Canonical model in $\mathbb{P}^{ 7 }$ defined by 15 equations
| $ 0 $ | $=$ | $ 2 x^{2} + x y + x w + x v + x r + y v - 2 z^{2} + 2 z w + z v - z r - t u + t r $ |
| $=$ | $x^{2} + x y + 2 x z - x w - x t + x u - x v + y z + z^{2} - z w - z t - z v + z r$ |
| $=$ | $x^{2} + x y - 2 x z - x w + x t - x v - x r + y z + y t + y u - y v + z^{2} - z w - z v + z r + t^{2} + \cdots + v r$ |
| $=$ | $x z + x w - x u - x v - 2 x r + 2 y z + y u - 2 y v - y r + z^{2} - z w + z u - z v - w u + w r$ |
| $=$ | $\cdots$ |
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Singular plane model Singular plane model
| $ 0 $ | $=$ | $ 288 x^{11} + 336 x^{10} y - 1056 x^{10} z - 40 x^{9} y^{2} + 128 x^{9} y z + 736 x^{9} z^{2} + \cdots + 96 y^{3} z^{8} $ |
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This modular curve has 2 rational cusps but no known non-cuspidal rational points. The following are the coordinates of the rational cusps on this modular curve.
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
30.60.4.b.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle x$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle y$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle z$ |
| $\displaystyle W$ |
$=$ |
$\displaystyle x+y+z-w$ |
Equation of the image curve:
| $0$ |
$=$ |
$ X^{2}-4XY+XZ+3YZ-XW+2W^{2} $ |
|
$=$ |
$ X^{3}-X^{2}Y+X^{2}Z-2XYZ-Y^{2}Z+YZ^{2}-2X^{2}W-XYW-XZW+XW^{2}+ZW^{2} $ |
Map
of degree 1 from the canonical model of this modular curve to the plane model of the modular curve
30.120.8.f.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle x$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle z$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle t$ |
Equation of the image curve:
| $0$ |
$=$ |
$ 288X^{11}+336X^{10}Y-1056X^{10}Z-40X^{9}Y^{2}+128X^{9}YZ+736X^{9}Z^{2}-712X^{8}Y^{3}+1164X^{8}Y^{2}Z-2768X^{8}YZ^{2}+736X^{8}Z^{3}-816X^{7}Y^{4}+2050X^{7}Y^{3}Z-598X^{7}Y^{2}Z^{2}+1760X^{7}YZ^{3}-352X^{7}Z^{4}-519X^{6}Y^{5}+626X^{6}Y^{4}Z+41X^{6}Y^{3}Z^{2}-3138X^{6}Y^{2}Z^{3}+2112X^{6}YZ^{4}-288X^{6}Z^{5}-158X^{5}Y^{6}+131X^{5}Y^{5}Z+2301X^{5}Y^{4}Z^{2}-984X^{5}Y^{3}Z^{3}+1076X^{5}Y^{2}Z^{4}-656X^{5}YZ^{5}-192X^{5}Z^{6}-37X^{4}Y^{7}-229X^{4}Y^{6}Z-13X^{4}Y^{5}Z^{2}-1312X^{4}Y^{4}Z^{3}-1736X^{4}Y^{3}Z^{4}+2064X^{4}Y^{2}Z^{5}-480X^{4}YZ^{6}-10X^{3}Y^{8}-91X^{3}Y^{7}Z+118X^{3}Y^{6}Z^{2}+1071X^{3}Y^{5}Z^{3}-318X^{3}Y^{4}Z^{4}+84X^{3}Y^{3}Z^{5}-160X^{3}Y^{2}Z^{6}-384X^{3}YZ^{7}-11X^{2}Y^{9}-60X^{2}Y^{8}Z-187X^{2}Y^{7}Z^{2}-343X^{2}Y^{6}Z^{3}-375X^{2}Y^{5}Z^{4}-494X^{2}Y^{4}Z^{5}+808X^{2}Y^{3}Z^{6}-96X^{2}Y^{2}Z^{7}+33XY^{8}Z^{2}+180XY^{7}Z^{3}+322XY^{6}Z^{4}+138XY^{5}Z^{5}-100XY^{4}Z^{6}+144XY^{3}Z^{7}-192XY^{2}Z^{8}-11Y^{7}Z^{4}-60Y^{6}Z^{5}-96Y^{5}Z^{6}+96Y^{3}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.
