K12a358
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+5 q^7-12 q^6+21 q^5-31 q^4+38 q^3-40 q^2+38 q-30+21 q^{-1} -12 q^{-2} +5 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-28 t^2+56 t-69+56 t^{-1} -28 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 1-z^8 }[/math] |
| Determinant | 255 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -4 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-8 z^4 a^{-2} +5 z^4 a^{-4} -z^4 a^{-6} +5 z^4-a^2 z^2-6 z^2 a^{-2} +4 z^2 a^{-4} -z^2 a^{-6} +4 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-1} +3 z^{11} a^{-3} +20 z^{10} a^{-2} +11 z^{10} a^{-4} +9 z^{10}+10 a z^9+22 z^9 a^{-1} +30 z^9 a^{-3} +18 z^9 a^{-5} +5 a^2 z^8-27 z^8 a^{-2} +7 z^8 a^{-4} +18 z^8 a^{-6} -11 z^8+a^3 z^7-27 a z^7-78 z^7 a^{-1} -82 z^7 a^{-3} -20 z^7 a^{-5} +12 z^7 a^{-7} -13 a^2 z^6-30 z^6 a^{-2} -51 z^6 a^{-4} -24 z^6 a^{-6} +5 z^6 a^{-8} -21 z^6-2 a^3 z^5+21 a z^5+69 z^5 a^{-1} +59 z^5 a^{-3} -z^5 a^{-5} -13 z^5 a^{-7} +z^5 a^{-9} +10 a^2 z^4+53 z^4 a^{-2} +44 z^4 a^{-4} +11 z^4 a^{-6} -3 z^4 a^{-8} +33 z^4+a^3 z^3-5 a z^3-17 z^3 a^{-1} -11 z^3 a^{-3} +4 z^3 a^{-5} +4 z^3 a^{-7} -3 a^2 z^2-18 z^2 a^{-2} -12 z^2 a^{-4} -3 z^2 a^{-6} -12 z^2+1 }[/math] |
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