K12a751
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-8 q^3+14 q^2-20 q+24-25 q^{-1} +23 q^{-2} -18 q^{-3} +13 q^{-4} -7 q^{-5} +3 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+14 t^2-38 t+53-38 t^{-1} +14 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+2 z^4+1 }[/math] |
| Determinant | 161 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6-a^6+2 z^4 a^4+3 z^2 a^4+2 a^4-z^6 a^2-z^4 a^2-z^2 a^2-z^6-z^4-2 z^2-1+2 z^4 a^{-2} +2 z^2 a^{-2} + a^{-2} -z^2 a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+5 a^4 z^{10}+11 a^2 z^{10}+6 z^{10}+5 a^5 z^9+5 a^3 z^9+8 a z^9+8 z^9 a^{-1} +3 a^6 z^8-14 a^4 z^8-34 a^2 z^8+8 z^8 a^{-2} -9 z^8+a^7 z^7-17 a^5 z^7-35 a^3 z^7-35 a z^7-11 z^7 a^{-1} +7 z^7 a^{-3} -11 a^6 z^6+8 a^4 z^6+39 a^2 z^6-8 z^6 a^{-2} +4 z^6 a^{-4} +8 z^6-4 a^7 z^5+16 a^5 z^5+51 a^3 z^5+47 a z^5+5 z^5 a^{-1} -10 z^5 a^{-3} +z^5 a^{-5} +11 a^6 z^4+2 a^4 z^4-19 a^2 z^4-4 z^4 a^{-2} -6 z^4 a^{-4} -8 z^4+4 a^7 z^3-7 a^5 z^3-29 a^3 z^3-23 a z^3-z^3 a^{-1} +3 z^3 a^{-3} -z^3 a^{-5} -5 a^6 z^2-5 a^4 z^2+4 a^2 z^2+5 z^2 a^{-2} +2 z^2 a^{-4} +7 z^2-a^7 z+a^5 z+5 a^3 z+3 a z+a^6+2 a^4- a^{-2} -1 }[/math] |
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