K12a588
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-5 q^8+13 q^7-23 q^6+32 q^5-39 q^4+41 q^3-37 q^2+30 q-19+10 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+11 t^3-30 t^2+53 t-63+53 t^{-1} -30 t^{-2} +11 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-5 z^6-4 z^4+1 }[/math] |
| Determinant | 255 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -4 z^6 a^{-2} -3 z^6 a^{-4} +z^6 a^{-6} +z^6-7 z^4 a^{-2} -2 z^4 a^{-4} +2 z^4 a^{-6} +3 z^4-5 z^2 a^{-2} +z^2 a^{-4} +z^2 a^{-6} +3 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-3} +3 z^{11} a^{-5} +8 z^{10} a^{-2} +19 z^{10} a^{-4} +11 z^{10} a^{-6} +10 z^9 a^{-1} +20 z^9 a^{-3} +26 z^9 a^{-5} +16 z^9 a^{-7} +z^8 a^{-2} -23 z^8 a^{-4} -4 z^8 a^{-6} +12 z^8 a^{-8} +8 z^8+4 a z^7-13 z^7 a^{-1} -50 z^7 a^{-3} -68 z^7 a^{-5} -30 z^7 a^{-7} +5 z^7 a^{-9} +a^2 z^6-26 z^6 a^{-2} -12 z^6 a^{-4} -25 z^6 a^{-6} -22 z^6 a^{-8} +z^6 a^{-10} -15 z^6-8 a z^5+z^5 a^{-1} +36 z^5 a^{-3} +52 z^5 a^{-5} +18 z^5 a^{-7} -7 z^5 a^{-9} -2 a^2 z^4+30 z^4 a^{-2} +25 z^4 a^{-4} +21 z^4 a^{-6} +12 z^4 a^{-8} -z^4 a^{-10} +11 z^4+5 a z^3+5 z^3 a^{-1} -6 z^3 a^{-3} -15 z^3 a^{-5} -7 z^3 a^{-7} +2 z^3 a^{-9} +a^2 z^2-12 z^2 a^{-2} -8 z^2 a^{-4} -5 z^2 a^{-6} -3 z^2 a^{-8} -5 z^2-a z-2 z a^{-1} +2 z a^{-5} +z a^{-7} +1 }[/math] |
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