$\GL_2(\Z/56\Z)$-generators: |
$\begin{bmatrix}25&48\\32&11\end{bmatrix}$, $\begin{bmatrix}31&20\\40&35\end{bmatrix}$, $\begin{bmatrix}33&44\\14&5\end{bmatrix}$, $\begin{bmatrix}49&24\\22&15\end{bmatrix}$, $\begin{bmatrix}55&40\\14&33\end{bmatrix}$ |
Contains $-I$: |
yes |
Quadratic refinements: |
56.96.1-56.bf.2.1, 56.96.1-56.bf.2.2, 56.96.1-56.bf.2.3, 56.96.1-56.bf.2.4, 56.96.1-56.bf.2.5, 56.96.1-56.bf.2.6, 56.96.1-56.bf.2.7, 56.96.1-56.bf.2.8, 56.96.1-56.bf.2.9, 56.96.1-56.bf.2.10, 56.96.1-56.bf.2.11, 56.96.1-56.bf.2.12, 56.96.1-56.bf.2.13, 56.96.1-56.bf.2.14, 56.96.1-56.bf.2.15, 56.96.1-56.bf.2.16, 168.96.1-56.bf.2.1, 168.96.1-56.bf.2.2, 168.96.1-56.bf.2.3, 168.96.1-56.bf.2.4, 168.96.1-56.bf.2.5, 168.96.1-56.bf.2.6, 168.96.1-56.bf.2.7, 168.96.1-56.bf.2.8, 168.96.1-56.bf.2.9, 168.96.1-56.bf.2.10, 168.96.1-56.bf.2.11, 168.96.1-56.bf.2.12, 168.96.1-56.bf.2.13, 168.96.1-56.bf.2.14, 168.96.1-56.bf.2.15, 168.96.1-56.bf.2.16, 280.96.1-56.bf.2.1, 280.96.1-56.bf.2.2, 280.96.1-56.bf.2.3, 280.96.1-56.bf.2.4, 280.96.1-56.bf.2.5, 280.96.1-56.bf.2.6, 280.96.1-56.bf.2.7, 280.96.1-56.bf.2.8, 280.96.1-56.bf.2.9, 280.96.1-56.bf.2.10, 280.96.1-56.bf.2.11, 280.96.1-56.bf.2.12, 280.96.1-56.bf.2.13, 280.96.1-56.bf.2.14, 280.96.1-56.bf.2.15, 280.96.1-56.bf.2.16 |
Cyclic 56-isogeny field degree: |
$16$ |
Cyclic 56-torsion field degree: |
$384$ |
Full 56-torsion field degree: |
$64512$ |
This modular curve has infinitely many rational points, including 1 stored non-cuspidal point.
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.