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arXiv · 1001.0100

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

Yu Tsumura
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Abstract

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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Yu Tsumura. 2010-01-03. The quadratic character of 1+\sqrt{2} and an elliptic curve. https://arxiv.org/abs/1001.0100

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