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arXiv · 1208.2149

On non-congruent numbers with 1 modulo 4 prime factors

Yi Ouyang·Shenxing Zhang
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Abstract

In this paper, we use the 2-decent method to find a series of odd non-congruent numbers $\equiv1\pmod 8$ whose prime factors are $\equiv1\pmod4$ such that the congruent elliptic curves have second lowest Selmer groups, which includes Li and Tian's result (Li and Tian, 2000) as special cases.

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Yi Ouyang, Shenxing Zhang. 2012-08-10. On non-congruent numbers with 1 modulo 4 prime factors. https://arxiv.org/abs/1208.2149

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