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 | $1^{2}\cdot2\cdot4\cdot8^{2}$ | 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: | 8I0 |
Level structure
$\GL_2(\Z/208\Z)$-generators: | $\begin{bmatrix}48&37\\59&122\end{bmatrix}$, $\begin{bmatrix}75&10\\194&147\end{bmatrix}$, $\begin{bmatrix}75&14\\112&33\end{bmatrix}$, $\begin{bmatrix}79&28\\130&73\end{bmatrix}$, $\begin{bmatrix}196&189\\33&152\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 104.24.0.cb.2 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 | $16$ | $2$ | $2$ | $0$ | $0$ |
208.24.0-8.n.1.5 | $208$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
208.96.0-104.bd.1.12 | $208$ | $2$ | $2$ | $0$ |
208.96.0-104.be.2.1 | $208$ | $2$ | $2$ | $0$ |
208.96.0-104.bf.2.7 | $208$ | $2$ | $2$ | $0$ |
208.96.0-104.bh.1.5 | $208$ | $2$ | $2$ | $0$ |
208.96.0-104.bj.2.6 | $208$ | $2$ | $2$ | $0$ |
208.96.0-104.bk.2.6 | $208$ | $2$ | $2$ | $0$ |
208.96.0-104.bm.1.5 | $208$ | $2$ | $2$ | $0$ |
208.96.0-104.bp.2.2 | $208$ | $2$ | $2$ | $0$ |
208.96.0-208.bl.1.3 | $208$ | $2$ | $2$ | $0$ |
208.96.0-208.br.1.2 | $208$ | $2$ | $2$ | $0$ |
208.96.0-208.bt.2.3 | $208$ | $2$ | $2$ | $0$ |
208.96.0-208.bz.1.5 | $208$ | $2$ | $2$ | $0$ |
208.96.0-208.cb.1.3 | $208$ | $2$ | $2$ | $0$ |
208.96.0-208.cd.1.2 | $208$ | $2$ | $2$ | $0$ |
208.96.0-208.cf.2.3 | $208$ | $2$ | $2$ | $0$ |
208.96.0-208.ch.1.5 | $208$ | $2$ | $2$ | $0$ |
208.96.1-208.bh.1.5 | $208$ | $2$ | $2$ | $1$ |
208.96.1-208.bj.2.3 | $208$ | $2$ | $2$ | $1$ |
208.96.1-208.bl.1.2 | $208$ | $2$ | $2$ | $1$ |
208.96.1-208.bn.1.3 | $208$ | $2$ | $2$ | $1$ |
208.96.1-208.br.1.5 | $208$ | $2$ | $2$ | $1$ |
208.96.1-208.bx.2.3 | $208$ | $2$ | $2$ | $1$ |
208.96.1-208.bz.1.2 | $208$ | $2$ | $2$ | $1$ |
208.96.1-208.cf.1.3 | $208$ | $2$ | $2$ | $1$ |