I believe there must be some error in the code that implements the Tutte 
polynomial of a graph in Sage. For example, the code

G = Graph();
G.allow_multiple_edges(True);
#edges are (u,v,l), where (u,v) is the edge and l is the label, which 
determines edge order
G.add_edges([(0,1,1),(1,5,2),(5,3,3),(5,2,4),(2,4,5),(0,2,6),(0,3,7),(0,4,8),(0,5,9)]);
g = G.tutte_polynomial();
print g(1,1);
print G.spanning_trees_count();

produces

T(1,1): 60 Number of spanning trees: 52

But of course T_G(1,1) should be equal to the number of spanning trees. And 
I am tending to believe that the error is with the Tutte polynomial 
computation and not the second "spanning_trees_count()" method.

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