Canonical model in $\mathbb{P}^{ 4 }$ defined by 3 equations
| $ 0 $ | $=$ | $ 5 x^{2} - 3 x y + 7 x z + x w - y t - 2 w t + t^{2} $ |
| $=$ | $3 x y - x w + x t - 5 y^{2} - 7 y z + y w + w^{2} - t^{2}$ |
| $=$ | $x^{2} + 4 x y + 7 x z + x w + 2 x t + y^{2} + 7 y z - 3 y w + 2 y t + 14 z^{2} - 3 w^{2} + 4 w t - 4 t^{2}$ |
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Singular plane model Singular plane model
| $ 0 $ | $=$ | $ 30976 x^{8} + 83424 x^{7} z - 60340 x^{6} y^{2} + 60340 x^{6} y z - 12068 x^{6} z^{2} - 50120 x^{5} y^{2} z + \cdots + 46 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
:
| $\displaystyle X$ |
$=$ |
$\displaystyle x+y+3z$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle -2x+3y-z$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle -3x+2y+z$ |
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
70.120.5.b.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle x$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle w$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle t$ |
Equation of the image curve:
| $0$ |
$=$ |
$ 30976X^{8}-60340X^{6}Y^{2}+10780X^{4}Y^{4}+83424X^{7}Z+60340X^{6}YZ-50120X^{5}Y^{2}Z-21560X^{4}Y^{3}Z+16660X^{3}Y^{4}Z-12068X^{6}Z^{2}+50120X^{5}YZ^{2}+74935X^{4}Y^{2}Z^{2}-33320X^{3}Y^{3}Z^{2}-15680X^{2}Y^{4}Z^{2}-95368X^{5}Z^{3}-64155X^{4}YZ^{3}+40845X^{3}Y^{2}Z^{3}+31360X^{2}Y^{3}Z^{3}-1960XY^{4}Z^{3}+22470X^{4}Z^{4}-24185X^{3}YZ^{4}-33460X^{2}Y^{2}Z^{4}+3920XY^{3}Z^{4}+980Y^{4}Z^{4}+13958X^{3}Z^{5}+17780X^{2}YZ^{5}-4690XY^{2}Z^{5}-1960Y^{3}Z^{5}-1988X^{2}Z^{6}+2730XYZ^{6}+1400Y^{2}Z^{6}-464XZ^{7}-420YZ^{7}+46Z^{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.
