On non-congruent numbers with 1 modulo 4 prime factors
  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. 
Yi Ouyang and Shenxing Zhang
math.NT