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 | $1^{4}\cdot4\cdot16$ | 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: | 16C0 |
Level structure
| $\GL_2(\Z/208\Z)$-generators: | $\begin{bmatrix}41&42\\34&137\end{bmatrix}$, $\begin{bmatrix}143&42\\92&189\end{bmatrix}$, $\begin{bmatrix}157&198\\92&47\end{bmatrix}$, $\begin{bmatrix}162&93\\15&24\end{bmatrix}$, $\begin{bmatrix}164&37\\11&126\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 208.24.0.p.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.1.2 | $104$ | $2$ | $2$ | $0$ | $?$ |
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.bs.1.1 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.bs.2.3 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.bt.1.1 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.bt.2.3 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.bu.1.1 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.bu.2.5 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.bv.1.1 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.bv.2.3 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.bw.1.2 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.bw.2.1 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.bx.1.1 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.bx.2.3 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.by.1.2 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.by.2.1 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.bz.1.1 | $208$ | $2$ | $2$ | $0$ |
| 208.96.0-208.bz.2.2 | $208$ | $2$ | $2$ | $0$ |
| 208.96.1-208.a.2.3 | $208$ | $2$ | $2$ | $1$ |
| 208.96.1-208.f.1.9 | $208$ | $2$ | $2$ | $1$ |
| 208.96.1-208.g.1.9 | $208$ | $2$ | $2$ | $1$ |
| 208.96.1-208.j.1.9 | $208$ | $2$ | $2$ | $1$ |
| 208.96.1-208.q.1.9 | $208$ | $2$ | $2$ | $1$ |
| 208.96.1-208.t.1.1 | $208$ | $2$ | $2$ | $1$ |
| 208.96.1-208.u.1.13 | $208$ | $2$ | $2$ | $1$ |
| 208.96.1-208.x.1.9 | $208$ | $2$ | $2$ | $1$ |