# Questions tagged [elliptic-surfaces]

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2
questions

**5**

votes

**3**answers

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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

**1**answer

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....