ |
| Full 208-torsion field degree: | $13418496$ |
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 |
|---|---|---|---|---|---|---|
| 16.24.0-8.n.1.8 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 104.24.0-8.n.1.12 | $104$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 208.96.1-208.a.2.3 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 208.96.1-208.d.1.1 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 208.96.1-208.g.1.3 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 208.96.1-208.i.1.1 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 208.96.1-208.bq.1.2 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 208.96.1-208.bq.2.1 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 208.96.1-208.br.1.1 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 208.96.1-208.br.2.2 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 208.96.1-208.bs.1.2 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 208.96.1-208.bs.2.1 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 208.96.1-208.bt.1.1 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 208.96.1-208.bt.2.3 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 208.96.1-208.bu.1.1 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 208.96.1-208.bu.2.5 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 208.96.1-208.bv.1.1 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 208.96.1-208.bv.2.3 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 208.96.1-208.bw.1.1 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 208.96.1-208.bw.2.3 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 208.96.1-208.bx.1.1 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 208.96.1-208.bx.2.3 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 208.96.1-208.ch.1.3 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 208.96.1-208.ci.1.6 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 208.96.1-208.cl.1.1 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 208.96.1-208.cm.1.2 | $208$ | $2$ | $2$ | $1$ | $?$ | dimension zero |