K12a757
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+8 q^7-14 q^6+20 q^5-24 q^4+26 q^3-23 q^2+19 q-13+7 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+9 t^3-20 t^2+32 t-37+32 t^{-1} -20 t^{-2} +9 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-7 z^6-6 z^4+z^2+1 }[/math] |
| Determinant | 163 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -5 z^6 a^{-2} -4 z^6 a^{-4} +z^6 a^{-6} +z^6-10 z^4 a^{-2} -3 z^4 a^{-4} +3 z^4 a^{-6} +4 z^4-10 z^2 a^{-2} +5 z^2 a^{-4} +z^2 a^{-6} +5 z^2-4 a^{-2} +5 a^{-4} -2 a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +3 z^{10} a^{-2} +7 z^{10} a^{-4} +4 z^{10} a^{-6} +5 z^9 a^{-1} +9 z^9 a^{-3} +11 z^9 a^{-5} +7 z^9 a^{-7} +4 z^8 a^{-2} -7 z^8 a^{-4} +z^8 a^{-6} +7 z^8 a^{-8} +5 z^8+3 a z^7-7 z^7 a^{-1} -21 z^7 a^{-3} -29 z^7 a^{-5} -14 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-22 z^6 a^{-2} -8 z^6 a^{-4} -18 z^6 a^{-6} -18 z^6 a^{-8} +z^6 a^{-10} -12 z^6-8 a z^5-2 z^5 a^{-1} +16 z^5 a^{-3} +26 z^5 a^{-5} +6 z^5 a^{-7} -10 z^5 a^{-9} -3 a^2 z^4+29 z^4 a^{-2} +22 z^4 a^{-4} +21 z^4 a^{-6} +13 z^4 a^{-8} -2 z^4 a^{-10} +10 z^4+6 a z^3+7 z^3 a^{-1} -4 z^3 a^{-5} +2 z^3 a^{-7} +5 z^3 a^{-9} +2 a^2 z^2-18 z^2 a^{-2} -16 z^2 a^{-4} -9 z^2 a^{-6} -3 z^2 a^{-8} -6 z^2-2 a z-4 z a^{-1} -3 z a^{-3} -3 z a^{-5} -2 z a^{-7} +4 a^{-2} +5 a^{-4} +2 a^{-6} +2 }[/math] |
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