Explicit points on the Legendre curve III

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3 Scopus citations


We continue our study of the Legendre elliptic curve y2x(x+1)(x+t) over function fields Kd=Fpd,t1/d). When d = pf+1, we have previously exhibited explicit points generating a subgroup Vd ⊂ E (Kd) of rank d - 2 and of finite, p-power index. We also proved the finiteness of III(E/Kd) and a class number formula: (equation found). In this paper, we compute E(Kd)/Vdand III(E/Kd) explicitly as modules over Zp[Gal(Kd/Fp(t))].

Original languageEnglish (US)
Pages (from-to)2471-2522
Number of pages52
JournalAlgebra and Number Theory
Issue number10
StatePublished - 2014


  • Elliptic curves
  • Function fields
  • Tate-Shafarevich group

ASJC Scopus subject areas

  • Algebra and Number Theory


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