$\GL_2(\Z/40\Z)$-generators: |
$\begin{bmatrix}15&8\\8&39\end{bmatrix}$, $\begin{bmatrix}25&24\\38&29\end{bmatrix}$, $\begin{bmatrix}31&0\\19&33\end{bmatrix}$, $\begin{bmatrix}31&24\\20&11\end{bmatrix}$ |
Contains $-I$: |
yes |
Quadratic refinements: |
40.192.1-40.cl.1.1, 40.192.1-40.cl.1.2, 40.192.1-40.cl.1.3, 40.192.1-40.cl.1.4, 40.192.1-40.cl.1.5, 40.192.1-40.cl.1.6, 40.192.1-40.cl.1.7, 40.192.1-40.cl.1.8, 80.192.1-40.cl.1.1, 80.192.1-40.cl.1.2, 80.192.1-40.cl.1.3, 80.192.1-40.cl.1.4, 80.192.1-40.cl.1.5, 80.192.1-40.cl.1.6, 80.192.1-40.cl.1.7, 80.192.1-40.cl.1.8, 120.192.1-40.cl.1.1, 120.192.1-40.cl.1.2, 120.192.1-40.cl.1.3, 120.192.1-40.cl.1.4, 120.192.1-40.cl.1.5, 120.192.1-40.cl.1.6, 120.192.1-40.cl.1.7, 120.192.1-40.cl.1.8, 240.192.1-40.cl.1.1, 240.192.1-40.cl.1.2, 240.192.1-40.cl.1.3, 240.192.1-40.cl.1.4, 240.192.1-40.cl.1.5, 240.192.1-40.cl.1.6, 240.192.1-40.cl.1.7, 240.192.1-40.cl.1.8, 280.192.1-40.cl.1.1, 280.192.1-40.cl.1.2, 280.192.1-40.cl.1.3, 280.192.1-40.cl.1.4, 280.192.1-40.cl.1.5, 280.192.1-40.cl.1.6, 280.192.1-40.cl.1.7, 280.192.1-40.cl.1.8 |
Cyclic 40-isogeny field degree: |
$6$ |
Cyclic 40-torsion field degree: |
$96$ |
Full 40-torsion field degree: |
$7680$ |
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.