K12a663
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^7-4 q^6+8 q^5-14 q^4+21 q^3-25 q^2+27 q-25+21 q^{-1} -15 q^{-2} +9 q^{-3} -4 q^{-4} + q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-17 t^2+41 t-53+41 t^{-1} -17 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+z^4+1 }[/math] |
| Determinant | 175 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +2 z^6-3 a^2 z^4-2 z^4 a^{-4} +6 z^4+a^4 z^2-6 a^2 z^2-2 z^2 a^{-2} -2 z^2 a^{-4} +z^2 a^{-6} +8 z^2+a^4-3 a^2- a^{-2} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +5 a^2 z^{10}+8 z^{10} a^{-2} +13 z^{10}+4 a^3 z^9+9 a z^9+19 z^9 a^{-1} +14 z^9 a^{-3} +a^4 z^8-15 a^2 z^8-2 z^8 a^{-2} +15 z^8 a^{-4} -33 z^8-17 a^3 z^7-59 a z^7-80 z^7 a^{-1} -26 z^7 a^{-3} +12 z^7 a^{-5} -4 a^4 z^6+2 a^2 z^6-46 z^6 a^{-2} -25 z^6 a^{-4} +8 z^6 a^{-6} -7 z^6+24 a^3 z^5+81 a z^5+81 z^5 a^{-1} +7 z^5 a^{-3} -13 z^5 a^{-5} +4 z^5 a^{-7} +6 a^4 z^4+23 a^2 z^4+54 z^4 a^{-2} +11 z^4 a^{-4} -6 z^4 a^{-6} +z^4 a^{-8} +53 z^4-13 a^3 z^3-36 a z^3-25 z^3 a^{-1} +2 z^3 a^{-3} +2 z^3 a^{-5} -2 z^3 a^{-7} -4 a^4 z^2-18 a^2 z^2-18 z^2 a^{-2} -2 z^2 a^{-4} +z^2 a^{-6} -29 z^2+2 a^3 z+4 a z+2 z a^{-1} +a^4+3 a^2+ a^{-2} +4 }[/math] |
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