K12a467
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-5 q^2+13 q-23+34 q^{-1} -41 q^{-2} +44 q^{-3} -40 q^{-4} +32 q^{-5} -22 q^{-6} +11 q^{-7} -4 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-29 t^2+60 t-75+60 t^{-1} -29 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^4+1 }[/math] |
| Determinant | 271 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8+a^8-3 z^4 a^6-5 z^2 a^6-3 a^6+3 z^6 a^4+8 z^4 a^4+8 z^2 a^4+3 a^4-z^8 a^2-4 z^6 a^2-8 z^4 a^2-6 z^2 a^2-a^2+z^6+2 z^4+2 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^5 z^{11}+3 a^3 z^{11}+10 a^6 z^{10}+21 a^4 z^{10}+11 a^2 z^{10}+13 a^7 z^9+29 a^5 z^9+32 a^3 z^9+16 a z^9+9 a^8 z^8-a^6 z^8-20 a^4 z^8+2 a^2 z^8+12 z^8+4 a^9 z^7-23 a^7 z^7-80 a^5 z^7-86 a^3 z^7-28 a z^7+5 z^7 a^{-1} +a^{10} z^6-16 a^8 z^6-29 a^6 z^6-32 a^4 z^6-43 a^2 z^6+z^6 a^{-2} -22 z^6-7 a^9 z^5+19 a^7 z^5+78 a^5 z^5+75 a^3 z^5+16 a z^5-7 z^5 a^{-1} -2 a^{10} z^4+12 a^8 z^4+35 a^6 z^4+49 a^4 z^4+43 a^2 z^4-z^4 a^{-2} +14 z^4+4 a^9 z^3-10 a^7 z^3-37 a^5 z^3-31 a^3 z^3-6 a z^3+2 z^3 a^{-1} +a^{10} z^2-5 a^8 z^2-17 a^6 z^2-21 a^4 z^2-15 a^2 z^2-5 z^2-a^9 z+a^7 z+7 a^5 z+7 a^3 z+2 a z+a^8+3 a^6+3 a^4+a^2+1 }[/math] |
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