K12a380
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^3+3 q^2-5 q+7-9 q^{-1} +11 q^{-2} -10 q^{-3} +10 q^{-4} -8 q^{-5} +6 q^{-6} -4 q^{-7} +2 q^{-8} - q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 6 t^2-19 t+27-19 t^{-1} +6 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 6 z^4+5 z^2+1 }[/math] |
| Determinant | 77 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^8-a^8+z^4 a^6+z^2 a^6+2 z^4 a^4+3 z^2 a^4+a^4+2 z^4 a^2+3 z^2 a^2+2 a^2+z^4-1-z^2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^7 z^{11}+a^5 z^{11}+2 a^8 z^{10}+5 a^6 z^{10}+3 a^4 z^{10}+a^9 z^9-2 a^7 z^9+2 a^5 z^9+5 a^3 z^9-13 a^8 z^8-26 a^6 z^8-7 a^4 z^8+6 a^2 z^8-7 a^9 z^7-13 a^7 z^7-26 a^5 z^7-14 a^3 z^7+6 a z^7+28 a^8 z^6+39 a^6 z^6-8 a^4 z^6-13 a^2 z^6+6 z^6+17 a^9 z^5+41 a^7 z^5+42 a^5 z^5+5 a^3 z^5-8 a z^5+5 z^5 a^{-1} -23 a^8 z^4-16 a^6 z^4+18 a^4 z^4+a^2 z^4+3 z^4 a^{-2} -7 z^4-17 a^9 z^3-35 a^7 z^3-18 a^5 z^3+2 a^3 z^3-3 a z^3-4 z^3 a^{-1} +z^3 a^{-3} +6 a^8 z^2-5 a^4 z^2+4 a^2 z^2-z^2 a^{-2} +2 z^2+6 a^9 z+8 a^7 z+2 a^5 z+a z+z a^{-1} -a^8+a^4-2 a^2-1 }[/math] |
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