Anivia Freljord Invoker 1g

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Anivia's Frostbite sends out an ice shard towards her target, dealing magic damage to them. If that enemy is Chilled, the ability Critically Strikes.
As a 1-cost Invoker, Anivia will likely be used to enable the two-piece bonus. However, with Chill support, she could deal a good chunk of damage.
Sona Demacia Invoker 1g

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Sona is a basic supporting unit that deals magic damage and restores health to the lowest Health ally. In Demacia, this could prove to be quite useful, helping to save near-death frontliners or fragile carries. Worst case, she's another 1-cost Invoker that'll give more mana to your team.
Orianna Piltover Invoker 2g

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Orianna is a relatively easy unlock as long as you're playing Piltover. Collecting three is all you need, and then you'll gain free access.
Her Command: Protect ability sends a ball at the target, dealing magic damage to it and nearby enemies. It also Shields the two weakest allies. Overall a pretty basic AP support, but given the requirements you can't ask for much more.
Kobuko & Yuumi Yordle Bruiser Invoker 3g

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Kobuko & Yuumi's "You & Me!" ability causes them to dance and restore health over a short period. As a passive, Yuumi rotates between healing your lowest Health ally and raising the Attack Speed of your top DPS unit.
With three solid traits and a great supporting ability, Kobuko & Yuumi is a welcome addition. Again, they unlock naturally, following six stars of Yordle, Bruiser, or Invoker. Hard to argue with that.
LeBlanc Noxus Invoker 3g

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LeBlanc is yet another Unlockable unit, but this time with a more specific condition. You'll need to field a Sion with two items in combat, but honestly, that should be pretty easy.
Her Distortions ability has her summon dashing mirror images, each one striking the target and foes close by. The main target also gets Stunned, granting her some great CC utility. Once again, another impressive Invoker.
Milio Ixtal Invoker 3g

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Milio's "Ultra Mega Fire Kick!!!" launches a bouncing "fuemigo" towards the target, dealing magic damage to all enemies hit. As an Ixtal champ, Milio does aid towards your Quest for Sunshards.
Overall, this is probably the simplest Invoker of the bunch, but if you need the trait he's serviceable enough.
Lissandra Freljord Invoker 4g

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Lissandra pairs nicely with Anivia as they both share the exact same traits. While she doesn't apply Chill herself, she can definitely take advantage of it, as her ability deals more to Chilled enemies.
Frozen Tomb encases the target in ice, Stunning them for a duration and dealing magic damage. If it's a killing blow, shards launch outwards to deal the excess damage to the two nearest foes.
Zilean Chronokeeper Invoker 5g

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Zilean's value comes from his unique trait, Chronokeeper. This lets him store 1 XP every two casts, then once you're close enough to level-up, it all gets transferred to you (at level 10, gains 15% Damage Amp).
On the battlefield he throws Time Bombs on enemies, dealing magic damage to them each second. When the afflicted enemy dies, it harms foes within range and restores some Mana to Zilean (perfect with Invoker).
If an enemy happens to survive long enough with a Time Bomb and Zilean is still alive, the clock strikes and the enemy is instantly deleted. While probably unlikely to occur often, it's great inevitability against tanks if you can keep Zilean safe.
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