Swordmage Implement with Wizard powers?

[UngeheuerLich]

No, you can't then, either.
WotST says you can use a longsword as an implement you're specialised in.
An MC wizard isn't specialised in any implement.

No, it actually says:

Corellon’s Implement (11th level): Choose an arcane implement that you specialize in, whether the wand, staff, or orb. You can use a longsword as if it were that type of arcane implement when casting your spells.

so it says: chose an implement that you specialize in, not: in which you are specialized in... which actually means a second type of specialization which you find in the Arcane Implement Mastery...

of course, its best to combine both specializations, but as it is written it is not mandatory...

 

[Kordeth]

No, it actually says:

Corellon’s Implement (11th level): Choose an arcane implement that you specialize in, whether the wand, staff, or orb. You can use a longsword as if it were that type of arcane implement when casting your spells.

so it says: chose an implement that you specialize in, not: in which you are specialized in... which actually means a second type of specialization which you find in the Arcane Implement Mastery...

of course, its best to combine both specializations, but as it is written it is not mandatory...

Ummm...what? There's only one kind of implement specialization, and that's from Arcane Implement Mastery:

You specialize in the use of one kind of implement to gain additional abilities when you wield it.

Only characters who began their career as wizards get Arcane Implement Mastery, therefore only a wizard multiclassing into swordmage could use a longsword as an implement for both class's powers. There is no way for a swordmage multiclassed into wizard to be specialized in staff, orb, or wand, so he can't fulfill the requirements of Corellon's Implement.