K12a72
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+4 q^6-9 q^5+16 q^4-23 q^3+29 q^2-31 q+29-24 q^{-1} +17 q^{-2} -9 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+16 t^2-47 t+67-47 t^{-1} +16 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+4 z^4-z^2+1 }[/math] |
| Determinant | 197 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} -z^6+2 a^2 z^4+2 z^4 a^{-4} -a^4 z^2+a^2 z^2+z^2 a^{-4} -z^2 a^{-6} -z^2+a^2+ a^{-2} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +13 z^{10} a^{-2} +6 z^{10} a^{-4} +7 z^{10}+11 a z^9+17 z^9 a^{-1} +13 z^9 a^{-3} +7 z^9 a^{-5} +11 a^2 z^8-25 z^8 a^{-2} -10 z^8 a^{-4} +4 z^8 a^{-6} +8 a^3 z^7-14 a z^7-53 z^7 a^{-1} -54 z^7 a^{-3} -22 z^7 a^{-5} +z^7 a^{-7} +4 a^4 z^6-14 a^2 z^6+4 z^6 a^{-2} -9 z^6 a^{-4} -13 z^6 a^{-6} -18 z^6+a^5 z^5-10 a^3 z^5+7 a z^5+56 z^5 a^{-1} +62 z^5 a^{-3} +21 z^5 a^{-5} -3 z^5 a^{-7} -5 a^4 z^4+5 a^2 z^4+11 z^4 a^{-2} +18 z^4 a^{-4} +12 z^4 a^{-6} +15 z^4-a^5 z^3+4 a^3 z^3-4 a z^3-28 z^3 a^{-1} -30 z^3 a^{-3} -9 z^3 a^{-5} +2 z^3 a^{-7} +2 a^4 z^2+a^2 z^2-3 z^2 a^{-2} -6 z^2 a^{-4} -4 z^2 a^{-6} -2 z^2+a z+5 z a^{-1} +6 z a^{-3} +2 z a^{-5} -a^2- a^{-2} -1 }[/math] |
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