K12a534
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+4 q-9+15 q^{-1} -20 q^{-2} +25 q^{-3} -25 q^{-4} +23 q^{-5} -18 q^{-6} +12 q^{-7} -7 q^{-8} +3 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-17 t^2+37 t-47+37 t^{-1} -17 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+7 z^4+5 z^2+1 }[/math] |
| Determinant | 163 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-2 z^2 a^8-a^8+z^6 a^6+2 z^4 a^6+z^2 a^6-a^6+2 z^6 a^4+6 z^4 a^4+8 z^2 a^4+4 a^4+z^6 a^2+z^4 a^2-z^2 a^2-a^2-z^4-z^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-4 z^5 a^{11}+5 z^3 a^{11}-2 z a^{11}+3 z^8 a^{10}-11 z^6 a^{10}+12 z^4 a^{10}-4 z^2 a^{10}+4 z^9 a^9-11 z^7 a^9+6 z^5 a^9+z^3 a^9+3 z^{10} a^8-2 z^8 a^8-12 z^6 a^8+12 z^4 a^8-z^2 a^8-a^8+z^{11} a^7+8 z^9 a^7-26 z^7 a^7+22 z^5 a^7-8 z^3 a^7+z a^7+7 z^{10} a^6-8 z^8 a^6-10 z^6 a^6+16 z^4 a^6-7 z^2 a^6+a^6+z^{11} a^5+12 z^9 a^5-29 z^7 a^5+21 z^5 a^5-3 z^3 a^5-2 z a^5+4 z^{10} a^4+7 z^8 a^4-29 z^6 a^4+32 z^4 a^4-16 z^2 a^4+4 a^4+8 z^9 a^3-7 z^7 a^3-4 z^5 a^3+7 z^3 a^3-2 z a^3+10 z^8 a^2-16 z^6 a^2+11 z^4 a^2-5 z^2 a^2+a^2+8 z^7 a-12 z^5 a+5 z^3 a-z a+4 z^6-5 z^4+z^2+z^5 a^{-1} -z^3 a^{-1} }[/math] |
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