Invariants
Level: | $208$ | $\SL_2$-level: | $16$ | ||||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $1^{4}\cdot2^{2}\cdot4^{2}\cdot16^{2}$ | Cusp orbits | $2^{5}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $1 \le \gamma \le 2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16H0 |
Level structure
$\GL_2(\Z/208\Z)$-generators: | $\begin{bmatrix}9&132\\128&205\end{bmatrix}$, $\begin{bmatrix}20&189\\33&184\end{bmatrix}$, $\begin{bmatrix}91&32\\144&147\end{bmatrix}$, $\begin{bmatrix}163&176\\122&201\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 208.48.0.bk.2 for the level structure with $-I$) |
Cyclic 208-isogeny field degree: | $28$ |
Cyclic 208-torsion field degree: | $1344$ |
Full 208-torsion field degree: | $6709248$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
16.48.0-16.e.2.1 | $16$ | $2$ | $2$ | $0$ | $0$ |
104.48.0-104.ca.2.6 | $104$ | $2$ | $2$ | $0$ | $?$ |
208.48.0-16.e.2.4 | $208$ | $2$ | $2$ | $0$ | $?$ |
208.48.0-208.o.1.1 | $208$ | $2$ | $2$ | $0$ | $?$ |
208.48.0-208.o.1.15 | $208$ | $2$ | $2$ | $0$ | $?$ |
208.48.0-104.ca.2.12 | $208$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
208.192.1-208.p.1.2 | $208$ | $2$ | $2$ | $1$ |
208.192.1-208.u.1.1 | $208$ | $2$ | $2$ | $1$ |
208.192.1-208.bg.1.5 | $208$ | $2$ | $2$ | $1$ |
208.192.1-208.bv.2.2 | $208$ | $2$ | $2$ | $1$ |
208.192.1-208.cj.1.1 | $208$ | $2$ | $2$ | $1$ |
208.192.1-208.cm.1.1 | $208$ | $2$ | $2$ | $1$ |
208.192.1-208.cy.1.2 | $208$ | $2$ | $2$ | $1$ |
208.192.1-208.dd.1.4 | $208$ | $2$ | $2$ | $1$ |