K12a760
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+3 q^3-6 q^2+10 q-13+16 q^{-1} -17 q^{-2} +16 q^{-3} -12 q^{-4} +9 q^{-5} -5 q^{-6} +2 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-14 t^2+24 t-27+24 t^{-1} -14 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+10 z^4+4 z^2+1 }[/math] |
| Determinant | 111 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^6-3 z^2 a^6-2 a^6+z^6 a^4+3 z^4 a^4+3 z^2 a^4+2 a^4+2 z^6 a^2+7 z^4 a^2+7 z^2 a^2+2 a^2+z^6+2 z^4-z^2-1-z^4 a^{-2} -2 z^2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+2 a^4 z^{10}+5 a^2 z^{10}+3 z^{10}+3 a^5 z^9+a^3 z^9+2 a z^9+4 z^9 a^{-1} +4 a^6 z^8-16 a^2 z^8+3 z^8 a^{-2} -9 z^8+3 a^7 z^7-3 a^5 z^7-2 a^3 z^7-12 a z^7-15 z^7 a^{-1} +z^7 a^{-3} +2 a^8 z^6-10 a^6 z^6-8 a^4 z^6+26 a^2 z^6-12 z^6 a^{-2} +10 z^6+a^9 z^5-5 a^7 z^5-3 a^5 z^5-4 a^3 z^5+14 a z^5+17 z^5 a^{-1} -4 z^5 a^{-3} -4 a^8 z^4+16 a^6 z^4+17 a^4 z^4-28 a^2 z^4+13 z^4 a^{-2} -12 z^4-3 a^9 z^3+2 a^7 z^3+12 a^5 z^3+8 a^3 z^3-12 a z^3-9 z^3 a^{-1} +4 z^3 a^{-3} +a^8 z^2-12 a^6 z^2-9 a^4 z^2+13 a^2 z^2-3 z^2 a^{-2} +6 z^2+2 a^9 z-a^7 z-5 a^5 z-a^3 z+3 a z+2 z a^{-1} +2 a^6+2 a^4-2 a^2-1 }[/math] |
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