K12a819
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+8 q^4-14 q^3+20 q^2-24 q+27-24 q^{-1} +20 q^{-2} -14 q^{-3} +8 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^5+5 t^4-12 t^3+21 t^2-29 t+33-29 t^{-1} +21 t^{-2} -12 t^{-3} +5 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^{10}-5 z^8-7 z^6-z^4+2 z^2+1 }[/math] |
| Determinant | 169 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^{10}+a^2 z^8+z^8 a^{-2} -7 z^8+5 a^2 z^6+5 z^6 a^{-2} -17 z^6+7 a^2 z^4+7 z^4 a^{-2} -15 z^4+a^2 z^2+z^2 a^{-2} -2 a^2-2 a^{-2} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +7 a^2 z^{10}+7 z^{10} a^{-2} +14 z^{10}+8 a^3 z^9+a z^9+z^9 a^{-1} +8 z^9 a^{-3} +7 a^4 z^8-19 a^2 z^8-19 z^8 a^{-2} +7 z^8 a^{-4} -52 z^8+4 a^5 z^7-20 a^3 z^7-22 a z^7-22 z^7 a^{-1} -20 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-18 a^4 z^6+22 a^2 z^6+22 z^6 a^{-2} -18 z^6 a^{-4} +z^6 a^{-6} +82 z^6-10 a^5 z^5+13 a^3 z^5+40 a z^5+40 z^5 a^{-1} +13 z^5 a^{-3} -10 z^5 a^{-5} -2 a^6 z^4+10 a^4 z^4-11 a^2 z^4-11 z^4 a^{-2} +10 z^4 a^{-4} -2 z^4 a^{-6} -46 z^4+4 a^5 z^3-a^3 z^3-18 a z^3-18 z^3 a^{-1} -z^3 a^{-3} +4 z^3 a^{-5} -a^4 z^2-z^2 a^{-4} +2 z^2-a^3 z-a z-z a^{-1} -z a^{-3} +2 a^2+2 a^{-2} +5 }[/math] |
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