Canonical model in $\mathbb{P}^{ 8 }$ defined by 21 equations
| $ 0 $ | $=$ | $ y^{2} + y w + z^{2} - z w $ |
| $=$ | $x w - 2 y u - y v - y s - z s + w^{2} - w u - 2 w v$ |
| $=$ | $x y + 3 x z + y w + y u - y v + y s - z u$ |
| $=$ | $x y - 2 x z - x t + x u - x s - y^{2} - y w + y v + y s - z u + z s + w u + w v + w s - t^{2} + t u + \cdots + v r$ |
| $=$ | $\cdots$ |
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Singular plane model Singular plane model
| $ 0 $ | $=$ | $ 612900 x^{4} y^{12} - 2790000 x^{4} y^{11} z + 5689800 x^{4} y^{10} z^{2} - 6044400 x^{4} y^{9} z^{3} + \cdots + z^{16} $ |
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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 between models of this curve
Birational map from canonical model to plane model:
| $\displaystyle X$ |
$=$ |
$\displaystyle x$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle 6y$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle 6z$ |
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
60.80.5.k.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle x$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle -y-z$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle t$ |
| $\displaystyle W$ |
$=$ |
$\displaystyle -y+z-w$ |
| $\displaystyle T$ |
$=$ |
$\displaystyle z-w+v$ |
Equation of the image curve:
| $0$ |
$=$ |
$ 10XY+2Y^{2}+YZ+5XW-5YW-3ZW+2W^{2}+3YT-4WT $ |
|
$=$ |
$ 10X^{2}-4Y^{2}-2YZ+2Z^{2}-5YW+4ZW-W^{2}+4YT-8ZT-8WT+8T^{2} $ |
|
$=$ |
$ 20XZ-22YZ-28Z^{2}+10XW+YW-6ZW+10W^{2}-20XT+4YT+12ZT+2WT-2T^{2} $ |
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Cover information
Click on a modular curve in the diagram to see information about it.
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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.
