number of biquadratic polynomials, f(n,m)=an²+bnm+cm²

[bhelmes]

A pleasant night for everyone,


i have 30 different polynomials with negativ discriminant and
256 different polynomials with positiv discriminant

of the form f(n)=n²+bn+c


( complete list under http://devalco.de/poly_sec.php )


how many possibilities exist for the biquadratic forms f(n,m)=an²+bnm+cm²


I found the list of OEIS

https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS


but i do not understand the relationship:
Can i combine every two polynomials

of the form f(n), f(m) into the form f(n,m) ?


Would be nice if you give me a hint.


Greetings from x²+Ny²

(the book Primes of the form x²+ny² from David A. Cox is very interesting)

Bernhard

[science_man_88]

http://mathworld.wolfram.com/BiquadraticEquation.html

gcd(m,n)=1
gcd(a,b,c)=1
gcd(c,n)=1
gcd(a,m)=1

just for a start to not not have a non-trivial factor.