This in turn led them to make a general conjecture about the behaviour of a curve's L-function "L"("E", "s") at "s" = 1, namely that it would have a zero of order "r" at this point. This was a far-sighted conjecture for the time, given that the analytic continuation of "L"("E", "s") there was only established for curves with complex multiplication, which were also the main source of numerical examples. (NB that the reciprocal of the L-function is from some points of view a more natural object of study; on occasion this means that one should consider poles rather than zeroes.)