$\GL_2(\Z/24\Z)$-generators: |
$\begin{bmatrix}1&16\\18&11\end{bmatrix}$, $\begin{bmatrix}7&22\\0&11\end{bmatrix}$, $\begin{bmatrix}11&7\\0&19\end{bmatrix}$, $\begin{bmatrix}11&13\\0&1\end{bmatrix}$, $\begin{bmatrix}19&5\\0&7\end{bmatrix}$ |
Contains $-I$: |
yes |
Quadratic refinements: |
24.48.1-24.eq.1.1, 24.48.1-24.eq.1.2, 24.48.1-24.eq.1.3, 24.48.1-24.eq.1.4, 24.48.1-24.eq.1.5, 24.48.1-24.eq.1.6, 24.48.1-24.eq.1.7, 24.48.1-24.eq.1.8, 24.48.1-24.eq.1.9, 24.48.1-24.eq.1.10, 24.48.1-24.eq.1.11, 24.48.1-24.eq.1.12, 24.48.1-24.eq.1.13, 24.48.1-24.eq.1.14, 24.48.1-24.eq.1.15, 24.48.1-24.eq.1.16, 120.48.1-24.eq.1.1, 120.48.1-24.eq.1.2, 120.48.1-24.eq.1.3, 120.48.1-24.eq.1.4, 120.48.1-24.eq.1.5, 120.48.1-24.eq.1.6, 120.48.1-24.eq.1.7, 120.48.1-24.eq.1.8, 120.48.1-24.eq.1.9, 120.48.1-24.eq.1.10, 120.48.1-24.eq.1.11, 120.48.1-24.eq.1.12, 120.48.1-24.eq.1.13, 120.48.1-24.eq.1.14, 120.48.1-24.eq.1.15, 120.48.1-24.eq.1.16, 168.48.1-24.eq.1.1, 168.48.1-24.eq.1.2, 168.48.1-24.eq.1.3, 168.48.1-24.eq.1.4, 168.48.1-24.eq.1.5, 168.48.1-24.eq.1.6, 168.48.1-24.eq.1.7, 168.48.1-24.eq.1.8, 168.48.1-24.eq.1.9, 168.48.1-24.eq.1.10, 168.48.1-24.eq.1.11, 168.48.1-24.eq.1.12, 168.48.1-24.eq.1.13, 168.48.1-24.eq.1.14, 168.48.1-24.eq.1.15, 168.48.1-24.eq.1.16, 264.48.1-24.eq.1.1, 264.48.1-24.eq.1.2, 264.48.1-24.eq.1.3, 264.48.1-24.eq.1.4, 264.48.1-24.eq.1.5, 264.48.1-24.eq.1.6, 264.48.1-24.eq.1.7, 264.48.1-24.eq.1.8, 264.48.1-24.eq.1.9, 264.48.1-24.eq.1.10, 264.48.1-24.eq.1.11, 264.48.1-24.eq.1.12, 264.48.1-24.eq.1.13, 264.48.1-24.eq.1.14, 264.48.1-24.eq.1.15, 264.48.1-24.eq.1.16, 312.48.1-24.eq.1.1, 312.48.1-24.eq.1.2, 312.48.1-24.eq.1.3, 312.48.1-24.eq.1.4, 312.48.1-24.eq.1.5, 312.48.1-24.eq.1.6, 312.48.1-24.eq.1.7, 312.48.1-24.eq.1.8, 312.48.1-24.eq.1.9, 312.48.1-24.eq.1.10, 312.48.1-24.eq.1.11, 312.48.1-24.eq.1.12, 312.48.1-24.eq.1.13, 312.48.1-24.eq.1.14, 312.48.1-24.eq.1.15, 312.48.1-24.eq.1.16 |
Cyclic 24-isogeny field degree: |
$4$ |
Cyclic 24-torsion field degree: |
$32$ |
Full 24-torsion field degree: |
$3072$ |
Weierstrass model Weierstrass model
$ y^{2} $ | $=$ | $ x^{3} - 876x - 9520 $ |
This modular curve has infinitely many rational points, including 4 stored non-cuspidal points.
Maps to other modular curves
$j$-invariant map
of degree 24 from the Weierstrass model of this modular curve to the modular curve
$X(1)$
:
$\displaystyle j$ |
$=$ |
$\displaystyle \frac{1}{2^6\cdot3^6}\cdot\frac{24x^{2}y^{6}+392688x^{2}y^{4}z^{2}+1715447808x^{2}y^{2}z^{4}+2481592329216x^{2}z^{6}+1176xy^{6}z+13374720xy^{4}z^{3}+58582206720xy^{2}z^{5}+85595676880896xz^{7}+y^{8}+19968y^{6}z^{2}+146437632y^{4}z^{4}+524385073152y^{2}z^{6}+720863480254464z^{8}}{z^{4}y^{2}(48x^{2}+1632xz+y^{2}+13440z^{2})}$ |
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.