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: | $\begin{bmatrix}57&112\\2&23\end{bmatrix}$, $\begin{bmatrix}95&142\\160&157\end{bmatrix}$, $\begin{bmatrix}125&98\\12&171\end{bmatrix}$, $\begin{bmatrix}162&89\\11&152\end{bmatrix}$, $\begin{bmatrix}174&141\\169&42\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 208.24.0.n.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 |
|---|---|---|---|---|---|
| 16.24.0-8.n.1.8 | $16$ | $2$ | $2$ | $0$ | $0$ |
| 104.24.0-8.n.1.7 | $104$ | $2$ | $2$ | $0$ | $?$ |
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.2.10 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.h.1.9 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.m.1.17 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.n.1.10 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.ba.1.1 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.bd.2.9 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.bf.2.2 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.bg.1.11 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.bo.2.1 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.bp.2.3 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.bw.2.5 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.bx.1.1 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.cc.2.1 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.cd.2.3 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.cg.2.5 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.ch.1.1 | $208$ | $2$ | $2$ | $0$ |
| 208.96.1-208.bi.2.1 | $208$ | $2$ | $2$ | $1$ |
| 208.96.1-208.bj.2.3 | $208$ | $2$ | $2$ | $1$ |
| 208.96.1-208.bm.2.2 | $208$ | $2$ | $2$ | $1$ |
| 208.96.1-208.bn.2.1 | $208$ | $2$ | $2$ | $1$ |
| 208.96.1-208.bu.2.1 | $208$ | $2$ | $2$ | $1$ |
| 208.96.1-208.bv.2.3 | $208$ | $2$ | $2$ | $1$ |
| 208.96.1-208.cc.2.2 | $208$ | $2$ | $2$ | $1$ |
| 208.96.1-208.cd.2.1 | $208$ | $2$ | $2$ | $1$ |