Canonical model in $\mathbb{P}^{ 6 }$ defined by 10 equations
| $ 0 $ | $=$ | $ 2 x z - x w + y u - y v + t u + t v $ |
| $=$ | $x^{2} - 2 y^{2} + 2 y t + z^{2} + z w + u^{2} - v^{2}$ |
| $=$ | $x z + 2 x w + y v + 2 t u + t v$ |
| $=$ | $x y - 3 x t - z v + w u$ |
| $=$ | $\cdots$ |
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Singular plane model Singular plane model
| $ 0 $ | $=$ | $ x^{12} + 8 x^{10} y^{2} - 4 x^{10} z^{2} + 24 x^{8} y^{4} - 18 x^{8} y^{2} z^{2} + 6 x^{8} z^{4} + \cdots + y^{4} z^{8} $ |
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This modular curve has no $\Q_p$ points for $p=7$, 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
20.60.3.a.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle -5x$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle -3y-t$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle y-3t$ |
Equation of the image curve:
| $0$ |
$=$ |
$ X^{4}+9X^{2}Y^{2}+14Y^{4}-X^{2}YZ+8Y^{3}Z-14X^{2}Z^{2}-19Y^{2}Z^{2}+7YZ^{3}-Z^{4} $ |
Map
of degree 1 from the canonical model of this modular curve to the plane model of the modular curve
20.120.7.o.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle x$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle y$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle z$ |
Equation of the image curve:
| $0$ |
$=$ |
$ X^{12}+8X^{10}Y^{2}-4X^{10}Z^{2}+24X^{8}Y^{4}-18X^{8}Y^{2}Z^{2}+6X^{8}Z^{4}+32X^{6}Y^{6}-32X^{6}Y^{4}Z^{2}+15X^{6}Y^{2}Z^{4}-4X^{6}Z^{6}+16X^{4}Y^{8}-40X^{4}Y^{6}Z^{2}-23X^{4}Y^{4}Z^{4}-8X^{4}Y^{2}Z^{6}+X^{4}Z^{8}-32X^{2}Y^{8}Z^{2}+14X^{2}Y^{4}Z^{6}+3X^{2}Y^{2}Z^{8}+16Y^{8}Z^{4}+8Y^{6}Z^{6}+Y^{4}Z^{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.
