read ConicIsom:

# Pick some arbitrary conic:
v := [30030, 7429, -1363783];

# Compute a simpler conic with the same BadPrimes (ramified primes).
w := SimplifyConic(v);

BadPrimes(v);  # The ramified primes of conic v.
BadPrimes(w);  # The same, so v and w are isomorphic.

# Compute isomorphism:
ConicIsomorphism(v, w);


# A simpler example:
v := [1,2,3];
w := [1,1,1];
M := ConicIsomorphism(v,w);

# Check correctness:
P := M . <1,1,I>;  # Note that <1,1,I> is on v since 1*1^2+2*1^2+3*I^2 = 0
w[1]*P[1]^2 + w[2]*P[2]^2 + w[3]*P[3]^2; # Should be 0.

# Other examples
ConicIsomorphism([26455, 14, 1767], [37, 5, 1]);

ConicIsomorphism([3009008874, 44044, -46918], [958, 1892000, -1003002958]);

v := [23456345763547,29387465928374562,29837465928375629];
w := SimplifyConic(v);
ConicIsomorphism(v,w);
ConicIsomorphism(w,v);


v := [23456345763530498657039456447,
      293874643563456355928374562,
      298374567456745465928375629];
BadPrimes(v);
w := SimplifyConic(v);

ConicIsomorphism(v,w);
#  It's often a good idea to let the second argument be the smallest
#  one, this example would take much longer if you do ConicIsomorphism(w,v);