Canonical model in $\mathbb{P}^{ 4 }$ defined by 3 equations
| $ 0 $ | $=$ | $ x^{2} + 3 x y + y^{2} + z t - w^{2} $ |
| $=$ | $2 x w - 2 y w - 3 z^{2} - 2 z t + 2 w^{2}$ |
| $=$ | $2 x^{2} + x y + 2 y^{2} + 2 z^{2} + z t + 3 w^{2} - 2 t^{2}$ |
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Singular plane model Singular plane model
| $ 0 $ | $=$ | $ 100 x^{4} y^{4} - 100 x^{4} y^{2} z^{2} + 25 x^{4} z^{4} - 1360 x^{2} y^{6} + 360 x^{2} y^{4} z^{2} + \cdots + 25 z^{8} $ |
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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
Map
of degree 2 from the canonical model of this modular curve to the canonical model of the modular curve
20.48.3.i.2
:
| $\displaystyle X$ |
$=$ |
$\displaystyle 3x+2y+3w$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle 4x+y-w$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle 2x-2y+2w$ |
Equation of the image curve:
| $0$ |
$=$ |
$ 6X^{3}Y-22X^{2}Y^{2}+6XY^{3}+12X^{2}YZ+14XY^{2}Z-6Y^{3}Z-3X^{2}Z^{2}-2XYZ^{2}+5Y^{2}Z^{2}-10YZ^{3}+2Z^{4} $ |
Map
of degree 1 from the canonical model of this modular curve to the plane model of the modular curve
40.96.5.n.2
:
| $\displaystyle X$ |
$=$ |
$\displaystyle x+y$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle \frac{1}{2}z$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle w$ |
Equation of the image curve:
| $0$ |
$=$ |
$ 100X^{4}Y^{4}-100X^{4}Y^{2}Z^{2}+25X^{4}Z^{4}-1360X^{2}Y^{6}+360X^{2}Y^{4}Z^{2}+100X^{2}Y^{2}Z^{4}-50X^{2}Z^{6}+4624Y^{8}-1824Y^{6}Z^{2}+1464Y^{4}Z^{4}-360Y^{2}Z^{6}+25Z^{8} $ |
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.
