K12a824
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+2 q^3-5 q^2+9 q-12+16 q^{-1} -16 q^{-2} +16 q^{-3} -13 q^{-4} +9 q^{-5} -5 q^{-6} +2 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^5-3 t^4+7 t^3-13 t^2+19 t-21+19 t^{-1} -13 t^{-2} +7 t^{-3} -3 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{10}+7 z^8+18 z^6+19 z^4+7 z^2+1 }[/math] |
| Determinant | 107 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^{10}-a^4 z^8+9 a^2 z^8-z^8-7 a^4 z^6+32 a^2 z^6-7 z^6-18 a^4 z^4+55 a^2 z^4-18 z^4-19 a^4 z^2+45 a^2 z^2-19 z^2-7 a^4+14 a^2-6 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+3 a^4 z^{10}+6 a^2 z^{10}+3 z^{10}+4 a^5 z^9+3 a^3 z^9+2 a z^9+3 z^9 a^{-1} +4 a^6 z^8-8 a^4 z^8-27 a^2 z^8+2 z^8 a^{-2} -13 z^8+3 a^7 z^7-10 a^5 z^7-19 a^3 z^7-19 a z^7-12 z^7 a^{-1} +z^7 a^{-3} +2 a^8 z^6-9 a^6 z^6+16 a^4 z^6+63 a^2 z^6-8 z^6 a^{-2} +28 z^6+a^9 z^5-5 a^7 z^5+14 a^5 z^5+41 a^3 z^5+42 a z^5+16 z^5 a^{-1} -5 z^5 a^{-3} -4 a^8 z^4+11 a^6 z^4-20 a^4 z^4-83 a^2 z^4+8 z^4 a^{-2} -40 z^4-3 a^9 z^3+2 a^7 z^3-5 a^5 z^3-37 a^3 z^3-45 a z^3-11 z^3 a^{-1} +7 z^3 a^{-3} +a^8 z^2-5 a^6 z^2+21 a^4 z^2+53 a^2 z^2-z^2 a^{-2} +25 z^2+2 a^9 z-a^7 z+a^5 z+13 a^3 z+14 a z+3 z a^{-1} -2 z a^{-3} -7 a^4-14 a^2-6 }[/math] |
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