Canonical model in $\mathbb{P}^{ 6 }$ defined by 10 equations
| $ 0 $ | $=$ | $ x w + x t - x v + z u $ |
| $=$ | $x w - x t - x u - y u + z u$ |
| $=$ | $y w + y t - y v - 2 z t - z u + z v$ |
| $=$ | $2 x^{2} + 6 x y + 2 x z - t u$ |
| $=$ | $\cdots$ |
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Singular plane model Singular plane model
| $ 0 $ | $=$ | $ 2500 x^{12} - 3500 x^{10} y^{2} + 3500 x^{10} y z + 1750 x^{10} z^{2} + 1225 x^{8} y^{4} + \cdots + 16 y^{2} z^{10} $ |
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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
10.60.3.a.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle 2x+y-3z$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle -4x-2y+z$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle -x-3y-z$ |
Equation of the image curve:
| $0$ |
$=$ |
$ 2X^{4}-3X^{3}Y-5X^{2}Y^{2}-4XY^{3}-2Y^{4}+3X^{3}Z-18X^{2}YZ-17XY^{2}Z+4Y^{3}Z-5X^{2}Z^{2}+17XYZ^{2}-6Y^{2}Z^{2}+4XZ^{3}+4YZ^{3}-2Z^{4} $ |
Map
of degree 1 from the canonical model of this modular curve to the plane model of the modular curve
40.120.7.f.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle x$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle \frac{1}{2}v$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle \frac{1}{2}u$ |
Equation of the image curve:
| $0$ |
$=$ |
$ 2500X^{12}-3500X^{10}Y^{2}+1225X^{8}Y^{4}+3500X^{10}YZ-2450X^{8}Y^{3}Z+1750X^{10}Z^{2}-4825X^{8}Y^{2}Z^{2}+5200X^{6}Y^{4}Z^{2}+6050X^{8}YZ^{3}-10400X^{6}Y^{3}Z^{3}-900X^{8}Z^{4}+4500X^{6}Y^{2}Z^{4}+2200X^{4}Y^{4}Z^{4}+700X^{6}YZ^{5}-4400X^{4}Y^{3}Z^{5}-600X^{6}Z^{6}+2640X^{4}Y^{2}Z^{6}+320X^{2}Y^{4}Z^{6}-440X^{4}YZ^{7}-640X^{2}Y^{3}Z^{7}-80X^{4}Z^{8}+400X^{2}Y^{2}Z^{8}+16Y^{4}Z^{8}-80X^{2}YZ^{9}-32Y^{3}Z^{9}+16Y^{2}Z^{10} $ |
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.
