K12a742
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^5-3 q^4+6 q^3-11 q^2+16 q-18+21 q^{-1} -20 q^{-2} +16 q^{-3} -12 q^{-4} +7 q^{-5} -3 q^{-6} + q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+8 t^3-17 t^2+26 t-29+26 t^{-1} -17 t^{-2} +8 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-8 z^6-9 z^4-2 z^2+1 }[/math] |
| Determinant | 135 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8-z^8+a^4 z^6-5 a^2 z^6+z^6 a^{-2} -5 z^6+4 a^4 z^4-9 a^2 z^4+4 z^4 a^{-2} -8 z^4+5 a^4 z^2-8 a^2 z^2+4 z^2 a^{-2} -3 z^2+2 a^4-4 a^2+3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +4 a^2 z^{10}+3 z^{10} a^{-2} +7 z^{10}+8 a^3 z^9+11 a z^9+6 z^9 a^{-1} +3 z^9 a^{-3} +10 a^4 z^8+4 a^2 z^8-10 z^8 a^{-2} +z^8 a^{-4} -17 z^8+9 a^5 z^7-11 a^3 z^7-41 a z^7-36 z^7 a^{-1} -15 z^7 a^{-3} +6 a^6 z^6-18 a^4 z^6-37 a^2 z^6+5 z^6 a^{-2} -5 z^6 a^{-4} -3 z^6+3 a^7 z^5-14 a^5 z^5-6 a^3 z^5+34 a z^5+48 z^5 a^{-1} +25 z^5 a^{-3} +a^8 z^4-6 a^6 z^4+14 a^4 z^4+41 a^2 z^4+6 z^4 a^{-2} +8 z^4 a^{-4} +18 z^4-2 a^7 z^3+12 a^5 z^3+13 a^3 z^3-6 a z^3-20 z^3 a^{-1} -15 z^3 a^{-3} -a^8 z^2+3 a^6 z^2-7 a^4 z^2-19 a^2 z^2-2 z^2 a^{-2} -4 z^2 a^{-4} -6 z^2-4 a^5 z-7 a^3 z-3 a z+z a^{-1} +z a^{-3} +2 a^4+4 a^2+3 }[/math] |
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