Canonical model in $\mathbb{P}^{ 6 }$ defined by 10 equations
| $ 0 $ | $=$ | $ x w + 2 x t - x v + z u + z v $ |
| $=$ | $x w - x u - y w + y t + y u - y v - z w - z t$ |
| $=$ | $2 x w - x t + x u - x v + y u + y v - z u - z v$ |
| $=$ | $x w - x u - 2 y w - y t + y u + 2 z w + z u - 2 z v$ |
| $=$ | $\cdots$ |
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Singular plane model Singular plane model
| $ 0 $ | $=$ | $ 7200 x^{12} + 28800 x^{11} y - 40800 x^{10} y^{2} + 1600 x^{10} z^{2} - 60000 x^{9} y^{3} + \cdots + 2 y^{4} 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
10.60.3.a.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle x+y-3z$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle -2x+3y+z$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle 2x+2y-z$ |
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.g.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle x$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle y$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle w$ |
Equation of the image curve:
| $0$ |
$=$ |
$ 7200X^{12}+28800X^{11}Y-40800X^{10}Y^{2}+1600X^{10}Z^{2}-60000X^{9}Y^{3}+9200X^{9}YZ^{2}+293000X^{8}Y^{4}-9000X^{8}Y^{2}Z^{2}+160X^{8}Z^{4}-457200X^{7}Y^{5}+34050X^{7}Y^{3}Z^{2}+320X^{7}YZ^{4}+368200X^{6}Y^{6}-101825X^{6}Y^{4}Z^{2}+3610X^{6}Y^{2}Z^{4}-145200X^{5}Y^{7}+98150X^{5}Y^{5}Z^{2}-8570X^{5}Y^{3}Z^{4}+80X^{5}YZ^{6}-12000X^{4}Y^{8}-27000X^{4}Y^{6}Z^{2}+6110X^{4}Y^{4}Z^{4}-180X^{4}Y^{2}Z^{6}+30000X^{3}Y^{9}-4300X^{3}Y^{7}Z^{2}-2330X^{3}Y^{5}Z^{4}+220X^{3}Y^{3}Z^{6}-3800X^{2}Y^{10}+325X^{2}Y^{8}Z^{2}+1010X^{2}Y^{6}Z^{4}-160X^{2}Y^{4}Z^{6}+2X^{2}Y^{2}Z^{8}-1200XY^{11}+500XY^{9}Z^{2}-200XY^{7}Z^{4}+60XY^{5}Z^{6}-4XY^{3}Z^{8}+200Y^{12}-100Y^{10}Z^{2}+50Y^{8}Z^{4}-20Y^{6}Z^{6}+2Y^{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.
