Canonical model in $\mathbb{P}^{ 6 }$ defined by 10 equations
| $ 0 $ | $=$ | $ 2 x^{2} + 2 x z - y v + z w - w^{2} $ |
| $=$ | $x^{2} - 3 x w + y t - y u - y v + z^{2} - w^{2} + t^{2} - t u$ |
| $=$ | $3 x y - x t - y w - z t - z v - w u$ |
| $=$ | $x y - 2 x u + x v - 2 y z + y w + z t + z v - w u + w v$ |
| $=$ | $\cdots$ |
![Copy content]()
![Toggle raw display]()
Singular plane model Singular plane model
| $ 0 $ | $=$ | $ 256 x^{10} + 480 x^{9} z - 20 x^{8} y^{2} - 607 x^{8} z^{2} + 352 x^{7} y^{2} z - 1996 x^{7} z^{3} + \cdots + z^{10} $ |
![Copy content]()
![Toggle raw display]()
This modular curve has no $\Q_p$ points for $p=3$, and therefore no 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
20.60.3.c.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle 5x+z-2w$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle -z-3w$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle -3z+w$ |
Equation of the image curve:
| $0$ |
$=$ |
$ 2X^{4}-4X^{3}Y+6X^{2}Y^{2}-4XY^{3}+2Y^{4}+4X^{3}Z+17X^{2}YZ-17XY^{2}Z-4Y^{3}Z+5X^{2}Z^{2}+18XYZ^{2}+5Y^{2}Z^{2}+3XZ^{3}-3YZ^{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.cj.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle x$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle y$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle w$ |
Equation of the image curve:
| $0$ |
$=$ |
$ 256X^{10}+480X^{9}Z-20X^{8}Y^{2}-607X^{8}Z^{2}+352X^{7}Y^{2}Z-1996X^{7}Z^{3}-9X^{6}Y^{4}+624X^{6}Y^{2}Z^{2}-912X^{6}Z^{4}-150X^{5}Y^{4}Z-303X^{5}Y^{2}Z^{3}+1524X^{5}Z^{5}-20X^{4}Y^{6}+40X^{4}Y^{4}Z^{2}-1300X^{4}Y^{2}Z^{4}+2142X^{4}Z^{6}-4X^{3}Y^{6}Z+386X^{3}Y^{4}Z^{3}-1094X^{3}Y^{2}Z^{5}+1116X^{3}Z^{7}+4X^{2}Y^{8}-28X^{2}Y^{6}Z^{2}+269X^{2}Y^{4}Z^{4}-420X^{2}Y^{2}Z^{6}+272X^{2}Z^{8}-28XY^{6}Z^{3}+52XY^{4}Z^{5}-75XY^{2}Z^{7}+28XZ^{9}+4Y^{4}Z^{6}-4Y^{2}Z^{8}+Z^{10} $ |
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.
