K12a435
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+10 q^4-19 q^3+27 q^2-33 q+37-33 q^{-1} +27 q^{-2} -19 q^{-3} +10 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+26 t^2-48 t+59-48 t^{-1} +26 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-2 z^4+1 }[/math] |
| Determinant | 225 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +4 z^6+a^4 z^4-6 a^2 z^4-6 z^4 a^{-2} +z^4 a^{-4} +8 z^4+2 a^4 z^2-7 a^2 z^2-7 z^2 a^{-2} +2 z^2 a^{-4} +10 z^2+a^4-4 a^2-4 a^{-2} + a^{-4} +7 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +5 a^2 z^{10}+5 z^{10} a^{-2} +10 z^{10}+9 a^3 z^9+24 a z^9+24 z^9 a^{-1} +9 z^9 a^{-3} +8 a^4 z^8+15 a^2 z^8+15 z^8 a^{-2} +8 z^8 a^{-4} +14 z^8+4 a^5 z^7-9 a^3 z^7-46 a z^7-46 z^7 a^{-1} -9 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-15 a^4 z^6-53 a^2 z^6-53 z^6 a^{-2} -15 z^6 a^{-4} +z^6 a^{-6} -74 z^6-8 a^5 z^5-7 a^3 z^5+16 a z^5+16 z^5 a^{-1} -7 z^5 a^{-3} -8 z^5 a^{-5} -2 a^6 z^4+11 a^4 z^4+50 a^2 z^4+50 z^4 a^{-2} +11 z^4 a^{-4} -2 z^4 a^{-6} +74 z^4+6 a^5 z^3+12 a^3 z^3+12 a z^3+12 z^3 a^{-1} +12 z^3 a^{-3} +6 z^3 a^{-5} +a^6 z^2-5 a^4 z^2-20 a^2 z^2-20 z^2 a^{-2} -5 z^2 a^{-4} +z^2 a^{-6} -28 z^2-2 a^5 z-6 a^3 z-8 a z-8 z a^{-1} -6 z a^{-3} -2 z a^{-5} +a^4+4 a^2+4 a^{-2} + a^{-4} +7 }[/math] |
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