Below is the list of tables from the database along with their columns and datatype. Need to generate an accurate SQL query for the question.
Only use the columns present in the respective table. Only use the columns which are required to generate the SQL query. Only use table joins if required and not otherwise.

### Tables ###
TABLE: CREATE TABLE table_name_62 (pick__number INTEGER, position VARCHAR, cfl_team VARCHAR)

### Question ###
What is the lowest Pick #, when Position is REC, and when CFL Team is Hamilton Tiger-Cats?

### Accurate SQL ###

SELECT MIN(pick__number) FROM table_name_62 WHERE position = "rec" AND cfl_team = "hamilton tiger-cats"