Invigorate

• WWizards of the Coast2020-08-07
  Official Ruling
  To determine the total cost of a spell, start with the mana cost or alternative cost you're paying (such as the alternative cost of Invigorate), add any cost increases, then apply any cost reductions. The mana value of the spell remains unchanged, no matter what the total cost to cast it was.
• WWizards of the Coast2020-08-07
  Official Ruling
  If an effect says that an opponent can't gain life, you can't have that player gain life to pay Invigorate's alternative cost. If an effect instead replaces life gain, such as that of Sulfuric Vortex, you may choose to pay the cost even though the cost's action is replaced with nothing.

Rulings via Scryfall

• WO
  Wizards of the Coast2013-02-01 · edited

  Invigorate was banned in pauper on February 1, 2013. Invigorate costs zero mana, but the additional damage is equal to 40% of the poison counters needed to win. It also lets the Infect player, even when tapped out, protect an infect creature from a wide variety of damage-based removal, making it particularly difficult for other decks to effectively interact with the Infect deck. Source: https://magic.wizards.com/en/news/latest-developments/rapid-hybrid-ization-2013-02-01
• WO
  Wizards of the Coast2013-01-28

  Invigorate was banned in pauper on January 28, 2013. No public reasoning provided. Source: https://magic.wizards.com/en/news/january-28-2013-dci-banned-restricted-list-announcement-2013-01-28