Special election for unexpired term ending January 4, 1858. James L. English had been appointed on February 13, 1857 to fill the vacancy caused by Henry Bates' resignation. English ran to complete the term, but did not run in the simultaneous regular election for the next term.
Candidates' party affiliations obtained from the 9/19/1857 Placer Herald (of Auburn). https://www.cdnc.ucr.edu/?a=d&d=PH18570919.2.2&srpos=38&e=-------en--20--1--txt-txIN--------
Source for Popular Vote data: California State Archives, "For State Treasurer To Fill Vacancy," Statement of the Votes Polled in the State of California, on the Second Day of September, A.D. 1857 (Sacramento, 1857)