Founding Titan

The coordinate (also referred as the invincible power) is an ability that is most recognizable for allowing the user to control the titans (this power is seen when Eren commanded unconsciously nearby titans to eat the Smiling titan). However the real limit of this power is unknown. The coordinate also allows the user to erase the memory of a person (Frieda erased Historia's memories about her), and allows the user to remember the lost memories of mankind, giving the user omniscient knowledge about the world. The total control of the coordinate makes the wielder able to control both humans and titans, and due to the vast knowledge given to the user, this person is called God by Rod Reiss.

The power originally belonged to the Reiss bloodline; mankind's monarch had the power during his government, but when the heir had to inherit the crown, the heir was told to become a titan using the serum and to eat the prior king. By doing so, the coordinate passed generation to generation. However it was stolen by Grisha Yeager by eating the current wielder. Later on, Grisha was eaten by Eren's initial titan form, making the boy the new user of the coordinate.

Trivia

 * Although this is just speculation, this powers may have been used to built all three walls by controlling the titans and ordering them to harden themselves. This would explain why there are titans inside the walls.
 * Also this power may have been used by the monarchy to delete all mankind's old memories about titans.
 * The coordinate is retained in the user's spinal cord, so it is not necessary to eat the whole wielder.
 * This power may be the reason why Reiner, Bertholdt and Annie were looking after Eren.
 * According to Rod, this powers can only be fully dominated if the user is a descendant of the Reiss family. That is why Rod tried that Historia ate Eren, due to the fact that she was the only heir remaining of the Reiss bloodline.