Canonical model in $\mathbb{P}^{ 6 }$ defined by 10 equations
| $ 0 $ | $=$ | $ x t - x u - x v - y w - y t - y u - 2 y v - z w + z t $ |
| $=$ | $x w + x u - 2 y t - y u - 2 y v + z w + z t + z u + 2 z v$ |
| $=$ | $2 x^{2} + 2 y^{2} + 2 y z - 2 z^{2} + w t + w v + u v + v^{2}$ |
| $=$ | $2 x^{2} - 2 x z - 2 y z - 4 z^{2} - w u + t^{2} - t u + t v - u^{2} - u v$ |
| $=$ | $\cdots$ |
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Singular plane model Singular plane model
| $ 0 $ | $=$ | $ 256 x^{10} - 384 x^{9} y - 176 x^{8} y^{2} - 40 x^{8} z^{2} + 752 x^{7} y^{3} + 456 x^{7} y z^{2} + \cdots + y^{2} 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
:
| $\displaystyle X$ |
$=$ |
$\displaystyle -2x-y-3z$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle 4x+2y+z$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle x+3y-z$ |
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
40.120.7.a.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle y$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle z$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle w$ |
Equation of the image curve:
| $0$ |
$=$ |
$ 256X^{10}-384X^{9}Y-176X^{8}Y^{2}-40X^{8}Z^{2}+752X^{7}Y^{3}+456X^{7}YZ^{2}-476X^{6}Y^{4}-328X^{6}Y^{2}Z^{2}-29X^{6}Z^{4}-176X^{5}Y^{5}-230X^{5}Y^{3}Z^{2}-145X^{5}YZ^{4}+376X^{4}Y^{6}+240X^{4}Y^{4}Z^{2}+190X^{4}Y^{2}Z^{4}+30X^{4}Z^{6}-192X^{3}Y^{7}+98X^{3}Y^{5}Z^{2}+83X^{3}Y^{3}Z^{4}-12X^{3}YZ^{6}+36X^{2}Y^{8}-196X^{2}Y^{6}Z^{2}-111X^{2}Y^{4}Z^{4}-52X^{2}Y^{2}Z^{6}-X^{2}Z^{8}+72XY^{7}Z^{2}+4XY^{5}Z^{4}-12XY^{3}Z^{6}+XYZ^{8}+36Y^{6}Z^{4}+8Y^{4}Z^{6}+Y^{2}Z^{8} $ |
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.
