Due to not participating in the previous editions my standard of what defines a swordmage may differ from the DnD standard that seems to focus on short range teleportation to supplement standard attacks
My concept of a swordmage is one who’s weapon is used as the medium to deliver various magical strikes and effects, existing spells I would highlight would be booming blade, green flame blade, zephyr strike, lightning arrow and elemental weapon, some of the smite spells too, ice knife is close to their wheelhouse