The quadratic character of 1+\sqrt{2} and an elliptic curve

Details The quadratic character of 1+\sqrt{2} and an elliptic curve The quadratic character of 1+\sqrt{2} and an elliptic curve

2010-01-03

arxiv.org/abs/1001.0100v1

Mathematics

Number Theory

4 pages

Scientific paper

When p is congruent to 1 mod 8, we have a criterion of the quadratic
character of 1+\sqrt{2}, which is related to the class number of \Q(\sqrt{-p}).
In this paper, we obtain a similar criterion using an elliptic curve, which
contrasts to the proof using algebraic number theory for the old one.

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