K12a692
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+2-5 q^{-1} +11 q^{-2} -15 q^{-3} +22 q^{-4} -24 q^{-5} +23 q^{-6} -21 q^{-7} +15 q^{-8} -9 q^{-9} +4 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-8 t^3+19 t^2-30 t+35-30 t^{-1} +19 t^{-2} -8 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+8 z^6+11 z^4+6 z^2+1 }[/math] |
| Determinant | 153 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-3 z^4 a^8-2 z^2 a^8+a^8+z^8 a^6+4 z^6 a^6+3 z^4 a^6-6 z^2 a^6-8 a^6+z^8 a^4+6 z^6 a^4+16 z^4 a^4+22 z^2 a^4+12 a^4-z^6 a^2-5 z^4 a^2-8 z^2 a^2-4 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-z^3 a^{13}+4 z^6 a^{12}-5 z^4 a^{12}+z^2 a^{12}+8 z^7 a^{11}-12 z^5 a^{11}+6 z^3 a^{11}-2 z a^{11}+10 z^8 a^{10}-15 z^6 a^{10}+7 z^4 a^{10}-z^2 a^{10}+8 z^9 a^9-7 z^7 a^9-6 z^5 a^9+11 z^3 a^9-4 z a^9+4 z^{10} a^8+4 z^8 a^8-16 z^6 a^8+10 z^4 a^8+a^8+z^{11} a^7+9 z^9 a^7-17 z^7 a^7+z^5 a^7+17 z^3 a^7-12 z a^7+6 z^{10} a^6-9 z^8 a^6+2 z^6 a^6+4 z^4 a^6-11 z^2 a^6+8 a^6+z^{11} a^5+3 z^9 a^5-5 z^7 a^5-13 z^5 a^5+28 z^3 a^5-18 z a^5+2 z^{10} a^4-z^8 a^4-9 z^6 a^4+17 z^4 a^4-21 z^2 a^4+12 a^4+2 z^9 a^3-2 z^7 a^3-12 z^5 a^3+23 z^3 a^3-12 z a^3+2 z^8 a^2-8 z^6 a^2+11 z^4 a^2-8 z^2 a^2+4 a^2+z^7 a-5 z^5 a+8 z^3 a-4 z a }[/math] |
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