K12a717
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+3-5 q^{-1} +8 q^{-2} -10 q^{-3} +13 q^{-4} -13 q^{-5} +12 q^{-6} -10 q^{-7} +7 q^{-8} -4 q^{-9} +2 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-7 t^3+13 t^2-15 t+15-15 t^{-1} +13 t^{-2} -7 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+9 z^6+11 z^4+6 z^2+1 }[/math] |
| Determinant | 89 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-5 z^4 a^8-7 z^2 a^8-3 a^8+z^8 a^6+6 z^6 a^6+13 z^4 a^6+13 z^2 a^6+4 a^6+z^8 a^4+5 z^6 a^4+7 z^4 a^4+3 z^2 a^4-z^6 a^2-4 z^4 a^2-3 z^2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-3 z^3 a^{13}+2 z a^{13}+2 z^6 a^{12}-5 z^4 a^{12}+3 z^2 a^{12}+2 z^7 a^{11}-2 z^5 a^{11}-2 z^3 a^{11}+z a^{11}+2 z^8 a^{10}-2 z^6 a^{10}+z^4 a^{10}-z^2 a^{10}+2 z^9 a^9-4 z^7 a^9+8 z^5 a^9-7 z^3 a^9+2 z a^9+2 z^{10} a^8-7 z^8 a^8+17 z^6 a^8-19 z^4 a^8+12 z^2 a^8-3 a^8+z^{11} a^7-z^9 a^7-4 z^7 a^7+14 z^5 a^7-13 z^3 a^7+4 z a^7+5 z^{10} a^6-23 z^8 a^6+44 z^6 a^6-43 z^4 a^6+21 z^2 a^6-4 a^6+z^{11} a^5+z^9 a^5-16 z^7 a^5+26 z^5 a^5-15 z^3 a^5+2 z a^5+3 z^{10} a^4-11 z^8 a^4+10 z^6 a^4-4 z^4 a^4+z^2 a^4+4 z^9 a^3-17 z^7 a^3+19 z^5 a^3-7 z^3 a^3+z a^3+3 z^8 a^2-13 z^6 a^2+14 z^4 a^2-4 z^2 a^2+z^7 a-4 z^5 a+3 z^3 a }[/math] |
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