Canonical model in $\mathbb{P}^{ 4 }$ defined by 3 equations
| $ 0 $ | $=$ | $ 2 x^{2} + x w + y z - 2 w^{2} - t^{2} $ |
| $=$ | $2 x^{2} - 4 x w - y^{2} - 2 y z - z^{2} - 2 w^{2}$ |
| $=$ | $9 x^{2} - 3 x w + 2 y^{2} + 3 y z + 2 y t + 2 z^{2} - 2 z t + 6 w^{2} + 3 t^{2}$ |
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Singular plane model Singular plane model
| $ 0 $ | $=$ | $ 50 x^{8} + 525 x^{6} y^{2} + 950 x^{6} y z + 465 x^{6} z^{2} + 50 x^{4} y^{4} + 300 x^{4} y^{3} z + \cdots + 8 y^{2} z^{6} $ |
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This modular curve has no real points, and therefore no 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
:
| $\displaystyle X$ |
$=$ |
$\displaystyle 3y+2z+3t$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle 4y+z-t$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle 2y-2z+2t$ |
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.h.2
:
| $\displaystyle X$ |
$=$ |
$\displaystyle x$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle y$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle t$ |
Equation of the image curve:
| $0$ |
$=$ |
$ 50X^{8}+525X^{6}Y^{2}+950X^{6}YZ+465X^{6}Z^{2}+50X^{4}Y^{4}+300X^{4}Y^{3}Z+870X^{4}Y^{2}Z^{2}+640X^{4}YZ^{3}+92X^{4}Z^{4}+40X^{2}Y^{4}Z^{2}+160X^{2}Y^{3}Z^{3}+220X^{2}Y^{2}Z^{4}+40X^{2}YZ^{5}+4X^{2}Z^{6}+8Y^{4}Z^{4}+16Y^{3}Z^{5}+8Y^{2}Z^{6} $ |
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.
