Ranks of elliptic curves in cubic extensions

Details Ranks of elliptic curves in cubic extensions Ranks of elliptic curves in cubic extensions

2005-10-25

arxiv.org/abs/math/0510533v1

Mathematics

Number Theory

3 pages

Scientific paper

For an elliptic curve E over a number field K, we prove that the algebraic
rank of E goes up in infinitely many extensions of K obtained by adjoining a
cube root of an element of K. As an example, we briefly discuss E=X_1(11) over
Q, and how the result relates to Iwasawa theory.

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