$\GL_2(\Z/40\Z)$-generators: |
$\begin{bmatrix}1&36\\28&31\end{bmatrix}$, $\begin{bmatrix}9&32\\38&23\end{bmatrix}$, $\begin{bmatrix}15&36\\2&23\end{bmatrix}$, $\begin{bmatrix}23&4\\32&3\end{bmatrix}$ |
Contains $-I$: |
yes |
Quadratic refinements: |
40.192.1-40.bg.1.1, 40.192.1-40.bg.1.2, 40.192.1-40.bg.1.3, 40.192.1-40.bg.1.4, 40.192.1-40.bg.1.5, 40.192.1-40.bg.1.6, 40.192.1-40.bg.1.7, 40.192.1-40.bg.1.8, 120.192.1-40.bg.1.1, 120.192.1-40.bg.1.2, 120.192.1-40.bg.1.3, 120.192.1-40.bg.1.4, 120.192.1-40.bg.1.5, 120.192.1-40.bg.1.6, 120.192.1-40.bg.1.7, 120.192.1-40.bg.1.8, 280.192.1-40.bg.1.1, 280.192.1-40.bg.1.2, 280.192.1-40.bg.1.3, 280.192.1-40.bg.1.4, 280.192.1-40.bg.1.5, 280.192.1-40.bg.1.6, 280.192.1-40.bg.1.7, 280.192.1-40.bg.1.8 |
Cyclic 40-isogeny field degree: |
$12$ |
Cyclic 40-torsion field degree: |
$96$ |
Full 40-torsion field degree: |
$7680$ |
Embedded model Embedded model in $\mathbb{P}^{3}$
$ 0 $ | $=$ | $ 5 x^{2} + y^{2} - 2 w^{2} $ |
| $=$ | $2 y^{2} + 5 z^{2} - 2 w^{2}$ |
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known 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
$X(1)$
:
$\displaystyle j$ |
$=$ |
$\displaystyle \frac{2^4}{5^4}\cdot\frac{(625z^{8}-100z^{4}w^{4}+16w^{8})^{3}}{w^{8}z^{8}(5z^{2}-2w^{2})^{2}(5z^{2}+2w^{2})^{2}}$ |
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.