K12a884
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+5 q^7-13 q^6+25 q^5-37 q^4+45 q^3-48 q^2+45 q-36+25 q^{-1} -13 q^{-2} +5 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+9 t^3-33 t^2+66 t-81+66 t^{-1} -33 t^{-2} +9 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+z^6+z^4-z^2+1 }[/math] |
| Determinant | 299 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -3 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-5 z^4 a^{-2} +4 z^4 a^{-4} -z^4 a^{-6} +4 z^4-a^2 z^2-5 z^2 a^{-2} +3 z^2 a^{-4} -z^2 a^{-6} +3 z^2-2 a^{-2} + a^{-4} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 5 z^{11} a^{-1} +5 z^{11} a^{-3} +30 z^{10} a^{-2} +18 z^{10} a^{-4} +12 z^{10}+11 a z^9+23 z^9 a^{-1} +39 z^9 a^{-3} +27 z^9 a^{-5} +5 a^2 z^8-52 z^8 a^{-2} -6 z^8 a^{-4} +23 z^8 a^{-6} -18 z^8+a^3 z^7-27 a z^7-87 z^7 a^{-1} -115 z^7 a^{-3} -43 z^7 a^{-5} +13 z^7 a^{-7} -12 a^2 z^6-5 z^6 a^{-2} -44 z^6 a^{-4} -32 z^6 a^{-6} +5 z^6 a^{-8} -10 z^6-2 a^3 z^5+22 a z^5+79 z^5 a^{-1} +91 z^5 a^{-3} +24 z^5 a^{-5} -11 z^5 a^{-7} +z^5 a^{-9} +10 a^2 z^4+34 z^4 a^{-2} +41 z^4 a^{-4} +18 z^4 a^{-6} -2 z^4 a^{-8} +23 z^4+a^3 z^3-7 a z^3-27 z^3 a^{-1} -27 z^3 a^{-3} -5 z^3 a^{-5} +3 z^3 a^{-7} -3 a^2 z^2-15 z^2 a^{-2} -11 z^2 a^{-4} -3 z^2 a^{-6} -10 z^2+a z+3 z a^{-1} +2 z a^{-3} +2 a^{-2} + a^{-4} +2 }[/math] |
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