Shares of Pleasanton-based Ellie Mae soared on their first day of trading Friday, marking an auspicious launch for the Bay Area’s newest publicly held company. Ellie Mae jumped 12.8 percent, or 77 cents, and finished at $6.77 on Friday. The company had priced its shares for the IPO at $6. That price, though, was down from the company’s prior proposal of an offering at $10. The company provides software and an electronic network to originate and process mortgages. The software system connects mortgage bankers, mortgage brokers, community banks, credit unions and other mortgage lenders. Mortgage originators can use the system to conduct transactions with lenders.