Canonical model in $\mathbb{P}^{ 6 }$ defined by 10 equations
| $ 0 $ | $=$ | $ x w - x t - x v - y u $ |
| $=$ | $x w + x t + y u - z u$ |
| $=$ | $2 y w - y v - z w + z t + z v$ |
| $=$ | $3 x z - 6 y z - 3 z^{2} - 2 w t + 2 w v + u v - v^{2}$ |
| $=$ | $\cdots$ |
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Singular plane model Singular plane model
| $ 0 $ | $=$ | $ 1822500 x^{12} - 1701000 x^{10} y^{2} + 850500 x^{10} y z + 212625 x^{10} z^{2} + 396900 x^{8} y^{4} + \cdots + y^{2} z^{10} $ |
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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
:
| $\displaystyle X$ |
$=$ |
$\displaystyle -x-3y+z$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle -3x+y-2z$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle -2x-y+2z$ |
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.f.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle x$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle \frac{1}{2}v$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle u$ |
Equation of the image curve:
| $0$ |
$=$ |
$ 1822500X^{12}-1701000X^{10}Y^{2}+396900X^{8}Y^{4}+850500X^{10}YZ-396900X^{8}Y^{3}Z+212625X^{10}Z^{2}-390825X^{8}Y^{2}Z^{2}+280800X^{6}Y^{4}Z^{2}+245025X^{8}YZ^{3}-280800X^{6}Y^{3}Z^{3}-18225X^{8}Z^{4}+60750X^{6}Y^{2}Z^{4}+19800X^{4}Y^{4}Z^{4}+4725X^{6}YZ^{5}-19800X^{4}Y^{3}Z^{5}-2025X^{6}Z^{6}+5940X^{4}Y^{2}Z^{6}+480X^{2}Y^{4}Z^{6}-495X^{4}YZ^{7}-480X^{2}Y^{3}Z^{7}-45X^{4}Z^{8}+150X^{2}Y^{2}Z^{8}+4Y^{4}Z^{8}-15X^{2}YZ^{9}-4Y^{3}Z^{9}+Y^{2}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.
