| $\GL_2(\Z/56\Z)$-generators: |
$\begin{bmatrix}9&20\\16&53\end{bmatrix}$, $\begin{bmatrix}22&17\\9&22\end{bmatrix}$, $\begin{bmatrix}42&51\\3&34\end{bmatrix}$, $\begin{bmatrix}55&26\\18&3\end{bmatrix}$ |
| Contains $-I$: |
yes |
| Quadratic refinements: |
56.96.1-56.dh.1.1, 56.96.1-56.dh.1.2, 56.96.1-56.dh.1.3, 56.96.1-56.dh.1.4, 168.96.1-56.dh.1.1, 168.96.1-56.dh.1.2, 168.96.1-56.dh.1.3, 168.96.1-56.dh.1.4, 280.96.1-56.dh.1.1, 280.96.1-56.dh.1.2, 280.96.1-56.dh.1.3, 280.96.1-56.dh.1.4 |
| 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^{2} - z w $ |
| $=$ | $56 y^{2} - z^{2} - w^{2}$ |
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Singular plane model Singular plane model
| $ 0 $ | $=$ | $ x^{4} - 14 y^{2} z^{2} + 49 z^{4} $ |
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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:
| $\displaystyle X$ |
$=$ |
$\displaystyle x$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle 2y$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle \frac{1}{7}w$ |
Maps to other modular curves
$j$-invariant map
of degree 48 from the embedded model of this modular curve to the modular curve
$X(1)$
:
| $\displaystyle j$ |
$=$ |
$\displaystyle -2^4\,\frac{(z^{2}-4zw+w^{2})^{3}(z^{2}+4zw+w^{2})^{3}}{w^{2}z^{2}(z^{2}+w^{2})^{4}}$ |
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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.
