K12a870
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-4 q^2+9 q-16+23 q^{-1} -27 q^{-2} +30 q^{-3} -27 q^{-4} +22 q^{-5} -15 q^{-6} +8 q^{-7} -4 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+10 t^3-23 t^2+37 t-43+37 t^{-1} -23 t^{-2} +10 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-6 z^6-3 z^4+3 z^2+1 }[/math] |
| Determinant | 187 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^4 z^8-a^2 z^8+a^6 z^6-4 a^4 z^6-4 a^2 z^6+z^6+3 a^6 z^4-4 a^4 z^4-5 a^2 z^4+3 z^4+a^6 z^2+2 a^4 z^2-2 a^2 z^2+2 z^2-2 a^6+3 a^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^5 z^{11}+3 a^3 z^{11}+7 a^6 z^{10}+15 a^4 z^{10}+8 a^2 z^{10}+8 a^7 z^9+4 a^5 z^9+6 a^3 z^9+10 a z^9+7 a^8 z^8-15 a^6 z^8-48 a^4 z^8-18 a^2 z^8+8 z^8+4 a^9 z^7-17 a^7 z^7-25 a^5 z^7-34 a^3 z^7-26 a z^7+4 z^7 a^{-1} +a^{10} z^6-17 a^8 z^6+15 a^6 z^6+70 a^4 z^6+16 a^2 z^6+z^6 a^{-2} -20 z^6-10 a^9 z^5+8 a^7 z^5+37 a^5 z^5+51 a^3 z^5+23 a z^5-9 z^5 a^{-1} -2 a^{10} z^4+10 a^8 z^4-8 a^6 z^4-41 a^4 z^4-6 a^2 z^4-2 z^4 a^{-2} +13 z^4+5 a^9 z^3+3 a^7 z^3-15 a^5 z^3-25 a^3 z^3-9 a z^3+3 z^3 a^{-1} -a^8 z^2+5 a^4 z^2+a^2 z^2-3 z^2-3 a^7 z-2 a^5 z+2 a^3 z+a z+2 a^6+3 a^4 }[/math] |
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