K12a951
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+5 q^3-13 q^2+24 q-35+44 q^{-1} -47 q^{-2} +45 q^{-3} -36 q^{-4} +25 q^{-5} -14 q^{-6} +5 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+9 t^3-32 t^2+65 t-81+65 t^{-1} -32 t^{-2} +9 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+z^6+2 z^4+2 z^2+1 }[/math] |
| Determinant | 295 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+2 a^4 z^6-3 a^2 z^6+2 z^6-a^6 z^4+4 a^4 z^4-4 a^2 z^4-z^4 a^{-2} +4 z^4-a^6 z^2+3 a^4 z^2-a^2 z^2-z^2 a^{-2} +2 z^2-a^6+a^4+a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 5 a^3 z^{11}+5 a z^{11}+17 a^4 z^{10}+29 a^2 z^{10}+12 z^{10}+26 a^5 z^9+35 a^3 z^9+20 a z^9+11 z^9 a^{-1} +24 a^6 z^8-3 a^4 z^8-53 a^2 z^8+5 z^8 a^{-2} -21 z^8+14 a^7 z^7-36 a^5 z^7-99 a^3 z^7-78 a z^7-28 z^7 a^{-1} +z^7 a^{-3} +5 a^8 z^6-34 a^6 z^6-42 a^4 z^6+8 a^2 z^6-12 z^6 a^{-2} -z^6+a^9 z^5-13 a^7 z^5+11 a^5 z^5+71 a^3 z^5+71 a z^5+23 z^5 a^{-1} -2 z^5 a^{-3} -a^8 z^4+19 a^6 z^4+30 a^4 z^4+14 a^2 z^4+9 z^4 a^{-2} +13 z^4+6 a^7 z^3+a^5 z^3-20 a^3 z^3-23 a z^3-7 z^3 a^{-1} +z^3 a^{-3} -5 a^6 z^2-6 a^4 z^2-2 a^2 z^2-2 z^2 a^{-2} -3 z^2-2 a^7 z-a^5 z+3 a^3 z+3 a z+z a^{-1} +a^6+a^4-a^2 }[/math] |
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