K12a125
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-3 q^5+8 q^4-15 q^3+22 q^2-27 q+29-27 q^{-1} +22 q^{-2} -15 q^{-3} +8 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^3+12 t^2-44 t+67-44 t^{-1} +12 t^{-2} - t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^6+6 z^4-5 z^2+1 }[/math] |
| Determinant | 181 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^6-3 z^2 a^4-a^4+3 z^4 a^2+z^2 a^2-z^6-z^2+1+3 z^4 a^{-2} +z^2 a^{-2} -3 z^2 a^{-4} - a^{-4} + a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +4 a^2 z^{10}+4 z^{10} a^{-2} +8 z^{10}+6 a^3 z^9+14 a z^9+14 z^9 a^{-1} +6 z^9 a^{-3} +5 a^4 z^8+3 a^2 z^8+3 z^8 a^{-2} +5 z^8 a^{-4} -4 z^8+3 a^5 z^7-8 a^3 z^7-34 a z^7-34 z^7 a^{-1} -8 z^7 a^{-3} +3 z^7 a^{-5} +a^6 z^6-8 a^4 z^6-15 a^2 z^6-15 z^6 a^{-2} -8 z^6 a^{-4} +z^6 a^{-6} -12 z^6-7 a^5 z^5+3 a^3 z^5+37 a z^5+37 z^5 a^{-1} +3 z^5 a^{-3} -7 z^5 a^{-5} -3 a^6 z^4+a^4 z^4+11 a^2 z^4+11 z^4 a^{-2} +z^4 a^{-4} -3 z^4 a^{-6} +14 z^4+5 a^5 z^3-3 a^3 z^3-24 a z^3-24 z^3 a^{-1} -3 z^3 a^{-3} +5 z^3 a^{-5} +3 a^6 z^2+3 a^4 z^2-3 a^2 z^2-3 z^2 a^{-2} +3 z^2 a^{-4} +3 z^2 a^{-6} -6 z^2-a^5 z+2 a^3 z+6 a z+6 z a^{-1} +2 z a^{-3} -z a^{-5} -a^6-a^4- a^{-4} - a^{-6} +1 }[/math] |
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