see under bad egg.
The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.
Examples from the Web for rotten egg
The explosive contact gave forth a blast of sputtering sparks and an offensive, rotten-egg smell.The Spell of the Rockies
Enos A. Mills