K12a424
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+2 q^3-5 q^2+10 q-14+19 q^{-1} -20 q^{-2} +20 q^{-3} -17 q^{-4} +12 q^{-5} -7 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-15 t^2+29 t-35+29 t^{-1} -15 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+9 z^4+5 z^2+1 }[/math] |
| Determinant | 131 |
| 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+5 z^2 a^2+a^2+z^6+3 z^4+4 z^2+3-z^4 a^{-2} -3 z^2 a^{-2} -2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+3 a^4 z^{10}+5 a^2 z^{10}+2 z^{10}+5 a^5 z^9+4 a^3 z^9+a z^9+2 z^9 a^{-1} +6 a^6 z^8-11 a^2 z^8+2 z^8 a^{-2} -3 z^8+5 a^7 z^7-4 a^5 z^7-6 a^3 z^7-a z^7-3 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6-8 a^6 z^6-2 a^4 z^6+16 a^2 z^6-8 z^6 a^{-2} -z^6+a^9 z^5-7 a^7 z^5-a^5 z^5+a^3 z^5-9 a z^5-8 z^5 a^{-1} -5 z^5 a^{-3} -5 a^8 z^4+5 a^6 z^4-19 a^2 z^4+10 z^4 a^{-2} +z^4-2 a^9 z^3+3 a^7 z^3+4 a^5 z^3-a^3 z^3+8 a z^3+16 z^3 a^{-1} +8 z^3 a^{-3} +2 a^8 z^2-2 a^6 z^2+a^4 z^2+7 a^2 z^2-5 z^2 a^{-2} -3 z^2+a^9 z-a^7 z-a^5 z+a^3 z-3 a z-7 z a^{-1} -4 z a^{-3} +a^6-a^2+2 a^{-2} +3 }[/math] |
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