Pairing Pythagorean Pairs

A pair ( a , b ) of positive integers is pythagorean if 2 + = □ i.e. square). called double-pythapotent there another k l such that pair, and it quadratic pythapotent which not multiple pair. To each we assign an elliptic curve Γ with torsion group Z / × 4 has rank over Q only Similarly, to 8 Moreover, in the later case obtain every isomorphic form where As side-result get then are infinitely many pairs multiples other, pair; analogous result holds for pairs.