| $\GL_2(\Z/56\Z)$-generators: |
$\begin{bmatrix}11&12\\52&35\end{bmatrix}$, $\begin{bmatrix}27&7\\0&17\end{bmatrix}$, $\begin{bmatrix}27&11\\28&17\end{bmatrix}$, $\begin{bmatrix}39&36\\20&51\end{bmatrix}$ |
| Contains $-I$: |
yes |
| Quadratic refinements: |
56.96.1-56.dg.1.1, 56.96.1-56.dg.1.2, 56.96.1-56.dg.1.3, 56.96.1-56.dg.1.4, 168.96.1-56.dg.1.1, 168.96.1-56.dg.1.2, 168.96.1-56.dg.1.3, 168.96.1-56.dg.1.4, 280.96.1-56.dg.1.1, 280.96.1-56.dg.1.2, 280.96.1-56.dg.1.3, 280.96.1-56.dg.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 $ | $=$ | $ 2 x^{2} + 2 x y - 4 x z - y^{2} $ |
| $=$ | $x^{2} + x y - 2 x z + 3 y^{2} - 7 y z + 7 z^{2} - 2 w^{2}$ |
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Singular plane model Singular plane model
| $ 0 $ | $=$ | $ x^{4} - 14 x^{2} y^{2} + 4 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:
| $\displaystyle X$ |
$=$ |
$\displaystyle x$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle \frac{2}{7}w$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle \frac{1}{2}y$ |
Maps to other modular curves
$j$-invariant map
of degree 48 from the embedded model of this modular curve to the modular curve
$X(1)$
:
| $\displaystyle j$ |
$=$ |
$\displaystyle 2^4\cdot7^2\,\frac{z^{3}(7z^{2}-4w^{2})(588yz^{4}w^{2}-336yz^{2}w^{4}-64yw^{6}-343z^{7}-196z^{5}w^{2}+560z^{3}w^{4}-128zw^{6})}{w^{8}(28yzw^{2}-49z^{4}+4w^{4})}$ |
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.
