Explicit points on the Legendre curve III

We continue our study of the Legendre elliptic curve $y^{2} = x (x + 1) (x + t)$ over function fields $K_{d} = F_{p} (μ_{d}, t^{1 / d})$ . When $d = p^{f} + 1$ , we have previously exhibited explicit points generating a subgroup $V_{d}$ of $E (K_{d})$ of rank $d - 2$ and of finite, $p$ -power index. We also proved the finiteness of $I I I (E / K_{d})$ and a class number formula: $[E (K_{d}) : V_{d}]^{2} = ∣ I I I (E / K_{d}) ∣$ . In this paper, we compute $E (K_{d}) / V_{d}$ and $I I I (E / K_{d})$ explicitly as modules over $Z_{p} [G a l (K_{d} / F_{p} (t))]$ .

Explicit points on the Legendre curve III

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Explicit points on the Legendre curve III

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Explicit points on the Legendre curve III

文献摘要

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|讲解博客

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Explicit points on the Legendre curve III

文献摘要

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讲解博客

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