K12a985
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+4-8 q^{-1} +14 q^{-2} -19 q^{-3} +23 q^{-4} -24 q^{-5} +23 q^{-6} -18 q^{-7} +12 q^{-8} -7 q^{-9} +3 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-9 t^3+21 t^2-30 t+33-30 t^{-1} +21 t^{-2} -9 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+7 z^6+7 z^4+5 z^2+1 }[/math] |
| Determinant | 157 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-4 z^4 a^8-5 z^2 a^8-3 a^8+z^8 a^6+5 z^6 a^6+10 z^4 a^6+11 z^2 a^6+5 a^6+z^8 a^4+4 z^6 a^4+4 z^4 a^4-2 a^4-z^6 a^2-3 z^4 a^2-z^2 a^2+a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-2 z^3 a^{13}+3 z^6 a^{12}-5 z^4 a^{12}+6 z^7 a^{11}-13 z^5 a^{11}+10 z^3 a^{11}-3 z a^{11}+8 z^8 a^{10}-19 z^6 a^{10}+20 z^4 a^{10}-6 z^2 a^{10}+8 z^9 a^9-19 z^7 a^9+21 z^5 a^9-6 z^3 a^9+2 z a^9+6 z^{10} a^8-13 z^8 a^8+15 z^6 a^8-9 z^4 a^8+9 z^2 a^8-3 a^8+2 z^{11} a^7+7 z^9 a^7-36 z^7 a^7+59 z^5 a^7-42 z^3 a^7+10 z a^7+11 z^{10} a^6-36 z^8 a^6+52 z^6 a^6-47 z^4 a^6+22 z^2 a^6-5 a^6+2 z^{11} a^5+5 z^9 a^5-31 z^7 a^5+42 z^5 a^5-30 z^3 a^5+7 z a^5+5 z^{10} a^4-11 z^8 a^4+z^6 a^4+5 z^2 a^4-2 a^4+6 z^9 a^3-19 z^7 a^3+15 z^5 a^3-4 z^3 a^3+2 z a^3+4 z^8 a^2-14 z^6 a^2+13 z^4 a^2-2 z^2 a^2-a^2+z^7 a-3 z^5 a+2 z^3 a }[/math] |
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