K12a1245
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-3 q^5+7 q^4-13 q^3+20 q^2-25 q+27-26 q^{-1} +22 q^{-2} -15 q^{-3} +9 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+18 t^2-39 t+51-39 t^{-1} +18 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-6 z^4-3 z^2+1 }[/math] |
| Determinant | 173 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^6-z^6 a^{-2} -2 z^6+a^4 z^4-a^2 z^4-2 z^4 a^{-2} +z^4 a^{-4} -5 z^4+a^4 z^2+a^2 z^2-2 z^2 a^{-2} +2 z^2 a^{-4} -5 z^2+2 a^2+ a^{-4} -2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +6 a^2 z^{10}+5 z^{10} a^{-2} +11 z^{10}+9 a^3 z^9+9 a z^9+6 z^9 a^{-1} +6 z^9 a^{-3} +8 a^4 z^8-7 a^2 z^8-9 z^8 a^{-2} +5 z^8 a^{-4} -29 z^8+4 a^5 z^7-22 a^3 z^7-35 a z^7-26 z^7 a^{-1} -14 z^7 a^{-3} +3 z^7 a^{-5} +a^6 z^6-21 a^4 z^6-7 a^2 z^6+9 z^6 a^{-2} -12 z^6 a^{-4} +z^6 a^{-6} +37 z^6-9 a^5 z^5+18 a^3 z^5+47 a z^5+44 z^5 a^{-1} +16 z^5 a^{-3} -8 z^5 a^{-5} -2 a^6 z^4+16 a^4 z^4+12 a^2 z^4-3 z^4 a^{-2} +9 z^4 a^{-4} -3 z^4 a^{-6} -21 z^4+3 a^5 z^3-8 a^3 z^3-25 a z^3-32 z^3 a^{-1} -13 z^3 a^{-3} +5 z^3 a^{-5} -5 a^4 z^2-3 z^2 a^{-2} -4 z^2 a^{-4} +2 z^2 a^{-6} +8 z^2+2 a^3 z+5 a z+7 z a^{-1} +4 z a^{-3} -2 a^2+ a^{-4} -2 }[/math] |
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