Canonical model in $\mathbb{P}^{ 6 }$ defined by 10 equations
| $ 0 $ | $=$ | $ x w - x t + x v + y w + y t - z w - z t - z u + 2 z v $ |
| $=$ | $x t + 2 x u - 2 x v + y w + y t + y u - 2 y v + z u - 2 z v$ |
| $=$ | $3 x w + x t - x u - x v + 2 y w - 2 y t - 3 z u$ |
| $=$ | $2 x w + 2 x t - x u - 2 y w + y u + y v + 2 z w - z t - 2 z u$ |
| $=$ | $\cdots$ |
![Copy content]()
![Toggle raw display]()
Singular plane model Singular plane model
| $ 0 $ | $=$ | $ - 16 x^{10} + 108 x^{8} y^{2} + 180 x^{8} z^{2} + 12 x^{7} y^{3} - 108 x^{7} y z^{2} + \cdots + 36 y^{6} z^{4} $ |
![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
10.60.3.a.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle x+3y-z$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle -2x-y-3z$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle 2x+y-2z$ |
Equation of the image curve:
| $0$ |
$=$ |
$ 2X^{4}-3X^{3}Y-5X^{2}Y^{2}-4XY^{3}-2Y^{4}+3X^{3}Z-18X^{2}YZ-17XY^{2}Z+4Y^{3}Z-5X^{2}Z^{2}+17XYZ^{2}-6Y^{2}Z^{2}+4XZ^{3}+4YZ^{3}-2Z^{4} $ |
Map
of degree 1 from the canonical model of this modular curve to the plane model of the modular curve
60.120.7.b.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle x+z$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle y$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle \frac{1}{3}w$ |
Equation of the image curve:
| $0$ |
$=$ |
$ -16X^{10}+108X^{8}Y^{2}+180X^{8}Z^{2}+12X^{7}Y^{3}-108X^{7}YZ^{2}-268X^{6}Y^{4}-888X^{6}Y^{2}Z^{2}-1044X^{6}Z^{4}-52X^{5}Y^{5}+528X^{5}Y^{3}Z^{2}+1260X^{5}YZ^{4}+307X^{4}Y^{6}+645X^{4}Y^{4}Z^{2}+135X^{4}Y^{2}Z^{4}+945X^{4}Z^{6}+63X^{3}Y^{7}-129X^{3}Y^{5}Z^{2}+837X^{3}Y^{3}Z^{4}+189X^{3}YZ^{6}-167X^{2}Y^{8}-120X^{2}Y^{6}Z^{2}-216X^{2}Y^{4}Z^{4}+54X^{2}Y^{2}Z^{6}+81X^{2}Z^{8}-24XY^{9}+30XY^{7}Z^{2}-144XY^{5}Z^{4}+162XY^{3}Z^{6}+36Y^{10}-48Y^{8}Z^{2}+36Y^{6}Z^{4} $ |
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.
