Canonical model in $\mathbb{P}^{ 6 }$ defined by 10 equations
| $ 0 $ | $=$ | $ x^{2} + 2 x z + x w - y t - y u + y v - z^{2} + w^{2} - t^{2} + t v $ |
| $=$ | $x^{2} + y t - y u - y v + z^{2} - 2 w^{2} + t^{2} - t u - t v$ |
| $=$ | $x y + x t + 2 x u + x v - y z - z t - z u + z v + w t + w u$ |
| $=$ | $2 x^{2} - x z + 2 x w - y t + y u + y v - z^{2} + z w + w^{2} + t u$ |
| $=$ | $\cdots$ |
![Copy content]()
![Toggle raw display]()
Singular plane model Singular plane model
| $ 0 $ | $=$ | $ - 441 x^{10} - 1764 x^{9} z + 468 x^{8} y^{2} + 609 x^{8} z^{2} + 2655 x^{7} y^{2} z + 672 x^{7} z^{3} + \cdots + z^{10} $ |
![Copy content]()
![Toggle raw display]()
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
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.cl.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle x$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle y$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle z$ |
Equation of the image curve:
| $0$ |
$=$ |
$ -441X^{10}-1764X^{9}Z+468X^{8}Y^{2}+609X^{8}Z^{2}+2655X^{7}Y^{2}Z+672X^{7}Z^{3}-180X^{6}Y^{4}+1600X^{6}Y^{2}Z^{2}-142X^{6}Z^{4}-954X^{5}Y^{4}Z-1485X^{5}Y^{2}Z^{3}+104X^{5}Z^{5}+36X^{4}Y^{6}-999X^{4}Y^{4}Z^{2}-992X^{4}Y^{2}Z^{4}-34X^{4}Z^{6}+63X^{3}Y^{6}Z-324X^{3}Y^{4}Z^{3}+1005X^{3}Y^{2}Z^{5}-32X^{3}Z^{7}-9X^{2}Y^{8}-32X^{2}Y^{6}Z^{2}-174X^{2}Y^{4}Z^{4}+592X^{2}Y^{2}Z^{6}+7X^{2}Z^{8}+9XY^{6}Z^{3}+14XY^{4}Z^{5}+65XY^{2}Z^{7}-4XZ^{9}+9Y^{4}Z^{6}-4Y^{2}Z^{8}+Z^{10} $ |
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.
