K12a527
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{11}+4 q^{10}-9 q^9+16 q^8-24 q^7+29 q^6-31 q^5+29 q^4-23 q^3+17 q^2-9 q+4- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-10 t^3+25 t^2-39 t+45-39 t^{-1} +25 t^{-2} -10 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+6 z^6+5 z^4+3 z^2+1 }[/math] |
| Determinant | 197 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} +z^8 a^{-6} -z^6 a^{-2} +4 z^6 a^{-4} +4 z^6 a^{-6} -z^6 a^{-8} -3 z^4 a^{-2} +6 z^4 a^{-4} +5 z^4 a^{-6} -3 z^4 a^{-8} -2 z^2 a^{-2} +6 z^2 a^{-4} +z^2 a^{-6} -2 z^2 a^{-8} +3 a^{-4} -2 a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-5} +2 z^{11} a^{-7} +5 z^{10} a^{-4} +12 z^{10} a^{-6} +7 z^{10} a^{-8} +6 z^9 a^{-3} +10 z^9 a^{-5} +15 z^9 a^{-7} +11 z^9 a^{-9} +4 z^8 a^{-2} -3 z^8 a^{-4} -19 z^8 a^{-6} -z^8 a^{-8} +11 z^8 a^{-10} +z^7 a^{-1} -14 z^7 a^{-3} -31 z^7 a^{-5} -39 z^7 a^{-7} -15 z^7 a^{-9} +8 z^7 a^{-11} -13 z^6 a^{-2} -21 z^6 a^{-4} -3 z^6 a^{-6} -15 z^6 a^{-8} -16 z^6 a^{-10} +4 z^6 a^{-12} -3 z^5 a^{-1} +3 z^5 a^{-3} +12 z^5 a^{-5} +24 z^5 a^{-7} +6 z^5 a^{-9} -11 z^5 a^{-11} +z^5 a^{-13} +14 z^4 a^{-2} +25 z^4 a^{-4} +10 z^4 a^{-6} +13 z^4 a^{-8} +9 z^4 a^{-10} -5 z^4 a^{-12} +3 z^3 a^{-1} +8 z^3 a^{-3} +9 z^3 a^{-5} +2 z^3 a^{-7} +4 z^3 a^{-9} +5 z^3 a^{-11} -z^3 a^{-13} -5 z^2 a^{-2} -11 z^2 a^{-4} -5 z^2 a^{-6} -z^2 a^{-8} -z^2 a^{-10} +z^2 a^{-12} -z a^{-1} -3 z a^{-3} -6 z a^{-5} -5 z a^{-7} -2 z a^{-9} -z a^{-11} +3 a^{-4} +2 a^{-6} }[/math] |
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