$\GL_2(\Z/24\Z)$-generators: |
$\begin{bmatrix}5&10\\16&19\end{bmatrix}$, $\begin{bmatrix}7&14\\0&19\end{bmatrix}$, $\begin{bmatrix}7&22\\0&5\end{bmatrix}$, $\begin{bmatrix}13&12\\16&17\end{bmatrix}$ |
$\GL_2(\Z/24\Z)$-subgroup: |
$C_2\times D_4\times \GL(2,3)$ |
Contains $-I$: |
yes |
Quadratic refinements: |
24.192.1-24.cf.2.1, 24.192.1-24.cf.2.2, 24.192.1-24.cf.2.3, 24.192.1-24.cf.2.4, 24.192.1-24.cf.2.5, 24.192.1-24.cf.2.6, 24.192.1-24.cf.2.7, 24.192.1-24.cf.2.8, 48.192.1-24.cf.2.1, 48.192.1-24.cf.2.2, 48.192.1-24.cf.2.3, 48.192.1-24.cf.2.4, 120.192.1-24.cf.2.1, 120.192.1-24.cf.2.2, 120.192.1-24.cf.2.3, 120.192.1-24.cf.2.4, 120.192.1-24.cf.2.5, 120.192.1-24.cf.2.6, 120.192.1-24.cf.2.7, 120.192.1-24.cf.2.8, 168.192.1-24.cf.2.1, 168.192.1-24.cf.2.2, 168.192.1-24.cf.2.3, 168.192.1-24.cf.2.4, 168.192.1-24.cf.2.5, 168.192.1-24.cf.2.6, 168.192.1-24.cf.2.7, 168.192.1-24.cf.2.8, 240.192.1-24.cf.2.1, 240.192.1-24.cf.2.2, 240.192.1-24.cf.2.3, 240.192.1-24.cf.2.4, 264.192.1-24.cf.2.1, 264.192.1-24.cf.2.2, 264.192.1-24.cf.2.3, 264.192.1-24.cf.2.4, 264.192.1-24.cf.2.5, 264.192.1-24.cf.2.6, 264.192.1-24.cf.2.7, 264.192.1-24.cf.2.8, 312.192.1-24.cf.2.1, 312.192.1-24.cf.2.2, 312.192.1-24.cf.2.3, 312.192.1-24.cf.2.4, 312.192.1-24.cf.2.5, 312.192.1-24.cf.2.6, 312.192.1-24.cf.2.7, 312.192.1-24.cf.2.8 |
Cyclic 24-isogeny field degree: |
$4$ |
Cyclic 24-torsion field degree: |
$32$ |
Full 24-torsion field degree: |
$768$ |
Embedded model Embedded model in $\mathbb{P}^{3}$
$ 0 $ | $=$ | $ 2 x^{2} - 2 y^{2} - z^{2} $ |
| $=$ | $3 x^{2} + 3 y^{2} - w^{2}$ |
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
$X(1)$
:
$\displaystyle j$ |
$=$ |
$\displaystyle \frac{2^2}{3^2}\cdot\frac{(81z^{8}+504z^{4}w^{4}+16w^{8})^{3}}{w^{4}z^{4}(3z^{2}-2w^{2})^{4}(3z^{2}+2w^{2})^{4}}$ |
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.