K12a984
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -1+3 q^{-1} -5 q^{-2} +9 q^{-3} -11 q^{-4} +14 q^{-5} -15 q^{-6} +14 q^{-7} -12 q^{-8} +9 q^{-9} -6 q^{-10} +3 q^{-11} - q^{-12} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^5-4 t^4+9 t^3-13 t^2+16 t-17+16 t^{-1} -13 t^{-2} +9 t^{-3} -4 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{10}+6 z^8+12 z^6+11 z^4+6 z^2+1 }[/math] |
| Determinant | 103 |
| Signature | -6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^6 z^{10}-a^8 z^8+8 a^6 z^8-a^4 z^8-6 a^8 z^6+24 a^6 z^6-6 a^4 z^6-12 a^8 z^4+34 a^6 z^4-11 a^4 z^4-10 a^8 z^2+22 a^6 z^2-6 a^4 z^2-3 a^8+4 a^6 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^3 a^{15}+3 z^4 a^{14}+6 z^5 a^{13}-4 z^3 a^{13}+z a^{13}+9 z^6 a^{12}-12 z^4 a^{12}+3 z^2 a^{12}+11 z^7 a^{11}-22 z^5 a^{11}+9 z^3 a^{11}-2 z a^{11}+11 z^8 a^{10}-28 z^6 a^{10}+15 z^4 a^{10}-4 z^2 a^{10}+9 z^9 a^9-26 z^7 a^9+13 z^5 a^9+z^3 a^9+6 z^{10} a^8-19 z^8 a^8+10 z^6 a^8+7 z^2 a^8-3 a^8+2 z^{11} a^7+z^9 a^7-36 z^7 a^7+65 z^5 a^7-35 z^3 a^7+6 z a^7+9 z^{10} a^6-49 z^8 a^6+88 z^6 a^6-65 z^4 a^6+24 z^2 a^6-4 a^6+2 z^{11} a^5-7 z^9 a^5-5 z^7 a^5+36 z^5 a^5-31 z^3 a^5+5 z a^5+3 z^{10} a^4-19 z^8 a^4+41 z^6 a^4-35 z^4 a^4+10 z^2 a^4+z^9 a^3-6 z^7 a^3+12 z^5 a^3-9 z^3 a^3+2 z a^3 }[/math] |
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