Founding Titan

"Frieda's Titan stood at the apex of all others, in other words, a Titan that held an invincible power."

- Rod on holding the Coordinate.

The Coordinate (座標) is an ability that is capable of allowing the user to control Titans, modify memories, and inherit memories. It is passed on to successors by a ceremony in which the current holder is eaten by a human-turned-Titan. It is currently in the possession of Eren Yeager.

Description
This power is a composition of three different abilities.

First and most noticeable of all, the Coordinate power grants the user the ability to control Titans at will and make them follow virtually any order. This is seen when Eren unintentionally commanded nearby Titans to eat the Smiling Titan and to attack the Armored Titan. It was also used by the First King to build the Walls, making Titans harden their bodies and confine themselves into the resulting structures. The real limit of this power is unknown, but as it can be observed, it extends to the point of making Titans perform actions that threaten their own lives. It was also mentioned by Rod Reiss that the power is so strong, it has the potential to wipe out all the Titans if the user is able to wield it to its full strength.

Secondly, the Coordinate allows the user to erase or modify the memory of a single person or even those of entire countries if they are skilled enough. It was used by Frieda Reiss to remove Historia's memories about her, and by the First King to make humanity forget all the history of the world before the building of the Walls. However, it is known that at least the Ackerman bloodline, the Asian races and the noble families are immune to this mental manipulation due to not sharing a common bloodline with the majority race within the walls. This caused the persecution of the former two at the hands of the monarchy.

Finally, the power allows the user to inherit the lost memories of mankind and those of the previous users, giving them omniscient-like knowledge about the world —such as the reason the Titans exist and how the Walls were created—. Nevertheless, it seems that only the Reiss bloodline can activate this ability from the beginning, since Uri and Frieda Reiss showed signs of being aware of that knowledge immediately after obtaining the Coordinate, while Eren has just unlocked some vague memories after years of having received it. The user is referred to as the living book of humanity because of this.

The overwhelming extent of these combined abilities causes the Coordinate to be referred to as the "invincible power", and the user to be called "God", as stated by Rod.

Even so, it is noteworthy that, despite the fact that all of the Coordinate users could use this power to easily wipe out all Titans and free humanity from their encagement if they wanted; and despite many, if not all the wielders expressed the desire to do that before obtaining the ability; once they received the memories of the events that led to the invasion more than 100 years ago, all of them decide to do nothing, and refuse to reveal the reason to anyone, showing a silent concern and culprit for the knowledge they received. Frieda used to suffer from fits of madness and depression due to those memories, and claimed that humans were sinners who deserved their punishment.

Like Titan Shifting, the Coordinate is apparently not inherited by bloodline, and the only way to get it is by eating the previous user. This is usually done by using a serum to transform into a Titan, then eating the holder and thus regaining human form, plus obtaining the Coordinate power and the Titan Shifting abilities. This means that all the Coordinate users have also been Titan Shifters.

The Coordinate originally belonged to the Reiss royal family, which passed it down generation to generation through the previously described process. However, seeing that they would never do something to stop the Titans despite having the capability, which allowed the invasion of Shiganshina and the death of his wife, Grisha Yeager stole the Coordinate by attacking the Reiss family in his Titan form and eating the former wielder, Frieda. He then transformed his son Eren into a Titan and allowed himself to be eaten by him, so that he could master the Coordinate without the memories and influence of the Reiss bloodline and accomplish the goal they never did.

Trivia

 * The Coordinate, as well as other Titan abilities, is retained in the user's spinal cord fluids, so it is not necessary to actually eat the whole wielder to obtain the power.
 * According to Rod, this power can only be used to its full potential by a descendant of the Reiss family. That is why Rod tried to have Historia eat Eren, due to the fact that she was the only remaining heir of the Reiss bloodline. However, the truth of this claim is unknown, as Rod was presumably luring Historia into simply killing Eren to reclaim the power.