K12a1231
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+9 q^4-16 q^3+23 q^2-28 q+31-28 q^{-1} +23 q^{-2} -16 q^{-3} +9 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^5+5 t^4-13 t^3+24 t^2-34 t+39-34 t^{-1} +24 t^{-2} -13 t^{-3} +5 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^{10}-5 z^8-8 z^6-4 z^4+1 }[/math] |
| Determinant | 193 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^{10}+a^2 z^8+z^8 a^{-2} -7 z^8+5 a^2 z^6+5 z^6 a^{-2} -18 z^6+8 a^2 z^4+8 z^4 a^{-2} -20 z^4+4 a^2 z^2+4 z^2 a^{-2} -8 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +7 a^2 z^{10}+8 z^{10} a^{-2} +15 z^{10}+8 a^3 z^9+5 a z^9+7 z^9 a^{-1} +10 z^9 a^{-3} +7 a^4 z^8-12 a^2 z^8-17 z^8 a^{-2} +8 z^8 a^{-4} -44 z^8+4 a^5 z^7-13 a^3 z^7-23 a z^7-36 z^7 a^{-1} -26 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-14 a^4 z^6+10 a^2 z^6+13 z^6 a^{-2} -20 z^6 a^{-4} +z^6 a^{-6} +59 z^6-9 a^5 z^5+28 a z^5+52 z^5 a^{-1} +24 z^5 a^{-3} -9 z^5 a^{-5} -2 a^6 z^4+5 a^4 z^4-9 a^2 z^4-2 z^4 a^{-2} +13 z^4 a^{-4} -2 z^4 a^{-6} -33 z^4+5 a^5 z^3+5 a^3 z^3-11 a z^3-24 z^3 a^{-1} -10 z^3 a^{-3} +3 z^3 a^{-5} +a^6 z^2+3 a^2 z^2-3 z^2 a^{-4} +7 z^2-a^5 z-2 a^3 z+2 z a^{-1} +z a^{-3} +1 }[/math] |
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