K12a748
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-3 q^7+6 q^6-11 q^5+16 q^4-19 q^3+21 q^2-20 q+17-12 q^{-1} +7 q^{-2} -3 q^{-3} + q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+16 t^2-30 t+37-30 t^{-1} +16 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-8 z^4-2 z^2+1 }[/math] |
| Determinant | 137 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -2 z^6 a^{-2} -z^6 a^{-4} -z^6+a^2 z^4-6 z^4 a^{-2} -2 z^4 a^{-4} +z^4 a^{-6} -2 z^4+2 a^2 z^2-5 z^2 a^{-2} +2 z^2 a^{-6} -z^2+a^2- a^{-2} + a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +4 z^{10} a^{-2} +7 z^{10} a^{-4} +3 z^{10} a^{-6} +8 z^9 a^{-1} +11 z^9 a^{-3} +6 z^9 a^{-5} +3 z^9 a^{-7} +4 z^8 a^{-2} -17 z^8 a^{-4} -10 z^8 a^{-6} +z^8 a^{-8} +10 z^8+9 a z^7-10 z^7 a^{-1} -40 z^7 a^{-3} -36 z^7 a^{-5} -15 z^7 a^{-7} +6 a^2 z^6-33 z^6 a^{-2} -z^6 a^{-4} +5 z^6 a^{-6} -5 z^6 a^{-8} -16 z^6+3 a^3 z^5-13 a z^5-6 z^5 a^{-1} +35 z^5 a^{-3} +50 z^5 a^{-5} +25 z^5 a^{-7} +a^4 z^4-6 a^2 z^4+31 z^4 a^{-2} +15 z^4 a^{-4} +7 z^4 a^{-6} +8 z^4 a^{-8} +8 z^4-2 a^3 z^3+10 a z^3+8 z^3 a^{-1} -13 z^3 a^{-3} -24 z^3 a^{-5} -15 z^3 a^{-7} -a^4 z^2+4 a^2 z^2-12 z^2 a^{-2} -6 z^2 a^{-4} -3 z^2 a^{-6} -4 z^2 a^{-8} -2 a z-2 z a^{-1} +2 z a^{-3} +4 z a^{-5} +2 z a^{-7} -a^2+ a^{-2} + a^{-4} }[/math] |
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