$\GL_2(\Z/24\Z)$-generators: |
$\begin{bmatrix}1&0\\18&17\end{bmatrix}$, $\begin{bmatrix}5&22\\18&5\end{bmatrix}$, $\begin{bmatrix}23&10\\20&11\end{bmatrix}$, $\begin{bmatrix}23&14\\12&17\end{bmatrix}$ |
Contains $-I$: |
yes |
Quadratic refinements: |
24.48.0-24.g.1.1, 24.48.0-24.g.1.2, 24.48.0-24.g.1.3, 24.48.0-24.g.1.4, 24.48.0-24.g.1.5, 24.48.0-24.g.1.6, 24.48.0-24.g.1.7, 24.48.0-24.g.1.8, 120.48.0-24.g.1.1, 120.48.0-24.g.1.2, 120.48.0-24.g.1.3, 120.48.0-24.g.1.4, 120.48.0-24.g.1.5, 120.48.0-24.g.1.6, 120.48.0-24.g.1.7, 120.48.0-24.g.1.8, 168.48.0-24.g.1.1, 168.48.0-24.g.1.2, 168.48.0-24.g.1.3, 168.48.0-24.g.1.4, 168.48.0-24.g.1.5, 168.48.0-24.g.1.6, 168.48.0-24.g.1.7, 168.48.0-24.g.1.8, 264.48.0-24.g.1.1, 264.48.0-24.g.1.2, 264.48.0-24.g.1.3, 264.48.0-24.g.1.4, 264.48.0-24.g.1.5, 264.48.0-24.g.1.6, 264.48.0-24.g.1.7, 264.48.0-24.g.1.8, 312.48.0-24.g.1.1, 312.48.0-24.g.1.2, 312.48.0-24.g.1.3, 312.48.0-24.g.1.4, 312.48.0-24.g.1.5, 312.48.0-24.g.1.6, 312.48.0-24.g.1.7, 312.48.0-24.g.1.8 |
Cyclic 24-isogeny field degree: |
$16$ |
Cyclic 24-torsion field degree: |
$128$ |
Full 24-torsion field degree: |
$3072$ |
Smooth plane model Smooth plane model
$ 0 $ | $=$ | $ 16 x^{2} + 3 y^{2} + 6 z^{2} $ |
This modular curve has no real points, and therefore no rational points.
Hi
|
Cover information
Click on a modular curve in the diagram to see information about it.
|
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.