$\GL_2(\Z/24\Z)$-generators: |
$\begin{bmatrix}7&4\\8&9\end{bmatrix}$, $\begin{bmatrix}9&20\\4&13\end{bmatrix}$, $\begin{bmatrix}11&12\\16&17\end{bmatrix}$, $\begin{bmatrix}13&2\\0&11\end{bmatrix}$, $\begin{bmatrix}13&4\\12&19\end{bmatrix}$ |
Contains $-I$: |
yes |
Quadratic refinements: |
24.96.0-24.h.1.1, 24.96.0-24.h.1.2, 24.96.0-24.h.1.3, 24.96.0-24.h.1.4, 24.96.0-24.h.1.5, 24.96.0-24.h.1.6, 24.96.0-24.h.1.7, 24.96.0-24.h.1.8, 24.96.0-24.h.1.9, 24.96.0-24.h.1.10, 24.96.0-24.h.1.11, 24.96.0-24.h.1.12, 24.96.0-24.h.1.13, 24.96.0-24.h.1.14, 24.96.0-24.h.1.15, 24.96.0-24.h.1.16, 120.96.0-24.h.1.1, 120.96.0-24.h.1.2, 120.96.0-24.h.1.3, 120.96.0-24.h.1.4, 120.96.0-24.h.1.5, 120.96.0-24.h.1.6, 120.96.0-24.h.1.7, 120.96.0-24.h.1.8, 120.96.0-24.h.1.9, 120.96.0-24.h.1.10, 120.96.0-24.h.1.11, 120.96.0-24.h.1.12, 120.96.0-24.h.1.13, 120.96.0-24.h.1.14, 120.96.0-24.h.1.15, 120.96.0-24.h.1.16, 168.96.0-24.h.1.1, 168.96.0-24.h.1.2, 168.96.0-24.h.1.3, 168.96.0-24.h.1.4, 168.96.0-24.h.1.5, 168.96.0-24.h.1.6, 168.96.0-24.h.1.7, 168.96.0-24.h.1.8, 168.96.0-24.h.1.9, 168.96.0-24.h.1.10, 168.96.0-24.h.1.11, 168.96.0-24.h.1.12, 168.96.0-24.h.1.13, 168.96.0-24.h.1.14, 168.96.0-24.h.1.15, 168.96.0-24.h.1.16, 264.96.0-24.h.1.1, 264.96.0-24.h.1.2, 264.96.0-24.h.1.3, 264.96.0-24.h.1.4, 264.96.0-24.h.1.5, 264.96.0-24.h.1.6, 264.96.0-24.h.1.7, 264.96.0-24.h.1.8, 264.96.0-24.h.1.9, 264.96.0-24.h.1.10, 264.96.0-24.h.1.11, 264.96.0-24.h.1.12, 264.96.0-24.h.1.13, 264.96.0-24.h.1.14, 264.96.0-24.h.1.15, 264.96.0-24.h.1.16, 312.96.0-24.h.1.1, 312.96.0-24.h.1.2, 312.96.0-24.h.1.3, 312.96.0-24.h.1.4, 312.96.0-24.h.1.5, 312.96.0-24.h.1.6, 312.96.0-24.h.1.7, 312.96.0-24.h.1.8, 312.96.0-24.h.1.9, 312.96.0-24.h.1.10, 312.96.0-24.h.1.11, 312.96.0-24.h.1.12, 312.96.0-24.h.1.13, 312.96.0-24.h.1.14, 312.96.0-24.h.1.15, 312.96.0-24.h.1.16 |
Cyclic 24-isogeny field degree: |
$8$ |
Cyclic 24-torsion field degree: |
$64$ |
Full 24-torsion field degree: |
$1536$ |
Smooth plane model Smooth plane model
$ 0 $ | $=$ | $ x^{2} - x z + 3 y^{2} + 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.