Invariants
| Level: | $208$ | $\SL_2$-level: | $16$ | ||||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $1^{2}\cdot2^{3}\cdot16$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16D0 |
Level structure
| $\GL_2(\Z/208\Z)$-generators: | $\begin{bmatrix}0&25\\141&196\end{bmatrix}$, $\begin{bmatrix}67&138\\176&77\end{bmatrix}$, $\begin{bmatrix}85&204\\198&115\end{bmatrix}$, $\begin{bmatrix}118&63\\17&52\end{bmatrix}$, $\begin{bmatrix}180&125\\35&62\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 208.24.0.m.1 for the level structure with $-I$) |
| Cyclic 208-isogeny field degree: | $28$ |
| Cyclic 208-torsion field degree: | $1344$ |
| Full 208-torsion field degree: | $13418496$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.24.0-8.n.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 208.24.0-8.n.1.4 | $208$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 208.96.0-208.f.1.9 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.g.1.6 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.l.1.3 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.n.1.7 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.bb.1.8 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.bc.2.6 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.be.2.6 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.bh.1.5 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.bm.1.2 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.bn.1.2 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.bu.1.4 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.bv.1.6 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.ca.1.1 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.cb.1.1 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.ce.1.3 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.cf.1.5 | $208$ | $2$ | $2$ | $0$ |
| 208.96.1-208.bg.1.11 | $208$ | $2$ | $2$ | $1$ |
| 208.96.1-208.bh.2.10 | $208$ | $2$ | $2$ | $1$ |
| 208.96.1-208.bk.1.14 | $208$ | $2$ | $2$ | $1$ |
| 208.96.1-208.bl.1.23 | $208$ | $2$ | $2$ | $1$ |
| 208.96.1-208.bs.1.9 | $208$ | $2$ | $2$ | $1$ |
| 208.96.1-208.bt.2.9 | $208$ | $2$ | $2$ | $1$ |
| 208.96.1-208.ca.1.13 | $208$ | $2$ | $2$ | $1$ |
| 208.96.1-208.cb.1.13 | $208$ | $2$ | $2$ | $1$ |