$\GL_2(\Z/60\Z)$-generators: |
$\begin{bmatrix}4&7\\39&50\end{bmatrix}$, $\begin{bmatrix}4&59\\3&52\end{bmatrix}$, $\begin{bmatrix}25&18\\42&59\end{bmatrix}$, $\begin{bmatrix}47&36\\36&11\end{bmatrix}$, $\begin{bmatrix}50&29\\51&2\end{bmatrix}$ |
Contains $-I$: |
yes |
Quadratic refinements: |
60.48.1-60.y.1.1, 60.48.1-60.y.1.2, 60.48.1-60.y.1.3, 60.48.1-60.y.1.4, 60.48.1-60.y.1.5, 60.48.1-60.y.1.6, 60.48.1-60.y.1.7, 60.48.1-60.y.1.8, 60.48.1-60.y.1.9, 60.48.1-60.y.1.10, 60.48.1-60.y.1.11, 60.48.1-60.y.1.12, 60.48.1-60.y.1.13, 60.48.1-60.y.1.14, 60.48.1-60.y.1.15, 60.48.1-60.y.1.16, 120.48.1-60.y.1.1, 120.48.1-60.y.1.2, 120.48.1-60.y.1.3, 120.48.1-60.y.1.4, 120.48.1-60.y.1.5, 120.48.1-60.y.1.6, 120.48.1-60.y.1.7, 120.48.1-60.y.1.8, 120.48.1-60.y.1.9, 120.48.1-60.y.1.10, 120.48.1-60.y.1.11, 120.48.1-60.y.1.12, 120.48.1-60.y.1.13, 120.48.1-60.y.1.14, 120.48.1-60.y.1.15, 120.48.1-60.y.1.16 |
Cyclic 60-isogeny field degree: |
$12$ |
Cyclic 60-torsion field degree: |
$192$ |
Full 60-torsion field degree: |
$92160$ |
Weierstrass model Weierstrass model
$ y^{2} $ | $=$ | $ x^{3} - x^{2} - 608x + 5712 $ |
This modular curve has infinitely many rational points, including 12 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
$X(1)$
:
$\displaystyle j$ |
$=$ |
$\displaystyle \frac{1}{5^6}\cdot\frac{20x^{2}y^{6}-189375x^{2}y^{4}z^{2}+478750000x^{2}y^{2}z^{4}-400791015625x^{2}z^{6}-830xy^{6}z+5501250xy^{4}z^{3}-13943515625xy^{2}z^{5}+11787343750000xz^{7}-y^{8}+11830y^{6}z^{2}-50854375y^{4}z^{4}+106223984375y^{2}z^{6}-84734218750000z^{8}}{z^{4}y^{2}(40x^{2}-1160xz-y^{2}+8160z^{2})}$ |
Hi
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Cover information
Click on a modular curve in the diagram to see information about it.
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The following modular covers realize this modular curve as a fiber product over $X(1)$.
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.