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Sage code which wraps some fast Pari functions and implements a fast solver from Will Jagy

('Conway_positive_primitive' and 'Conway_positive_all') can be found at [1].

The main function combines several important cases in a single function:

represented_by_binaryQF(
    a, b, c,     # the coefficients
    M,           # limit
    primitively, # default false 
    prime,       # default false 
    verbose      # default true
)

See the many examples given there.

[1] http://oeis.org/wiki/User:Peter_Luschny/BinaryQuadraticForms

Sage code which wraps some fast Pari functions and implements a fast solver from Will Jagy

represented_by_binaryQF(
    a, b, c,     # the coefficients
    M,           # limit
    primitively, # default false 
    prime,       # default false 
    verbose      # default true
)