Canonical model in $\mathbb{P}^{ 7 }$ defined by 15 equations
| $ 0 $ | $=$ | $ x r + y v - 2 w u $ |
| $=$ | $x t + 2 y u + z v$ |
| $=$ | $x t - x u - y u - z v - w v + w r$ |
| $=$ | $2 x v + y v - y r - w t$ |
| $=$ | $\cdots$ |
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Singular plane model Singular plane model
| $ 0 $ | $=$ | $ 1024 x^{10} - 1152 x^{8} y^{2} + 2880 x^{8} z^{2} + 260 x^{6} y^{4} - 3380 x^{6} y^{2} z^{2} + \cdots + 250 y^{4} z^{6} $ |
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This modular curve has 2 rational cusps but no known non-cuspidal rational points. The following are the coordinates of the rational cusps on this modular curve.
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
40.60.4.bh.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle x$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle y$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle -v$ |
| $\displaystyle W$ |
$=$ |
$\displaystyle r$ |
Equation of the image curve:
| $0$ |
$=$ |
$ 70X^{2}+10Y^{2}+Z^{2}-W^{2} $ |
|
$=$ |
$ 10X^{3}-10XY^{2}-XZ^{2}-YZW $ |
Map
of degree 1 from the canonical model of this modular curve to the plane model of the modular curve
40.120.8.cp.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle x-y$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle z$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle \frac{1}{5}t$ |
Equation of the image curve:
| $0$ |
$=$ |
$ 1024X^{10}-1152X^{8}Y^{2}+2880X^{8}Z^{2}+260X^{6}Y^{4}-3380X^{6}Y^{2}Z^{2}+5225X^{6}Z^{4}-140X^{4}Y^{6}+490X^{4}Y^{4}Z^{2}-2150X^{4}Y^{2}Z^{4}+4500X^{4}Z^{6}+12X^{2}Y^{8}-40X^{2}Y^{6}Z^{2}+325X^{2}Y^{4}Z^{4}-1500X^{2}Y^{2}Z^{6}+2500X^{2}Z^{8}-4Y^{10}+50Y^{8}Z^{2}-200Y^{6}Z^{4}+250Y^{4}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.
