K12a754
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+5 q^7-13 q^6+23 q^5-33 q^4+40 q^3-42 q^2+39 q-30+21 q^{-1} -11 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+9 t^3-30 t^2+57 t-69+57 t^{-1} -30 t^{-2} +9 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+z^6+4 z^4+2 z^2+1 }[/math] |
| Determinant | 263 |
| 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^4-3 z^4 a^{-2} +4 z^4 a^{-4} -z^4 a^{-6} +5 z^4-2 a^2 z^2+z^2 a^{-4} -z^2 a^{-6} +4 z^2-a^2+ a^{-2} - a^{-4} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-1} +3 z^{11} a^{-3} +20 z^{10} a^{-2} +12 z^{10} a^{-4} +8 z^{10}+8 a z^9+20 z^9 a^{-1} +33 z^9 a^{-3} +21 z^9 a^{-5} +4 a^2 z^8-24 z^8 a^{-2} +10 z^8 a^{-4} +21 z^8 a^{-6} -9 z^8+a^3 z^7-20 a z^7-66 z^7 a^{-1} -83 z^7 a^{-3} -25 z^7 a^{-5} +13 z^7 a^{-7} -11 a^2 z^6-28 z^6 a^{-2} -59 z^6 a^{-4} -30 z^6 a^{-6} +5 z^6 a^{-8} -15 z^6-3 a^3 z^5+16 a z^5+55 z^5 a^{-1} +51 z^5 a^{-3} +z^5 a^{-5} -13 z^5 a^{-7} +z^5 a^{-9} +11 a^2 z^4+37 z^4 a^{-2} +44 z^4 a^{-4} +17 z^4 a^{-6} -2 z^4 a^{-8} +23 z^4+3 a^3 z^3-4 a z^3-14 z^3 a^{-1} -7 z^3 a^{-3} +5 z^3 a^{-5} +5 z^3 a^{-7} -5 a^2 z^2-7 z^2 a^{-2} -8 z^2 a^{-4} -5 z^2 a^{-6} -9 z^2-a^3 z-a z-z a^{-5} -z a^{-7} +a^2- a^{-2} - a^{-4} +2 }[/math] |
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