Statistics from the 12 genera for 36A for the weight 3/2 forms.
Number of even parity twists with positive rank:
Real twists 10463848 for 1 mod 24 6890215 for 5 mod 24 7273370 for 13 mod 24 9919768 for 17 mod 24 Imaginary twists 3927916 for 2 mod 48 3645536 for 10 mod 48 4772066 for 14 mod 48 5067135 for 22 mod 48 3932969 for 26 mod 48 3649766 for 34 mod 48 5502983 for 38 mod 48 5227451 for 46 mod 48