In this paper, we present a relative pose estimation algorithm based on lines knowing the vertical direction associated to each image. We demonstrate that a closed-form solution requiring only eight lines between three views is possible. As a linear solution, it is shown that our approach outperforms the standard trifocal estimation based on 13 triplets of lines and can be efficiently inserted into an hypothesize-and-test framework such as RANSAC. We also study our approach on different singular configurations of lines. The method is evaluated on both synthetic data and real-world sequences from KITTI and the Zurich Urban Micro Aerial Vehicle datasets. Our method is compared to 13 lines algorithm as well to points based methods such as 7-points, 5-points and 3-points.