K12a761
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+3 q^3-6 q^2+11 q-16+20 q^{-1} -21 q^{-2} +21 q^{-3} -17 q^{-4} +12 q^{-5} -7 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-16 t^2+31 t-37+31 t^{-1} -16 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+8 z^4+3 z^2+1 }[/math] |
| Determinant | 139 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^6-2 z^2 a^6-a^6+z^6 a^4+2 z^4 a^4+z^2 a^4+2 z^6 a^2+6 z^4 a^2+6 z^2 a^2+3 a^2+z^6+2 z^4-1-z^4 a^{-2} -2 z^2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+3 a^4 z^{10}+6 a^2 z^{10}+3 z^{10}+5 a^5 z^9+6 a^3 z^9+5 a z^9+4 z^9 a^{-1} +6 a^6 z^8+2 a^4 z^8-13 a^2 z^8+3 z^8 a^{-2} -6 z^8+5 a^7 z^7-3 a^5 z^7-13 a^3 z^7-20 a z^7-14 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6-8 a^6 z^6-9 a^4 z^6+15 a^2 z^6-12 z^6 a^{-2} +z^6+a^9 z^5-7 a^7 z^5-4 a^5 z^5+8 a^3 z^5+24 a z^5+16 z^5 a^{-1} -4 z^5 a^{-3} -5 a^8 z^4+6 a^6 z^4+7 a^4 z^4-19 a^2 z^4+14 z^4 a^{-2} -z^4-2 a^9 z^3+3 a^7 z^3+7 a^5 z^3-3 a^3 z^3-18 a z^3-9 z^3 a^{-1} +4 z^3 a^{-3} +2 a^8 z^2-4 a^6 z^2+12 a^2 z^2-4 z^2 a^{-2} +2 z^2+a^9 z-a^7 z-2 a^5 z+2 a^3 z+4 a z+2 z a^{-1} +a^6-3 a^2-1 }[/math] |
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