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The local-global principle for divisibility in CM elliptic curves over number fields. [PDF]

open access: yes, 2022
We investigate the local-global principle for divisibility by pn in elliptic curves over number fields. For p = 7 we find that the local-global principle for divisibility by pn holds for all n ∈ N for elliptic curves over quadratic fields, but could fail for some elliptic curves over cubic fields. We also extend to the result to certain elliptic curves
Lu, Sheng (Victor)
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