K12a712
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-6 q^2+16 q-27+40 q^{-1} -48 q^{-2} +50 q^{-3} -47 q^{-4} +37 q^{-5} -24 q^{-6} +13 q^{-7} -5 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+9 t^3-34 t^2+70 t-87+70 t^{-1} -34 t^{-2} +9 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+z^6-z^2+1 }[/math] |
| Determinant | 315 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8-3 z^4 a^6-3 z^2 a^6+a^6+3 z^6 a^4+6 z^4 a^4+2 z^2 a^4-2 a^4-z^8 a^2-3 z^6 a^2-4 z^4 a^2-z^2 a^2+a^2+z^6+z^4+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 a^5 z^{11}+4 a^3 z^{11}+13 a^6 z^{10}+28 a^4 z^{10}+15 a^2 z^{10}+17 a^7 z^9+38 a^5 z^9+43 a^3 z^9+22 a z^9+12 a^8 z^8-25 a^4 z^8+3 a^2 z^8+16 z^8+5 a^9 z^7-29 a^7 z^7-100 a^5 z^7-108 a^3 z^7-36 a z^7+6 z^7 a^{-1} +a^{10} z^6-21 a^8 z^6-40 a^6 z^6-44 a^4 z^6-52 a^2 z^6+z^6 a^{-2} -25 z^6-7 a^9 z^5+20 a^7 z^5+80 a^5 z^5+74 a^3 z^5+16 a z^5-5 z^5 a^{-1} -a^{10} z^4+14 a^8 z^4+40 a^6 z^4+49 a^4 z^4+34 a^2 z^4+10 z^4+2 a^9 z^3-7 a^7 z^3-21 a^5 z^3-16 a^3 z^3-4 a z^3-4 a^8 z^2-8 a^6 z^2-6 a^4 z^2-2 a^2 z^2+a^7 z-2 a^3 z-a z-a^6-2 a^4-a^2+1 }[/math] |
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