$\GL_2(\Z/40\Z)$-generators: |
$\begin{bmatrix}3&4\\2&25\end{bmatrix}$, $\begin{bmatrix}15&24\\12&9\end{bmatrix}$, $\begin{bmatrix}21&28\\33&35\end{bmatrix}$, $\begin{bmatrix}33&36\\35&1\end{bmatrix}$ |
Contains $-I$: |
yes |
Quadratic refinements: |
40.48.0-40.bx.1.1, 40.48.0-40.bx.1.2, 40.48.0-40.bx.1.3, 40.48.0-40.bx.1.4, 40.48.0-40.bx.1.5, 40.48.0-40.bx.1.6, 40.48.0-40.bx.1.7, 40.48.0-40.bx.1.8, 120.48.0-40.bx.1.1, 120.48.0-40.bx.1.2, 120.48.0-40.bx.1.3, 120.48.0-40.bx.1.4, 120.48.0-40.bx.1.5, 120.48.0-40.bx.1.6, 120.48.0-40.bx.1.7, 120.48.0-40.bx.1.8, 280.48.0-40.bx.1.1, 280.48.0-40.bx.1.2, 280.48.0-40.bx.1.3, 280.48.0-40.bx.1.4, 280.48.0-40.bx.1.5, 280.48.0-40.bx.1.6, 280.48.0-40.bx.1.7, 280.48.0-40.bx.1.8 |
Cyclic 40-isogeny field degree: |
$12$ |
Cyclic 40-torsion field degree: |
$192$ |
Full 40-torsion field degree: |
$30720$ |
Smooth plane model Smooth plane model
$ 0 $ | $=$ | $ 5 x^{2} + 16 y^{2} - 10 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.