Questions tagged [elliptic-surfaces]

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5
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3answers
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Is there a way to find any non-trivial $\mathbb{F}_p(t)$-point on the given elliptic curve?

Consider a finite field $\mathbb{F}_p$ (where $p \equiv 1 \ (\mathrm{mod} \ 3)$, $p \equiv 3 \ (\mathrm{mod} \ 4)$) and the elliptic curve $$ E\!:y^2 = x^3 + (t^6 + 1)^2 $$ over the univariate ...
2
votes
1answer
165 views

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....