| $\GL_2(\Z/52\Z)$-generators: |
$\begin{bmatrix}7&20\\23&19\end{bmatrix}$, $\begin{bmatrix}23&18\\14&17\end{bmatrix}$ |
| Contains $-I$: |
yes |
| Quadratic refinements: |
104.48.0-52.e.1.1, 104.48.0-52.e.1.2, 104.48.0-52.e.1.3, 104.48.0-52.e.1.4, 104.48.0-52.e.1.5, 104.48.0-52.e.1.6, 104.48.0-52.e.1.7, 104.48.0-52.e.1.8, 312.48.0-52.e.1.1, 312.48.0-52.e.1.2, 312.48.0-52.e.1.3, 312.48.0-52.e.1.4, 312.48.0-52.e.1.5, 312.48.0-52.e.1.6, 312.48.0-52.e.1.7, 312.48.0-52.e.1.8 |
| Cyclic 52-isogeny field degree: |
$28$ |
| Cyclic 52-torsion field degree: |
$672$ |
| Full 52-torsion field degree: |
$104832$ |
This modular curve is isomorphic to $\mathbb{P}^1$.
This modular curve has infinitely many rational points, including 14 stored non-cuspidal points.
Maps to other modular curves
$j$-invariant map
of degree 24 to the modular curve
$X(1)$
:
| $\displaystyle j$ |
$=$ |
$\displaystyle \frac{2^{14}}{13^3}\cdot\frac{(4x-3y)^{24}(27328512x^{8}-157188096x^{7}y+455483392x^{6}y^{2}-850397184x^{5}y^{3}+1055122432x^{4}y^{4}-844491648x^{3}y^{5}+415848160x^{2}y^{6}-115843416xy^{7}+14480427y^{8})^{3}}{(4x-3y)^{24}(16x^{2}-24xy+13y^{2})^{4}(5888x^{4}-19968x^{3}y+16224x^{2}y^{2}-2197y^{4})^{4}}$ |
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.
