  We prove consequences of functional equations of p-adic L-functions for
elliptic curves at supersingular primes p. The results include a relationship
between the leading and sub-leading terms (for which we use ideas of Wuthrich
and Bianchi), a parity result of orders of vanishing, and invariance of
Iwasaswa invariants under conjugate twists of the p-adic L-functions.
