Let the hyperbola $C : \frac { x ^ { 2 } } { a ^ { 2 } } - \frac { y ^ { 2 } } { b ^ { 2 } } = 1 ( a > 0 , b > 0 )$ have left and right foci $F _ { 1 } , F _ { 2 }$ respectively. A line through $F _ { 2 }$ parallel to the $y$-axis intersects $C$ at points $A$ and $B$ . If $\left| F _ { 1 } A \right| = 13 , | A B | = 10$ , then the eccentricity of $C$ is $\_\_\_\_$ .