$\GL_2(\Z/24\Z)$-generators: |
$\begin{bmatrix}3&10\\8&17\end{bmatrix}$, $\begin{bmatrix}7&14\\0&7\end{bmatrix}$, $\begin{bmatrix}13&6\\8&1\end{bmatrix}$, $\begin{bmatrix}13&6\\8&11\end{bmatrix}$, $\begin{bmatrix}19&22\\8&15\end{bmatrix}$ |
Contains $-I$: |
yes |
Quadratic refinements: |
24.96.0-24.bc.1.1, 24.96.0-24.bc.1.2, 24.96.0-24.bc.1.3, 24.96.0-24.bc.1.4, 24.96.0-24.bc.1.5, 24.96.0-24.bc.1.6, 24.96.0-24.bc.1.7, 24.96.0-24.bc.1.8, 24.96.0-24.bc.1.9, 24.96.0-24.bc.1.10, 24.96.0-24.bc.1.11, 24.96.0-24.bc.1.12, 48.96.0-24.bc.1.1, 48.96.0-24.bc.1.2, 48.96.0-24.bc.1.3, 48.96.0-24.bc.1.4, 48.96.0-24.bc.1.5, 48.96.0-24.bc.1.6, 48.96.0-24.bc.1.7, 48.96.0-24.bc.1.8, 120.96.0-24.bc.1.1, 120.96.0-24.bc.1.2, 120.96.0-24.bc.1.3, 120.96.0-24.bc.1.4, 120.96.0-24.bc.1.5, 120.96.0-24.bc.1.6, 120.96.0-24.bc.1.7, 120.96.0-24.bc.1.8, 120.96.0-24.bc.1.9, 120.96.0-24.bc.1.10, 120.96.0-24.bc.1.11, 120.96.0-24.bc.1.12, 168.96.0-24.bc.1.1, 168.96.0-24.bc.1.2, 168.96.0-24.bc.1.3, 168.96.0-24.bc.1.4, 168.96.0-24.bc.1.5, 168.96.0-24.bc.1.6, 168.96.0-24.bc.1.7, 168.96.0-24.bc.1.8, 168.96.0-24.bc.1.9, 168.96.0-24.bc.1.10, 168.96.0-24.bc.1.11, 168.96.0-24.bc.1.12, 240.96.0-24.bc.1.1, 240.96.0-24.bc.1.2, 240.96.0-24.bc.1.3, 240.96.0-24.bc.1.4, 240.96.0-24.bc.1.5, 240.96.0-24.bc.1.6, 240.96.0-24.bc.1.7, 240.96.0-24.bc.1.8, 264.96.0-24.bc.1.1, 264.96.0-24.bc.1.2, 264.96.0-24.bc.1.3, 264.96.0-24.bc.1.4, 264.96.0-24.bc.1.5, 264.96.0-24.bc.1.6, 264.96.0-24.bc.1.7, 264.96.0-24.bc.1.8, 264.96.0-24.bc.1.9, 264.96.0-24.bc.1.10, 264.96.0-24.bc.1.11, 264.96.0-24.bc.1.12, 312.96.0-24.bc.1.1, 312.96.0-24.bc.1.2, 312.96.0-24.bc.1.3, 312.96.0-24.bc.1.4, 312.96.0-24.bc.1.5, 312.96.0-24.bc.1.6, 312.96.0-24.bc.1.7, 312.96.0-24.bc.1.8, 312.96.0-24.bc.1.9, 312.96.0-24.bc.1.10, 312.96.0-24.bc.1.11, 312.96.0-24.bc.1.12 |
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 $ | $=$ | $ 3 x^{2} + 3 y^{2} + 8 z^{2} $ |
This modular curve has no real points, and therefore no rational points.
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.