Canonical model in $\mathbb{P}^{ 6 }$ defined by 10 equations
| $ 0 $ | $=$ | $ x^{2} + y^{2} + y v + z^{2} - 2 w^{2} - t^{2} + t v $ |
| $=$ | $2 x^{2} - 2 x z + x w - 2 y u - w^{2} - t u$ |
| $=$ | $2 x y + x t - x u + x v + z t - 2 z u - z v + w t - w u$ |
| $=$ | $x y + 3 x t + 2 x u - 2 x v - z t + z u + w u + w v$ |
| $=$ | $\cdots$ |
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Singular plane model Singular plane model
| $ 0 $ | $=$ | $ - 441 x^{10} + 1764 x^{9} z - 468 x^{8} y^{2} + 609 x^{8} z^{2} + 2655 x^{7} y^{2} z - 672 x^{7} z^{3} + \cdots + z^{10} $ |
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This modular curve has no $\Q_p$ points for $p=3$, and therefore no 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
20.60.3.c.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle 5x-z-2w$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle z-3w$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle 3z+w$ |
Equation of the image curve:
| $0$ |
$=$ |
$ 2X^{4}-4X^{3}Y+6X^{2}Y^{2}-4XY^{3}+2Y^{4}+4X^{3}Z+17X^{2}YZ-17XY^{2}Z-4Y^{3}Z+5X^{2}Z^{2}+18XYZ^{2}+5Y^{2}Z^{2}+3XZ^{3}-3YZ^{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.cu.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle x$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle y$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle z$ |
Equation of the image curve:
| $0$ |
$=$ |
$ -441X^{10}+1764X^{9}Z-468X^{8}Y^{2}+609X^{8}Z^{2}+2655X^{7}Y^{2}Z-672X^{7}Z^{3}-180X^{6}Y^{4}-1600X^{6}Y^{2}Z^{2}-142X^{6}Z^{4}+954X^{5}Y^{4}Z-1485X^{5}Y^{2}Z^{3}-104X^{5}Z^{5}-36X^{4}Y^{6}-999X^{4}Y^{4}Z^{2}+992X^{4}Y^{2}Z^{4}-34X^{4}Z^{6}+63X^{3}Y^{6}Z+324X^{3}Y^{4}Z^{3}+1005X^{3}Y^{2}Z^{5}+32X^{3}Z^{7}-9X^{2}Y^{8}+32X^{2}Y^{6}Z^{2}-174X^{2}Y^{4}Z^{4}-592X^{2}Y^{2}Z^{6}+7X^{2}Z^{8}+9XY^{6}Z^{3}-14XY^{4}Z^{5}+65XY^{2}Z^{7}+4XZ^{9}+9Y^{4}Z^{6}+4Y^{2}Z^{8}+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.
