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_10 (fa_cup_goals INTEGER, league_cup_goals VARCHAR, fa_cup_apps VARCHAR, total_goals VARCHAR, league_goals VARCHAR)

### Question ###
What is the lowest FA Cup Goals, when Total Goals is greater than 0, when League Goals is "4", when FA Cup Apps is "1", and when League Cup Goals is greater than 0?

### Accurate SQL ###

SELECT MIN(fa_cup_goals) FROM table_name_10 WHERE total_goals > 0 AND league_goals = 4 AND fa_cup_apps = "1" AND league_cup_goals > 0