Canonical model in $\mathbb{P}^{ 4 }$ defined by 3 equations
| $ 0 $ | $=$ | $ 2 y^{2} - w^{2} + w t $ |
| $=$ | $2 z^{2} - w t - t^{2}$ |
| $=$ | $2 x^{2} + y z$ |
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Singular plane model Singular plane model
| $ 0 $ | $=$ | $ 2 x^{8} - 3 x^{4} y^{2} z^{2} - 4 y^{6} z^{2} + y^{4} z^{4} $ |
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This modular curve has 4 rational cusps but no known non-cuspidal rational points. The following are the coordinates of the rational cusps on this modular curve.
| Canonical model |
|---|
| $(0:1:0:-1:1)$, $(0:-1:0:-1:1)$, $(0:0:-1:1:1)$, $(0:0:1:1:1)$ |
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
16.48.3.d.1
:
| $\displaystyle X$ |
$=$ |
$\displaystyle -2x$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle t$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle -w$ |
Equation of the image curve:
| $0$ |
$=$ |
$ X^{4}-Y^{3}Z+YZ^{3} $ |
Map
of degree 1 from the canonical model of this modular curve to the plane model of the modular curve
16.96.5.v.2
:
| $\displaystyle X$ |
$=$ |
$\displaystyle x$ |
| $\displaystyle Y$ |
$=$ |
$\displaystyle \frac{1}{2}z$ |
| $\displaystyle Z$ |
$=$ |
$\displaystyle w$ |
Equation of the image curve:
| $0$ |
$=$ |
$ 2X^{8}-3X^{4}Y^{2}Z^{2}-4Y^{6}Z^{2}+Y^{4}Z^{4} $ |
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.
