K12a352
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-5 q^2+13 q-23+33 q^{-1} -39 q^{-2} +42 q^{-3} -38 q^{-4} +30 q^{-5} -20 q^{-6} +10 q^{-7} -4 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-28 t^2+57 t-71+57 t^{-1} -28 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+z^2+1 }[/math] |
| Determinant | 259 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8+a^8-3 z^4 a^6-6 z^2 a^6-4 a^6+3 z^6 a^4+9 z^4 a^4+11 z^2 a^4+5 a^4-z^8 a^2-4 z^6 a^2-8 z^4 a^2-7 z^2 a^2-2 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}+9 a^6 z^{10}+20 a^4 z^{10}+11 a^2 z^{10}+11 a^7 z^9+24 a^5 z^9+29 a^3 z^9+16 a z^9+8 a^8 z^8-3 a^6 z^8-24 a^4 z^8-a^2 z^8+12 z^8+4 a^9 z^7-18 a^7 z^7-70 a^5 z^7-82 a^3 z^7-29 a z^7+5 z^7 a^{-1} +a^{10} z^6-14 a^8 z^6-21 a^6 z^6-21 a^4 z^6-38 a^2 z^6+z^6 a^{-2} -22 z^6-8 a^9 z^5+11 a^7 z^5+72 a^5 z^5+76 a^3 z^5+16 a z^5-7 z^5 a^{-1} -2 a^{10} z^4+8 a^8 z^4+30 a^6 z^4+47 a^4 z^4+41 a^2 z^4-z^4 a^{-2} +13 z^4+5 a^9 z^3-3 a^7 z^3-31 a^5 z^3-32 a^3 z^3-7 a z^3+2 z^3 a^{-1} +a^{10} z^2-3 a^8 z^2-17 a^6 z^2-25 a^4 z^2-17 a^2 z^2-5 z^2-a^9 z-a^7 z+4 a^5 z+6 a^3 z+2 a z+a^8+4 a^6+5 a^4+2 a^2+1 }[/math] |
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