13th century

The 13th century was defined by the calendar of Earth as occurring from the year 1201 through the year 1300.

Events[]

Sometime during this century, a planet becomes inhabited by a race known as the Crepusculans. (DIS: "The Vulcan Hello")
All life on the planet Zetar is extinguished in a war. Only about a hundred individuals survive as energy patterns representing their thoughts. (TOS: "The Lights of Zetar")
The Elysian Ruling Council is formed in the Delta Triangle region. (TAS: "The Time Trap")
The father of Wu is living on the planet Omega IV. (TOS: "The Omega Glory")

In 2268, Wu's father was "well over" a thousand years old, suggesting that he was born before the 13th century.

The family of Lwaxana Troi acquires a brooch, which will be passed down for thirty-six generations. (DS9: "The Forsaken")
The Fourth Crusade on Earth results in the Sack of Constantinople. (TOS: "The Squire of Gothos"; DS9: "Q-Less"; VOY: "The Killing Game")
Crusades Five through Nine on Earth. The Seventh was against an army made migrant by Genghis Khan's Mongol horde. (TOS: "The Squire of Gothos"; DS9: "Q-Less"; VOY: "The Killing Game")
Fall of the Sung Dynasty to the grandson of Genghis. All of China is henceforth administered from Xanadu, on the far edge of Mongolia. The Sung had reigned for over three hundred years; their artisans produced the statue of a horse that Captain Picard later presents to Lutan. (TNG: "Code of Honor")

According to the Star Trek Encyclopedia (3rd ed., pp. 171 and 283), the Magna Carta was signed into law by King John of England in 1215 and Genghis Khan dies in 1227.