$\GL_2(\Z/48\Z)$-generators: |
$\begin{bmatrix}3&8\\40&31\end{bmatrix}$, $\begin{bmatrix}5&39\\40&43\end{bmatrix}$, $\begin{bmatrix}11&3\\40&25\end{bmatrix}$, $\begin{bmatrix}15&38\\4&29\end{bmatrix}$, $\begin{bmatrix}17&15\\12&1\end{bmatrix}$ |
Contains $-I$: |
yes |
Quadratic refinements: |
48.192.1-48.dm.1.1, 48.192.1-48.dm.1.2, 48.192.1-48.dm.1.3, 48.192.1-48.dm.1.4, 48.192.1-48.dm.1.5, 48.192.1-48.dm.1.6, 48.192.1-48.dm.1.7, 48.192.1-48.dm.1.8, 48.192.1-48.dm.1.9, 48.192.1-48.dm.1.10, 48.192.1-48.dm.1.11, 48.192.1-48.dm.1.12, 96.192.1-48.dm.1.1, 96.192.1-48.dm.1.2, 96.192.1-48.dm.1.3, 96.192.1-48.dm.1.4, 96.192.1-48.dm.1.5, 96.192.1-48.dm.1.6, 96.192.1-48.dm.1.7, 96.192.1-48.dm.1.8, 240.192.1-48.dm.1.1, 240.192.1-48.dm.1.2, 240.192.1-48.dm.1.3, 240.192.1-48.dm.1.4, 240.192.1-48.dm.1.5, 240.192.1-48.dm.1.6, 240.192.1-48.dm.1.7, 240.192.1-48.dm.1.8, 240.192.1-48.dm.1.9, 240.192.1-48.dm.1.10, 240.192.1-48.dm.1.11, 240.192.1-48.dm.1.12 |
Cyclic 48-isogeny field degree: |
$4$ |
Cyclic 48-torsion field degree: |
$64$ |
Full 48-torsion field degree: |
$12288$ |
This modular curve has 4 rational cusps but no known non-cuspidal 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.