Arithmetic on certain families of elliptic curves
2000 ◽
Vol 61
(2)
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pp. 319-327
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Consider a family of elliptic curves (A, A0, d0 fixed integers). We prove that, under certain conditions on A0 and d0, the rational torsion subgroup of E(B) is either cyclic of order ≤ 3 or non-cyclic of order 4. Also, assuming standard conjectures, we establish estimates for the order of the Tate-Shafarevich groups as B varies.
2015 ◽
Vol 100
(1)
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pp. 33-41
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Keyword(s):
2016 ◽
Vol 102
(3)
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pp. 316-330
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2003 ◽
Vol 46
(1)
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pp. 157-160
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Keyword(s):
2010 ◽
Vol 214
(8)
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pp. 1340-1346
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Keyword(s):
2015 ◽
Vol 11
(06)
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pp. 1725-1734
Keyword(s):
2012 ◽
Vol 27
(3)
◽
pp. 497-503