$\GL_2(\Z/24\Z)$-generators: |
$\begin{bmatrix}9&2\\8&13\end{bmatrix}$, $\begin{bmatrix}9&4\\20&19\end{bmatrix}$, $\begin{bmatrix}13&9\\12&17\end{bmatrix}$, $\begin{bmatrix}23&23\\20&7\end{bmatrix}$ |
Contains $-I$: |
yes |
Quadratic refinements: |
24.96.0-24.bk.2.1, 24.96.0-24.bk.2.2, 24.96.0-24.bk.2.3, 24.96.0-24.bk.2.4, 24.96.0-24.bk.2.5, 24.96.0-24.bk.2.6, 24.96.0-24.bk.2.7, 24.96.0-24.bk.2.8, 48.96.0-24.bk.2.1, 48.96.0-24.bk.2.2, 48.96.0-24.bk.2.3, 48.96.0-24.bk.2.4, 48.96.0-24.bk.2.5, 48.96.0-24.bk.2.6, 48.96.0-24.bk.2.7, 48.96.0-24.bk.2.8, 120.96.0-24.bk.2.1, 120.96.0-24.bk.2.2, 120.96.0-24.bk.2.3, 120.96.0-24.bk.2.4, 120.96.0-24.bk.2.5, 120.96.0-24.bk.2.6, 120.96.0-24.bk.2.7, 120.96.0-24.bk.2.8, 168.96.0-24.bk.2.1, 168.96.0-24.bk.2.2, 168.96.0-24.bk.2.3, 168.96.0-24.bk.2.4, 168.96.0-24.bk.2.5, 168.96.0-24.bk.2.6, 168.96.0-24.bk.2.7, 168.96.0-24.bk.2.8, 240.96.0-24.bk.2.1, 240.96.0-24.bk.2.2, 240.96.0-24.bk.2.3, 240.96.0-24.bk.2.4, 240.96.0-24.bk.2.5, 240.96.0-24.bk.2.6, 240.96.0-24.bk.2.7, 240.96.0-24.bk.2.8, 264.96.0-24.bk.2.1, 264.96.0-24.bk.2.2, 264.96.0-24.bk.2.3, 264.96.0-24.bk.2.4, 264.96.0-24.bk.2.5, 264.96.0-24.bk.2.6, 264.96.0-24.bk.2.7, 264.96.0-24.bk.2.8, 312.96.0-24.bk.2.1, 312.96.0-24.bk.2.2, 312.96.0-24.bk.2.3, 312.96.0-24.bk.2.4, 312.96.0-24.bk.2.5, 312.96.0-24.bk.2.6, 312.96.0-24.bk.2.7, 312.96.0-24.bk.2.8 |
Cyclic 24-isogeny field degree: |
$4$ |
Cyclic 24-torsion field degree: |
$32$ |
Full 24-torsion field degree: |
$1536$ |
Smooth plane model Smooth plane model
$ 0 $ | $=$ | $ 2 x^{2} + 12 y^{2} + 3 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.