No, you have it backwards … sorta. There are seven different Epic Arcs available in the game, one level 1 Epic Arc, two different level 3 Pirate Epic Arcs and four different Empire level 4 Epic Arcs.
The first one - Epic Arc 3.0 - is the level 3 Pirate Epic Arc.
When you gain over +3.00 Minmatar or Amarr Faction standing, you can access the Angel level 3 Pirate Epic Arc through their ‘Double’ Agents.
When you gain over +3.00 Caldari or Gallente Faction standing, you can access the Guristas level 3 Pirate Epic Arc through their ‘Double’ Agents.
The next one - Epic Arc 5.0 - is the main ‘well known’ level 4 Epic Arcs.
When you gain over +5.00 Empire Faction standing, you can access the level 4 Empire Epic Arc. Empire Factions = Amarr, Caldari, Gallente and Minmatar Factions.
2 of those 4 Empire Epic Arcs have the option to complete it for another Faction. The Amarr Epic Arc allows you to complete it for either Amarr or Sansha. The Gallente Epic Arc allows you to complete it for either Gallente or The Syndicate.
The level 1 Sisters Of Eve Epic Arc allows you to choose one of the four Empire Factions for completion.
All Epic Arcs can be done again 90 days after completion.
Also remember that either Corporation or Faction standing can be used to access the Epic Arcs. If using the starting Agents Corporation standing for access, the Empire Faction must be above -2.00 standing.