Canonical model in $\mathbb{P}^{ 6 }$ defined by 10 equations
| $ 0 $ | $=$ | $ x v - t u $ |
| $=$ | $x v + w^{2} + t^{2}$ |
| $=$ | $z v + w u$ |
| $=$ | $x w + z t$ |
| $=$ | $\cdots$ |
![Copy content]()
![Toggle raw display]()
Singular plane model Singular plane model
| $ 0 $ | $=$ | $ - x^{9} - 2 x^{5} y^{2} z^{2} + 9 x^{4} y^{4} z - 8 x^{3} y^{6} - x y^{4} z^{4} + y^{6} z^{3} $ |
![Copy content]()
![Toggle raw display]()
This modular curve has 1 rational cusp 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
30.45.3.a.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle -x$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle w$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle x+w-v$ |
Equation of the image curve:
| $0$ |
$=$ |
$ 7X^{4}-6X^{3}Y+5X^{2}Y^{2}-5XY^{3}-Y^{4}-3X^{3}Z-3X^{2}YZ-5XY^{2}Z+2Y^{3}Z-3X^{2}Z^{2}+3XYZ^{2}-Y^{2}Z^{2}-XZ^{3} $ |
Map
of degree 1 from the canonical model of this modular curve to the plane model of the modular curve
60.90.7.b.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle x$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle y$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle w$ |
Equation of the image curve:
| $0$ |
$=$ |
$ -X^{9}-2X^{5}Y^{2}Z^{2}+9X^{4}Y^{4}Z-8X^{3}Y^{6}-XY^{4}Z^{4}+Y^{6}Z^{3} $ |
The following modular covers realize this modular curve as a fiber product over $X(1)$.
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.
