$\GL_2(\Z/20\Z)$-generators: |
$\begin{bmatrix}3&5\\13&4\end{bmatrix}$, $\begin{bmatrix}3&15\\14&1\end{bmatrix}$, $\begin{bmatrix}15&1\\12&11\end{bmatrix}$ |
Contains $-I$: |
yes |
Quadratic refinements: |
20.48.1-20.e.2.1, 20.48.1-20.e.2.2, 20.48.1-20.e.2.3, 20.48.1-20.e.2.4, 40.48.1-20.e.2.1, 40.48.1-20.e.2.2, 40.48.1-20.e.2.3, 40.48.1-20.e.2.4, 60.48.1-20.e.2.1, 60.48.1-20.e.2.2, 60.48.1-20.e.2.3, 60.48.1-20.e.2.4, 120.48.1-20.e.2.1, 120.48.1-20.e.2.2, 120.48.1-20.e.2.3, 120.48.1-20.e.2.4, 140.48.1-20.e.2.1, 140.48.1-20.e.2.2, 140.48.1-20.e.2.3, 140.48.1-20.e.2.4, 220.48.1-20.e.2.1, 220.48.1-20.e.2.2, 220.48.1-20.e.2.3, 220.48.1-20.e.2.4, 260.48.1-20.e.2.1, 260.48.1-20.e.2.2, 260.48.1-20.e.2.3, 260.48.1-20.e.2.4, 280.48.1-20.e.2.1, 280.48.1-20.e.2.2, 280.48.1-20.e.2.3, 280.48.1-20.e.2.4 |
Cyclic 20-isogeny field degree: |
$6$ |
Cyclic 20-torsion field degree: |
$48$ |
Full 20-torsion field degree: |
$1920$ |
Weierstrass model Weierstrass model
$ y^{2} $ | $=$ | $ x^{3} + x^{2} - 1033x + 12438 $ |
This modular curve has 2 rational cusps but no known non-cuspidal rational points. The following are the coordinates of the rational cusps on this modular curve.
Maps to other modular curves
$j$-invariant map
of degree 24 from the Weierstrass model of this modular curve to the modular curve
$X(1)$
:
$\displaystyle j$ |
$=$ |
$\displaystyle \frac{1}{5}\cdot\frac{3640x^{2}y^{6}-384408525000x^{2}y^{4}z^{2}+122261047308125000x^{2}y^{2}z^{4}-4471838474273671875000x^{2}z^{6}-4649440xy^{6}z+36733105500000xy^{4}z^{3}-5899143220042500000xy^{2}z^{5}+163002312183380312500000xz^{7}-y^{8}+2361868060y^{6}z^{2}-2272337493493750y^{4}z^{4}+147217083015393437500y^{2}z^{6}-1485165953636176181640625z^{8}}{y^{2}(x^{2}y^{4}-2750x^{2}y^{2}z^{2}-15625x^{2}z^{4}+74xy^{4}z-51625xy^{2}z^{3}-296875xz^{5}+1319y^{4}z^{2}+1923375y^{2}z^{4}+10796875z^{6})}$ |
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.