$\GL_2(\Z/40\Z)$-generators: |
$\begin{bmatrix}1&6\\12&13\end{bmatrix}$, $\begin{bmatrix}19&26\\12&25\end{bmatrix}$, $\begin{bmatrix}25&22\\36&17\end{bmatrix}$, $\begin{bmatrix}39&8\\32&15\end{bmatrix}$ |
Contains $-I$: |
yes |
Quadratic refinements: |
40.192.1-40.u.2.1, 40.192.1-40.u.2.2, 40.192.1-40.u.2.3, 40.192.1-40.u.2.4, 40.192.1-40.u.2.5, 40.192.1-40.u.2.6, 40.192.1-40.u.2.7, 40.192.1-40.u.2.8, 80.192.1-40.u.2.1, 80.192.1-40.u.2.2, 80.192.1-40.u.2.3, 80.192.1-40.u.2.4, 80.192.1-40.u.2.5, 80.192.1-40.u.2.6, 80.192.1-40.u.2.7, 80.192.1-40.u.2.8, 80.192.1-40.u.2.9, 80.192.1-40.u.2.10, 80.192.1-40.u.2.11, 80.192.1-40.u.2.12, 120.192.1-40.u.2.1, 120.192.1-40.u.2.2, 120.192.1-40.u.2.3, 120.192.1-40.u.2.4, 120.192.1-40.u.2.5, 120.192.1-40.u.2.6, 120.192.1-40.u.2.7, 120.192.1-40.u.2.8, 240.192.1-40.u.2.1, 240.192.1-40.u.2.2, 240.192.1-40.u.2.3, 240.192.1-40.u.2.4, 240.192.1-40.u.2.5, 240.192.1-40.u.2.6, 240.192.1-40.u.2.7, 240.192.1-40.u.2.8, 240.192.1-40.u.2.9, 240.192.1-40.u.2.10, 240.192.1-40.u.2.11, 240.192.1-40.u.2.12, 280.192.1-40.u.2.1, 280.192.1-40.u.2.2, 280.192.1-40.u.2.3, 280.192.1-40.u.2.4, 280.192.1-40.u.2.5, 280.192.1-40.u.2.6, 280.192.1-40.u.2.7, 280.192.1-40.u.2.8 |
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 $ | $=$ | $ 10 x^{2} - z^{2} - w^{2} $ |
| $=$ | $10 y^{2} - z^{2} - 2 w^{2}$ |
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
$X(1)$
:
$\displaystyle j$ |
$=$ |
$\displaystyle 2^8\,\frac{(z^{8}+4z^{6}w^{2}+5z^{4}w^{4}+2z^{2}w^{6}+w^{8})^{3}}{w^{8}z^{4}(z^{2}+w^{2})^{4}(z^{2}+2w^{2})^{2}}$ |
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.