K12a473
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+5 q^4-13 q^3+24 q^2-35 q+44-46 q^{-1} +43 q^{-2} -35 q^{-3} +24 q^{-4} -13 q^{-5} +5 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+30 t^2-64 t+83-64 t^{-1} +30 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+2 z^4+1 }[/math] |
| Determinant | 289 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-3 a^2 z^6-z^6 a^{-2} +4 z^6+3 a^4 z^4-7 a^2 z^4-2 z^4 a^{-2} +8 z^4-a^6 z^2+3 a^4 z^2-5 a^2 z^2-2 z^2 a^{-2} +5 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 a^3 z^{11}+4 a z^{11}+11 a^4 z^{10}+26 a^2 z^{10}+15 z^{10}+11 a^5 z^9+26 a^3 z^9+39 a z^9+24 z^9 a^{-1} +5 a^6 z^8-14 a^4 z^8-36 a^2 z^8+22 z^8 a^{-2} +5 z^8+a^7 z^7-28 a^5 z^7-90 a^3 z^7-107 a z^7-33 z^7 a^{-1} +13 z^7 a^{-3} -12 a^6 z^6-17 a^4 z^6-28 a^2 z^6-31 z^6 a^{-2} +5 z^6 a^{-4} -59 z^6-2 a^7 z^5+24 a^5 z^5+79 a^3 z^5+79 a z^5+13 z^5 a^{-1} -12 z^5 a^{-3} +z^5 a^{-5} +10 a^6 z^4+27 a^4 z^4+45 a^2 z^4+19 z^4 a^{-2} -2 z^4 a^{-4} +49 z^4+a^7 z^3-8 a^5 z^3-25 a^3 z^3-23 a z^3-3 z^3 a^{-1} +4 z^3 a^{-3} -3 a^6 z^2-8 a^4 z^2-12 a^2 z^2-5 z^2 a^{-2} -12 z^2+a^5 z+3 a^3 z+3 a z+z a^{-1} +1 }[/math] |
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