### is there a formula about the same absolute_discriminant but different absolute_polynomial?

some same degree polynomial,different terms,but absolute_discriminant is same

foe example:Q[zeta3,2^1/3],absolute_polynomial=x^6 - 3*x^5 + 6*x^4 - 11*x^3 + 12*x^2 + 3*x + 1

absolute_discriminant=-1 * 2^4 * 3^7,but when I find from LMFDB.org by absolute_discriminant or absolute_polynomial, polynomial given =x^6 - 3*x^5 + 5*x^3 - 3*x + 1

two polynomial has same discriminant,is there more this kands of polynomials?

http://www.lmfdb.org/NumberField/?natural=x%5E6+-+3*x%5E5+%2B+6*x%5E4+-+11*x%5E3+%2B+12*x%5E2+%2B+3*x+%2B+1&search=Go
http://cjsh716.blog.163.com/blog/static/213847199201311245475450/