$\GL_2(\Z/40\Z)$-generators: |
$\begin{bmatrix}1&20\\30&19\end{bmatrix}$, $\begin{bmatrix}9&24\\26&9\end{bmatrix}$, $\begin{bmatrix}11&16\\24&13\end{bmatrix}$, $\begin{bmatrix}13&0\\20&27\end{bmatrix}$ |
Contains $-I$: |
yes |
Quadratic refinements: |
40.192.1-40.bt.1.1, 40.192.1-40.bt.1.2, 40.192.1-40.bt.1.3, 40.192.1-40.bt.1.4, 40.192.1-40.bt.1.5, 40.192.1-40.bt.1.6, 40.192.1-40.bt.1.7, 40.192.1-40.bt.1.8, 120.192.1-40.bt.1.1, 120.192.1-40.bt.1.2, 120.192.1-40.bt.1.3, 120.192.1-40.bt.1.4, 120.192.1-40.bt.1.5, 120.192.1-40.bt.1.6, 120.192.1-40.bt.1.7, 120.192.1-40.bt.1.8, 280.192.1-40.bt.1.1, 280.192.1-40.bt.1.2, 280.192.1-40.bt.1.3, 280.192.1-40.bt.1.4, 280.192.1-40.bt.1.5, 280.192.1-40.bt.1.6, 280.192.1-40.bt.1.7, 280.192.1-40.bt.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} + y^{2} + z^{2} $ |
| $=$ | $4 x^{2} - 3 y^{2} - 8 z^{2} - 2 w^{2}$ |
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
$X(1)$
:
$\displaystyle j$ |
$=$ |
$\displaystyle \frac{2^4}{5^4}\cdot\frac{(625z^{8}+500z^{6}w^{2}+500z^{4}w^{4}+160z^{2}w^{6}+16w^{8})^{3}}{w^{4}z^{8}(5z^{2}+w^{2})^{2}(5z^{2}+2w^{2})^{4}}$ |
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.