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

asked 2013-12-23 22:48:55 -0600

cjsh gravatar image

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

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

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

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

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