K12a929
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^7-4 q^6+10 q^5-18 q^4+25 q^3-30 q^2+32 q-29+24 q^{-1} -16 q^{-2} +9 q^{-3} -4 q^{-4} + q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+10 t^3-25 t^2+41 t-47+41 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-z^2+1 }[/math] |
| Determinant | 203 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8+a^2 z^6-4 z^6 a^{-2} +z^6 a^{-4} -4 z^6+3 a^2 z^4-6 z^4 a^{-2} +3 z^4 a^{-4} -5 z^4+2 a^2 z^2-5 z^2 a^{-2} +3 z^2 a^{-4} -z^2-2 a^{-2} + a^{-4} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +6 a^2 z^{10}+11 z^{10} a^{-2} +17 z^{10}+4 a^3 z^9+4 a z^9+20 z^9 a^{-1} +20 z^9 a^{-3} +a^4 z^8-22 a^2 z^8-4 z^8 a^{-2} +23 z^8 a^{-4} -50 z^8-17 a^3 z^7-46 a z^7-82 z^7 a^{-1} -35 z^7 a^{-3} +18 z^7 a^{-5} -4 a^4 z^6+23 a^2 z^6-49 z^6 a^{-2} -42 z^6 a^{-4} +10 z^6 a^{-6} +30 z^6+24 a^3 z^5+66 a z^5+75 z^5 a^{-1} +5 z^5 a^{-3} -24 z^5 a^{-5} +4 z^5 a^{-7} +5 a^4 z^4-4 a^2 z^4+50 z^4 a^{-2} +24 z^4 a^{-4} -6 z^4 a^{-6} +z^4 a^{-8} +10 z^4-12 a^3 z^3-27 a z^3-20 z^3 a^{-1} +7 z^3 a^{-3} +12 z^3 a^{-5} -2 a^4 z^2-2 a^2 z^2-17 z^2 a^{-2} -7 z^2 a^{-4} +2 z^2 a^{-6} -8 z^2+a^3 z+2 a z-3 z a^{-3} -2 z a^{-5} +2 a^{-2} + a^{-4} +2 }[/math] |
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