$\GL_2(\Z/56\Z)$-generators: |
$\begin{bmatrix}17&52\\24&53\end{bmatrix}$, $\begin{bmatrix}21&26\\54&41\end{bmatrix}$, $\begin{bmatrix}53&26\\4&11\end{bmatrix}$, $\begin{bmatrix}55&38\\24&29\end{bmatrix}$ |
Contains $-I$: |
yes |
Quadratic refinements: |
56.192.1-56.ch.1.1, 56.192.1-56.ch.1.2, 56.192.1-56.ch.1.3, 56.192.1-56.ch.1.4, 56.192.1-56.ch.1.5, 56.192.1-56.ch.1.6, 56.192.1-56.ch.1.7, 56.192.1-56.ch.1.8, 112.192.1-56.ch.1.1, 112.192.1-56.ch.1.2, 112.192.1-56.ch.1.3, 112.192.1-56.ch.1.4, 112.192.1-56.ch.1.5, 112.192.1-56.ch.1.6, 112.192.1-56.ch.1.7, 112.192.1-56.ch.1.8, 112.192.1-56.ch.1.9, 112.192.1-56.ch.1.10, 112.192.1-56.ch.1.11, 112.192.1-56.ch.1.12, 168.192.1-56.ch.1.1, 168.192.1-56.ch.1.2, 168.192.1-56.ch.1.3, 168.192.1-56.ch.1.4, 168.192.1-56.ch.1.5, 168.192.1-56.ch.1.6, 168.192.1-56.ch.1.7, 168.192.1-56.ch.1.8, 280.192.1-56.ch.1.1, 280.192.1-56.ch.1.2, 280.192.1-56.ch.1.3, 280.192.1-56.ch.1.4, 280.192.1-56.ch.1.5, 280.192.1-56.ch.1.6, 280.192.1-56.ch.1.7, 280.192.1-56.ch.1.8 |
Cyclic 56-isogeny field degree: |
$8$ |
Cyclic 56-torsion field degree: |
$192$ |
Full 56-torsion field degree: |
$32256$ |
This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.
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.