$\GL_2(\Z/56\Z)$-generators: |
$\begin{bmatrix}1&40\\6&3\end{bmatrix}$, $\begin{bmatrix}15&16\\8&31\end{bmatrix}$, $\begin{bmatrix}39&18\\50&7\end{bmatrix}$, $\begin{bmatrix}43&54\\46&47\end{bmatrix}$ |
Contains $-I$: |
yes |
Quadratic refinements: |
56.192.1-56.bg.1.1, 56.192.1-56.bg.1.2, 56.192.1-56.bg.1.3, 56.192.1-56.bg.1.4, 56.192.1-56.bg.1.5, 56.192.1-56.bg.1.6, 56.192.1-56.bg.1.7, 56.192.1-56.bg.1.8, 168.192.1-56.bg.1.1, 168.192.1-56.bg.1.2, 168.192.1-56.bg.1.3, 168.192.1-56.bg.1.4, 168.192.1-56.bg.1.5, 168.192.1-56.bg.1.6, 168.192.1-56.bg.1.7, 168.192.1-56.bg.1.8, 280.192.1-56.bg.1.1, 280.192.1-56.bg.1.2, 280.192.1-56.bg.1.3, 280.192.1-56.bg.1.4, 280.192.1-56.bg.1.5, 280.192.1-56.bg.1.6, 280.192.1-56.bg.1.7, 280.192.1-56.bg.1.8 |
Cyclic 56-isogeny field degree: |
$16$ |
Cyclic 56-torsion field degree: |
$192$ |
Full 56-torsion field degree: |
$32256$ |
Embedded model Embedded model in $\mathbb{P}^{3}$
$ 0 $ | $=$ | $ 7 x^{2} - z^{2} + 2 w^{2} $ |
| $=$ | $7 y^{2} - 2 z^{2} + 2 w^{2}$ |
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Maps to other modular curves
$j$-invariant map
of degree 96 from the embedded model of this modular curve to the modular curve
$X(1)$
:
$\displaystyle j$ |
$=$ |
$\displaystyle 2^8\,\frac{(z^{8}-4z^{6}w^{2}+5z^{4}w^{4}-2z^{2}w^{6}+w^{8})^{3}}{w^{8}z^{4}(z-w)^{4}(z+w)^{4}(z^{2}-2w^{2})^{2}}$ |
Hi
|
Cover information
Click on a modular curve in the diagram to see information about it.
|
This modular curve minimally covers the modular curves listed below.
This modular curve is minimally covered by the modular curves in the database listed below.