$\GL_2(\Z/48\Z)$-generators: |
$\begin{bmatrix}1&31\\24&7\end{bmatrix}$, $\begin{bmatrix}9&25\\16&23\end{bmatrix}$, $\begin{bmatrix}9&37\\8&19\end{bmatrix}$, $\begin{bmatrix}11&42\\24&11\end{bmatrix}$, $\begin{bmatrix}37&12\\40&1\end{bmatrix}$ |
Contains $-I$: |
yes |
Quadratic refinements: |
48.192.1-48.bo.2.1, 48.192.1-48.bo.2.2, 48.192.1-48.bo.2.3, 48.192.1-48.bo.2.4, 48.192.1-48.bo.2.5, 48.192.1-48.bo.2.6, 48.192.1-48.bo.2.7, 48.192.1-48.bo.2.8, 48.192.1-48.bo.2.9, 48.192.1-48.bo.2.10, 48.192.1-48.bo.2.11, 48.192.1-48.bo.2.12, 96.192.1-48.bo.2.1, 96.192.1-48.bo.2.2, 96.192.1-48.bo.2.3, 96.192.1-48.bo.2.4, 96.192.1-48.bo.2.5, 96.192.1-48.bo.2.6, 96.192.1-48.bo.2.7, 96.192.1-48.bo.2.8, 240.192.1-48.bo.2.1, 240.192.1-48.bo.2.2, 240.192.1-48.bo.2.3, 240.192.1-48.bo.2.4, 240.192.1-48.bo.2.5, 240.192.1-48.bo.2.6, 240.192.1-48.bo.2.7, 240.192.1-48.bo.2.8, 240.192.1-48.bo.2.9, 240.192.1-48.bo.2.10, 240.192.1-48.bo.2.11, 240.192.1-48.bo.2.12 |
Cyclic 48-isogeny field degree: |
$4$ |
Cyclic 48-torsion field degree: |
$64$ |
Full 48-torsion field degree: |
$12288$ |
Embedded model Embedded model in $\mathbb{P}^{3}$
$ 0 $ | $=$ | $ 3 x^{2} - 3 y^{2} + w^{2} $ |
| $=$ | $3 x^{2} + 3 y^{2} - 4 z^{2}$ |
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Maps to other modular curves
$j$-invariant map
of degree 96 from the embedded model of this modular curve to the modular curve
$X(1)$
:
$\displaystyle j$ |
$=$ |
$\displaystyle -\frac{(16z^{8}-16z^{4}w^{4}+w^{8})^{3}}{w^{4}z^{16}(2z-w)(2z+w)(4z^{2}+w^{2})}$ |
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.