$\GL_2(\Z/56\Z)$-generators: |
$\begin{bmatrix}3&12\\52&13\end{bmatrix}$, $\begin{bmatrix}3&20\\20&3\end{bmatrix}$, $\begin{bmatrix}37&16\\34&37\end{bmatrix}$, $\begin{bmatrix}45&12\\52&35\end{bmatrix}$, $\begin{bmatrix}47&4\\16&11\end{bmatrix}$ |
Contains $-I$: |
yes |
Quadratic refinements: |
56.96.0-56.k.1.1, 56.96.0-56.k.1.2, 56.96.0-56.k.1.3, 56.96.0-56.k.1.4, 56.96.0-56.k.1.5, 56.96.0-56.k.1.6, 56.96.0-56.k.1.7, 56.96.0-56.k.1.8, 56.96.0-56.k.1.9, 56.96.0-56.k.1.10, 56.96.0-56.k.1.11, 56.96.0-56.k.1.12, 56.96.0-56.k.1.13, 56.96.0-56.k.1.14, 56.96.0-56.k.1.15, 56.96.0-56.k.1.16, 168.96.0-56.k.1.1, 168.96.0-56.k.1.2, 168.96.0-56.k.1.3, 168.96.0-56.k.1.4, 168.96.0-56.k.1.5, 168.96.0-56.k.1.6, 168.96.0-56.k.1.7, 168.96.0-56.k.1.8, 168.96.0-56.k.1.9, 168.96.0-56.k.1.10, 168.96.0-56.k.1.11, 168.96.0-56.k.1.12, 168.96.0-56.k.1.13, 168.96.0-56.k.1.14, 168.96.0-56.k.1.15, 168.96.0-56.k.1.16, 280.96.0-56.k.1.1, 280.96.0-56.k.1.2, 280.96.0-56.k.1.3, 280.96.0-56.k.1.4, 280.96.0-56.k.1.5, 280.96.0-56.k.1.6, 280.96.0-56.k.1.7, 280.96.0-56.k.1.8, 280.96.0-56.k.1.9, 280.96.0-56.k.1.10, 280.96.0-56.k.1.11, 280.96.0-56.k.1.12, 280.96.0-56.k.1.13, 280.96.0-56.k.1.14, 280.96.0-56.k.1.15, 280.96.0-56.k.1.16 |
Cyclic 56-isogeny field degree: |
$16$ |
Cyclic 56-torsion field degree: |
$384$ |
Full 56-torsion field degree: |
$64512$ |
Smooth plane model Smooth plane model
$ 0 $ | $=$ | $ 21 x^{2} + 14 x z - 2 y^{2} + 21 z^{2} $ |
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
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.