K12n772
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+4 q^7-10 q^6+15 q^5-19 q^4+22 q^3-20 q^2+17 q-11+6 q^{-1} -2 q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-13 t^2+29 t-37+29 t^{-1} -13 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+5 z^4+4 z^2+1 }[/math] |
| Determinant | 127 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ 2 z^6 a^{-2} +z^6 a^{-4} +7 z^4 a^{-2} +z^4 a^{-4} -z^4 a^{-6} -2 z^4+10 z^2 a^{-2} -z^2 a^{-4} -z^2 a^{-6} -4 z^2+5 a^{-2} - a^{-4} - a^{-6} -2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10} a^{-4} +3 z^9 a^{-1} +10 z^9 a^{-3} +7 z^9 a^{-5} +z^8 a^{-2} +11 z^8 a^{-4} +11 z^8 a^{-6} +z^8-5 z^7 a^{-1} -18 z^7 a^{-3} -4 z^7 a^{-5} +9 z^7 a^{-7} +3 z^6 a^{-2} -25 z^6 a^{-4} -20 z^6 a^{-6} +4 z^6 a^{-8} +4 z^6+3 a z^5+12 z^5 a^{-1} +16 z^5 a^{-3} -9 z^5 a^{-5} -15 z^5 a^{-7} +z^5 a^{-9} -16 z^4 a^{-2} +13 z^4 a^{-4} +14 z^4 a^{-6} -4 z^4 a^{-8} -11 z^4-6 a z^3-18 z^3 a^{-1} -12 z^3 a^{-3} +10 z^3 a^{-5} +9 z^3 a^{-7} -z^3 a^{-9} +14 z^2 a^{-2} +2 z^2 a^{-4} -5 z^2 a^{-6} +7 z^2+3 a z+7 z a^{-1} +5 z a^{-3} -3 z a^{-5} -4 z a^{-7} -5 a^{-2} - a^{-4} + a^{-6} -2 }[/math] |
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