K12a112
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+3 q^3-7 q^2+13 q-18+24 q^{-1} -26 q^{-2} +25 q^{-3} -21 q^{-4} +15 q^{-5} -9 q^{-6} +4 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-20 t^2+35 t-41+35 t^{-1} -20 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6+2 z^4+2 z^2+1 }[/math] |
| Determinant | 167 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+2 a^4 z^6-5 a^2 z^6+2 z^6-a^6 z^4+7 a^4 z^4-11 a^2 z^4-z^4 a^{-2} +8 z^4-2 a^6 z^2+8 a^4 z^2-12 a^2 z^2-3 z^2 a^{-2} +11 z^2-a^6+3 a^4-5 a^2-2 a^{-2} +6 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+4 a^4 z^{10}+7 a^2 z^{10}+3 z^{10}+8 a^5 z^9+13 a^3 z^9+9 a z^9+4 z^9 a^{-1} +10 a^6 z^8+9 a^4 z^8-4 a^2 z^8+3 z^8 a^{-2} +8 a^7 z^7-5 a^5 z^7-30 a^3 z^7-28 a z^7-10 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-15 a^6 z^6-35 a^4 z^6-27 a^2 z^6-11 z^6 a^{-2} -22 z^6+a^9 z^5-12 a^7 z^5-10 a^5 z^5+16 a^3 z^5+19 a z^5+2 z^5 a^{-1} -4 z^5 a^{-3} -5 a^8 z^4+9 a^6 z^4+37 a^4 z^4+42 a^2 z^4+13 z^4 a^{-2} +32 z^4-a^9 z^3+6 a^7 z^3+13 a^5 z^3+5 a^3 z^3+a z^3+7 z^3 a^{-1} +5 z^3 a^{-3} +a^8 z^2-4 a^6 z^2-16 a^4 z^2-24 a^2 z^2-7 z^2 a^{-2} -20 z^2-2 a^7 z-4 a^5 z-4 a^3 z-4 a z-4 z a^{-1} -2 z a^{-3} +a^6+3 a^4+5 a^2+2 a^{-2} +6 }[/math] |
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