$\GL_2(\Z/40\Z)$-generators: |
$\begin{bmatrix}9&12\\24&15\end{bmatrix}$, $\begin{bmatrix}29&16\\28&25\end{bmatrix}$, $\begin{bmatrix}29&32\\2&9\end{bmatrix}$, $\begin{bmatrix}39&28\\12&35\end{bmatrix}$, $\begin{bmatrix}39&36\\16&17\end{bmatrix}$ |
Contains $-I$: |
yes |
Quadratic refinements: |
40.96.0-40.q.2.1, 40.96.0-40.q.2.2, 40.96.0-40.q.2.3, 40.96.0-40.q.2.4, 40.96.0-40.q.2.5, 40.96.0-40.q.2.6, 40.96.0-40.q.2.7, 40.96.0-40.q.2.8, 40.96.0-40.q.2.9, 40.96.0-40.q.2.10, 40.96.0-40.q.2.11, 40.96.0-40.q.2.12, 40.96.0-40.q.2.13, 40.96.0-40.q.2.14, 40.96.0-40.q.2.15, 40.96.0-40.q.2.16, 120.96.0-40.q.2.1, 120.96.0-40.q.2.2, 120.96.0-40.q.2.3, 120.96.0-40.q.2.4, 120.96.0-40.q.2.5, 120.96.0-40.q.2.6, 120.96.0-40.q.2.7, 120.96.0-40.q.2.8, 120.96.0-40.q.2.9, 120.96.0-40.q.2.10, 120.96.0-40.q.2.11, 120.96.0-40.q.2.12, 120.96.0-40.q.2.13, 120.96.0-40.q.2.14, 120.96.0-40.q.2.15, 120.96.0-40.q.2.16, 280.96.0-40.q.2.1, 280.96.0-40.q.2.2, 280.96.0-40.q.2.3, 280.96.0-40.q.2.4, 280.96.0-40.q.2.5, 280.96.0-40.q.2.6, 280.96.0-40.q.2.7, 280.96.0-40.q.2.8, 280.96.0-40.q.2.9, 280.96.0-40.q.2.10, 280.96.0-40.q.2.11, 280.96.0-40.q.2.12, 280.96.0-40.q.2.13, 280.96.0-40.q.2.14, 280.96.0-40.q.2.15, 280.96.0-40.q.2.16 |
Cyclic 40-isogeny field degree: |
$12$ |
Cyclic 40-torsion field degree: |
$192$ |
Full 40-torsion field degree: |
$15360$ |
Smooth plane model Smooth plane model
$ 0 $ | $=$ | $ 10 x^{2} + 40 y^{2} + z^{2} $ |
This modular curve has no real points, and therefore no 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.