Infinite families of non-congruent numbers with arbitrarily many prime factors are produced by showing zero 2-Selmer rank on the corresponding elliptic curves via the Monsky matrix.
The parity of the rank of the Mordell-Weil group
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Monsky Matrix and 2-Selmer rank
Infinite families of non-congruent numbers with arbitrarily many prime factors are produced by showing zero 2-Selmer rank on the corresponding elliptic curves via the Monsky matrix.