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: | $10$ (of which $2$ are rational) | Cusp widths | $1^{4}\cdot2^{2}\cdot4^{2}\cdot16^{2}$ | Cusp orbits | $1^{2}\cdot2^{2}\cdot4$ | ||
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: | 16H0 |
Level structure
$\GL_2(\Z/208\Z)$-generators: | $\begin{bmatrix}32&81\\143&50\end{bmatrix}$, $\begin{bmatrix}35&84\\114&21\end{bmatrix}$, $\begin{bmatrix}152&49\\101&60\end{bmatrix}$, $\begin{bmatrix}201&88\\146&183\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 208.48.0.bn.1 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 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 |
---|---|---|---|---|---|
16.48.0-8.bb.1.6 | $16$ | $2$ | $2$ | $0$ | $0$ |
104.48.0-8.bb.1.8 | $104$ | $2$ | $2$ | $0$ | $?$ |
208.48.0-208.m.1.10 | $208$ | $2$ | $2$ | $0$ | $?$ |
208.48.0-208.m.1.15 | $208$ | $2$ | $2$ | $0$ | $?$ |
208.48.0-208.o.1.5 | $208$ | $2$ | $2$ | $0$ | $?$ |
208.48.0-208.o.1.8 | $208$ | $2$ | $2$ | $0$ | $?$ |
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.i.2.1 | $208$ | $2$ | $2$ | $1$ |
208.192.1-208.v.2.1 | $208$ | $2$ | $2$ | $1$ |
208.192.1-208.bj.2.7 | $208$ | $2$ | $2$ | $1$ |
208.192.1-208.bu.2.2 | $208$ | $2$ | $2$ | $1$ |
208.192.1-208.cj.1.3 | $208$ | $2$ | $2$ | $1$ |
208.192.1-208.cp.1.5 | $208$ | $2$ | $2$ | $1$ |
208.192.1-208.db.2.2 | $208$ | $2$ | $2$ | $1$ |
208.192.1-208.dd.2.6 | $208$ | $2$ | $2$ | $1$ |