Canonical model in $\mathbb{P}^{ 7 }$ defined by 15 equations
| $ 0 $ | $=$ | $ 2 x t - x u + y u - w v + w r $ |
| $=$ | $x t + 2 y u - z w - z v$ |
| $=$ | $x w + x r + y w + y v - 2 w u$ |
| $=$ | $2 x^{2} + x y + y^{2} - z w$ |
| $=$ | $\cdots$ |
![Copy content]()
![Toggle raw display]()
Singular plane model Singular plane model
| $ 0 $ | $=$ | $ - 256 x^{10} + 288 x^{8} y^{2} + 1440 x^{8} z^{2} - 65 x^{6} y^{4} - 1690 x^{6} y^{2} z^{2} + \cdots + 500 y^{4} z^{6} $ |
![Copy content]()
![Toggle raw display]()
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
20.60.4.l.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle -x$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle y$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle -w-v$ |
| $\displaystyle W$ |
$=$ |
$\displaystyle w+r$ |
Equation of the image curve:
| $0$ |
$=$ |
$ 35X^{2}+5Y^{2}-Z^{2}+W^{2} $ |
|
$=$ |
$ 5X^{3}-5XY^{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.cn.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle x-y$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle z$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle \frac{1}{5}t$ |
Equation of the image curve:
| $0$ |
$=$ |
$ -256X^{10}+288X^{8}Y^{2}+1440X^{8}Z^{2}-65X^{6}Y^{4}-1690X^{6}Y^{2}Z^{2}-5225X^{6}Z^{4}+35X^{4}Y^{6}+245X^{4}Y^{4}Z^{2}+2150X^{4}Y^{2}Z^{4}+9000X^{4}Z^{6}-3X^{2}Y^{8}-20X^{2}Y^{6}Z^{2}-325X^{2}Y^{4}Z^{4}-3000X^{2}Y^{2}Z^{6}-10000X^{2}Z^{8}+Y^{10}+25Y^{8}Z^{2}+200Y^{6}Z^{4}+500Y^{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.
