Canonical model in $\mathbb{P}^{ 6 }$ defined by 10 equations
| $ 0 $ | $=$ | $ x w - x t - x u + x v + y w - y t + y u + z t - z u $ |
| $=$ | $2 x w + x t + x v + y w + 2 y v + z t + z u$ |
| $=$ | $2 x u + x v + y t + y u + z w + z t + z u + 2 z v$ |
| $=$ | $3 x y + 3 x z + 3 y^{2} - 3 y z - u v$ |
| $=$ | $\cdots$ |
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Singular plane model Singular plane model
| $ 0 $ | $=$ | $ 2187 x^{12} + 40824 x^{11} y + 229392 x^{10} y^{2} + 6480 x^{10} z^{2} + 358992 x^{9} y^{3} + \cdots + 27 y^{4} z^{8} $ |
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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.c.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle x$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle y$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle w$ |
Equation of the image curve:
| $0$ |
$=$ |
$ 2187X^{12}+40824X^{11}Y+229392X^{10}Y^{2}+6480X^{10}Z^{2}+358992X^{9}Y^{3}+2106X^{9}YZ^{2}+134568X^{8}Y^{4}-123750X^{8}Y^{2}Z^{2}-3288X^{8}Z^{4}-52704X^{7}Y^{5}-240120X^{7}Y^{3}Z^{2}-8094X^{7}YZ^{4}-15552X^{6}Y^{6}-91368X^{6}Y^{4}Z^{2}+18645X^{6}Y^{2}Z^{4}+520X^{6}Z^{6}+1728X^{5}Y^{7}+33624X^{5}Y^{5}Z^{2}+51606X^{5}Y^{3}Z^{4}+1748X^{5}YZ^{6}+432X^{4}Y^{8}+9864X^{4}Y^{6}Z^{2}+21171X^{4}Y^{4}Z^{4}-262X^{4}Y^{2}Z^{6}-27X^{4}Z^{8}-1152X^{3}Y^{7}Z^{2}-5424X^{3}Y^{5}Z^{4}-4012X^{3}Y^{3}Z^{6}-108X^{3}YZ^{8}-288X^{2}Y^{8}Z^{2}-1584X^{2}Y^{6}Z^{4}-1986X^{2}Y^{4}Z^{6}-81X^{2}Y^{2}Z^{8}+192XY^{7}Z^{4}+24XY^{5}Z^{6}+54XY^{3}Z^{8}+48Y^{8}Z^{4}+8Y^{6}Z^{6}+27Y^{4}Z^{8} $ |
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.
