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4 questions
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Elliptic fibrations on some Kummer surface in characteristic $2$
In the question I ask about one elliptic fibration on the surface
$$
K\!: y^2 + x_1x_2y = (x_1x_2)^2(x_1 + x_2 + 1) + (x_1 + x_2)^2.
$$
over a finite field $\mathbb{F}_q$ of characteristic $2$ such ...
- 1,833
2
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1
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184
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Is there a way to find any $\mathbb{F}_2(t)$-point on the elliptic curve $\mathcal{E}$?
Consider the ordinary elliptic curves
$$
E\!:y_1^2 + x_1y_1 = x_1^3 + 1,\qquad E^\prime\!: y_2^2 + x_2y_2 = x_2^3 + x_2^2 + 1
$$
over the field $\mathbb{F}_2$. They are quadratic twists to each other....
- 1,833
3
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0
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144
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Are there three ordinary elliptic curves $E$, $E_1$, $E_2$ such that $E^2 \cong E_1 \!\times\! E_2$?
Consider the elliptic curve $E\!: y^2 = x^3 + 1$ of $j$-invariant $0$ over an algebraically closed field $k$ of characteristics $p$. Let me remind that $E$ is ordinary (i.e., non-supersingular) iff $p ...
- 1,833
2
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0
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137
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Is a supersingular Kummer surface $k$-unirational in characteristic 2?
Let $k$ be a perfect field of even characteristic. Consider the simplest example of a supersingular genus 2 curve, i.e.,
$$
C\!: y^2 + y = x^5.
$$
By the article of J. S. Müller "Explicit Kummer ...
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