K12a32
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+4 q^3-8 q^2+13 q-17+21 q^{-1} -22 q^{-2} +20 q^{-3} -16 q^{-4} +11 q^{-5} -6 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-13 t^2+34 t-45+34 t^{-1} -13 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-z^4+1 }[/math] |
| Determinant | 143 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^8+3 z^2 a^6+3 a^6-3 z^4 a^4-5 z^2 a^4-3 a^4+z^6 a^2+z^4 a^2+z^2 a^2+a^2+z^6+2 z^4+2 z^2+1-z^4 a^{-2} -z^2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+3 a^4 z^{10}+7 a^2 z^{10}+4 z^{10}+4 a^5 z^9+8 a^3 z^9+10 a z^9+6 z^9 a^{-1} +4 a^6 z^8-13 a^2 z^8+4 z^8 a^{-2} -5 z^8+4 a^7 z^7-a^5 z^7-25 a^3 z^7-41 a z^7-20 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6+a^6 z^6-2 a^4 z^6-3 a^2 z^6-14 z^6 a^{-2} -17 z^6+a^9 z^5-4 a^7 z^5-3 a^5 z^5+27 a^3 z^5+45 a z^5+17 z^5 a^{-1} -3 z^5 a^{-3} -6 a^8 z^4-12 a^6 z^4-5 a^4 z^4+14 a^2 z^4+13 z^4 a^{-2} +26 z^4-2 a^9 z^3-a^7 z^3+a^5 z^3-12 a^3 z^3-19 a z^3-5 z^3 a^{-1} +2 z^3 a^{-3} +4 a^8 z^2+11 a^6 z^2+9 a^4 z^2-4 a^2 z^2-4 z^2 a^{-2} -10 z^2+a^9 z+a^7 z+2 a^3 z+3 a z+z a^{-1} -a^8-3 a^6-3 a^4-a^2+1 }[/math] |
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