K12a1193
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-6 q^2+16 q-28+41 q^{-1} -49 q^{-2} +52 q^{-3} -48 q^{-4} +38 q^{-5} -25 q^{-6} +13 q^{-7} -5 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+13 t^3-38 t^2+68 t-81+68 t^{-1} -38 t^{-2} +13 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-3 z^6+z^2+1 }[/math] |
| Determinant | 323 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^4 z^8-a^2 z^8+a^6 z^6-3 a^4 z^6-2 a^2 z^6+z^6+2 a^6 z^4-4 a^4 z^4+a^2 z^4+z^4+a^6 z^2-3 a^4 z^2+4 a^2 z^2-z^2-a^4+2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 6 a^5 z^{11}+6 a^3 z^{11}+16 a^6 z^{10}+34 a^4 z^{10}+18 a^2 z^{10}+18 a^7 z^9+29 a^5 z^9+34 a^3 z^9+23 a z^9+12 a^8 z^8-16 a^6 z^8-56 a^4 z^8-12 a^2 z^8+16 z^8+5 a^9 z^7-32 a^7 z^7-86 a^5 z^7-93 a^3 z^7-38 a z^7+6 z^7 a^{-1} +a^{10} z^6-20 a^8 z^6-9 a^6 z^6+12 a^4 z^6-25 a^2 z^6+z^6 a^{-2} -24 z^6-7 a^9 z^5+22 a^7 z^5+72 a^5 z^5+63 a^3 z^5+15 a z^5-5 z^5 a^{-1} -a^{10} z^4+11 a^8 z^4+17 a^6 z^4+12 a^4 z^4+15 a^2 z^4+8 z^4+2 a^9 z^3-6 a^7 z^3-20 a^5 z^3-14 a^3 z^3-2 a z^3-2 a^8 z^2-5 a^6 z^2-2 a^4 z^2+2 a^2 z^2+z^2+a^5 z+a^3 z-a^4-2 a^2 }[/math] |
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