The vertices of the line_graph are the edges of the graph, including edge labels by default. If you don't want the labels, you can do:
sage: G = Graph([(2,3),(2,4),(2,1),(1,5),(5,6),(1,0),(0,12),(0,13),(14,0),(15,0),(7,0),(7,10),(11,7),(7,9),(7,8)])

sage: h.show(method='js',link_distance=100)