K12a949
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+9 q^7-17 q^6+25 q^5-30 q^4+33 q^3-31 q^2+25 q-17+10 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+10 t^3-25 t^2+42 t-49+42 t^{-1} -25 t^{-2} +10 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-6 z^6-5 z^4+1 }[/math] |
| Determinant | 207 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -4 z^6 a^{-2} -4 z^6 a^{-4} +z^6 a^{-6} +z^6-6 z^4 a^{-2} -5 z^4 a^{-4} +3 z^4 a^{-6} +3 z^4-5 z^2 a^{-2} +2 z^2 a^{-6} +3 z^2-3 a^{-2} +3 a^{-4} - a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-3} +3 z^{11} a^{-5} +9 z^{10} a^{-2} +16 z^{10} a^{-4} +7 z^{10} a^{-6} +12 z^9 a^{-1} +12 z^9 a^{-3} +8 z^9 a^{-5} +8 z^9 a^{-7} -16 z^8 a^{-2} -40 z^8 a^{-4} -8 z^8 a^{-6} +7 z^8 a^{-8} +9 z^8+4 a z^7-33 z^7 a^{-1} -50 z^7 a^{-3} -27 z^7 a^{-5} -10 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6+z^6 a^{-2} +41 z^6 a^{-4} +2 z^6 a^{-6} -13 z^6 a^{-8} +z^6 a^{-10} -23 z^6-8 a z^5+34 z^5 a^{-1} +64 z^5 a^{-3} +26 z^5 a^{-5} -5 z^5 a^{-7} -9 z^5 a^{-9} -2 a^2 z^4+20 z^4 a^{-2} -10 z^4 a^{-4} -3 z^4 a^{-6} +5 z^4 a^{-8} -2 z^4 a^{-10} +18 z^4+a z^3-15 z^3 a^{-1} -26 z^3 a^{-3} -8 z^3 a^{-5} +8 z^3 a^{-7} +6 z^3 a^{-9} -14 z^2 a^{-2} -7 z^2 a^{-4} -2 z^2 a^{-6} +z^2 a^{-10} -8 z^2+2 z a^{-1} +3 z a^{-3} -z a^{-5} -3 z a^{-7} -z a^{-9} +3 a^{-2} +3 a^{-4} + a^{-6} +2 }[/math] |
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