$\GL_2(\Z/40\Z)$-generators: |
$\begin{bmatrix}11&16\\34&5\end{bmatrix}$, $\begin{bmatrix}11&36\\0&9\end{bmatrix}$, $\begin{bmatrix}35&12\\36&27\end{bmatrix}$, $\begin{bmatrix}37&24\\14&9\end{bmatrix}$ |
Contains $-I$: |
yes |
Quadratic refinements: |
40.192.1-40.bb.1.1, 40.192.1-40.bb.1.2, 40.192.1-40.bb.1.3, 40.192.1-40.bb.1.4, 40.192.1-40.bb.1.5, 40.192.1-40.bb.1.6, 40.192.1-40.bb.1.7, 40.192.1-40.bb.1.8, 120.192.1-40.bb.1.1, 120.192.1-40.bb.1.2, 120.192.1-40.bb.1.3, 120.192.1-40.bb.1.4, 120.192.1-40.bb.1.5, 120.192.1-40.bb.1.6, 120.192.1-40.bb.1.7, 120.192.1-40.bb.1.8, 280.192.1-40.bb.1.1, 280.192.1-40.bb.1.2, 280.192.1-40.bb.1.3, 280.192.1-40.bb.1.4, 280.192.1-40.bb.1.5, 280.192.1-40.bb.1.6, 280.192.1-40.bb.1.7, 280.192.1-40.bb.1.8 |
Cyclic 40-isogeny field degree: |
$12$ |
Cyclic 40-torsion field degree: |
$192$ |
Full 40-torsion field degree: |
$7680$ |
Embedded model Embedded model in $\mathbb{P}^{3}$
$ 0 $ | $=$ | $ 2 x^{2} + 4 y^{2} + z^{2} $ |
| $=$ | $4 x^{2} - 2 y^{2} - 3 z^{2} + w^{2}$ |
This modular curve has no real points, and therefore no rational points.
Maps to other modular curves
$j$-invariant map
of degree 96 from the embedded model of this modular curve to the modular curve
$X(1)$
:
$\displaystyle j$ |
$=$ |
$\displaystyle \frac{2^8}{5^2}\cdot\frac{(625z^{8}-500z^{6}w^{2}+125z^{4}w^{4}-10z^{2}w^{6}+w^{8})^{3}}{w^{8}z^{4}(5z^{2}-2w^{2})^{2}(5z^{2}-w^{2})^{4}}$ |
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.