$\GL_2(\Z/56\Z)$-generators: |
$\begin{bmatrix}5&48\\8&41\end{bmatrix}$, $\begin{bmatrix}11&24\\48&3\end{bmatrix}$, $\begin{bmatrix}21&20\\18&23\end{bmatrix}$, $\begin{bmatrix}29&0\\22&15\end{bmatrix}$, $\begin{bmatrix}51&14\\52&41\end{bmatrix}$ |
Contains $-I$: |
yes |
Quadratic refinements: |
56.96.1-56.ba.1.1, 56.96.1-56.ba.1.2, 56.96.1-56.ba.1.3, 56.96.1-56.ba.1.4, 56.96.1-56.ba.1.5, 56.96.1-56.ba.1.6, 56.96.1-56.ba.1.7, 56.96.1-56.ba.1.8, 56.96.1-56.ba.1.9, 56.96.1-56.ba.1.10, 56.96.1-56.ba.1.11, 56.96.1-56.ba.1.12, 56.96.1-56.ba.1.13, 56.96.1-56.ba.1.14, 56.96.1-56.ba.1.15, 56.96.1-56.ba.1.16, 168.96.1-56.ba.1.1, 168.96.1-56.ba.1.2, 168.96.1-56.ba.1.3, 168.96.1-56.ba.1.4, 168.96.1-56.ba.1.5, 168.96.1-56.ba.1.6, 168.96.1-56.ba.1.7, 168.96.1-56.ba.1.8, 168.96.1-56.ba.1.9, 168.96.1-56.ba.1.10, 168.96.1-56.ba.1.11, 168.96.1-56.ba.1.12, 168.96.1-56.ba.1.13, 168.96.1-56.ba.1.14, 168.96.1-56.ba.1.15, 168.96.1-56.ba.1.16, 280.96.1-56.ba.1.1, 280.96.1-56.ba.1.2, 280.96.1-56.ba.1.3, 280.96.1-56.ba.1.4, 280.96.1-56.ba.1.5, 280.96.1-56.ba.1.6, 280.96.1-56.ba.1.7, 280.96.1-56.ba.1.8, 280.96.1-56.ba.1.9, 280.96.1-56.ba.1.10, 280.96.1-56.ba.1.11, 280.96.1-56.ba.1.12, 280.96.1-56.ba.1.13, 280.96.1-56.ba.1.14, 280.96.1-56.ba.1.15, 280.96.1-56.ba.1.16 |
Cyclic 56-isogeny field degree: |
$16$ |
Cyclic 56-torsion field degree: |
$384$ |
Full 56-torsion field degree: |
$64512$ |
Embedded model Embedded model in $\mathbb{P}^{3}$
$ 0 $ | $=$ | $ 7 x y - w^{2} $ |
| $=$ | $14 x^{2} - 14 y^{2} + z^{2}$ |
Singular plane model Singular plane model
$ 0 $ | $=$ | $ x^{4} - 14 x^{2} y^{2} - 49 z^{4} $ |
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Maps between models of this curve
Birational map from embedded model to plane model:
$\displaystyle X$ |
$=$ |
$\displaystyle y$ |
$\displaystyle Y$ |
$=$ |
$\displaystyle \frac{1}{14}z$ |
$\displaystyle Z$ |
$=$ |
$\displaystyle \frac{1}{7}w$ |
Maps to other modular curves
$j$-invariant map
of degree 48 from the embedded model of this modular curve to the modular curve
$X(1)$
:
$\displaystyle j$ |
$=$ |
$\displaystyle 2^4\,\frac{(z^{2}-2zw+2w^{2})^{3}(z^{2}+2zw+2w^{2})^{3}}{w^{8}z^{4}}$ |
Hi
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Cover information
Click on a modular curve in the diagram to see information about it.
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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.