K12a487
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^3-5 q^2+13 q-22+33 q^{-1} -40 q^{-2} +42 q^{-3} -39 q^{-4} +31 q^{-5} -21 q^{-6} +11 q^{-7} -4 q^{-8} + q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-29 t^2+58 t-71+58 t^{-1} -29 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^4-2 z^2+1 }[/math] |
| Determinant | 263 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8+a^8-3 z^4 a^6-5 z^2 a^6-2 a^6+3 z^6 a^4+8 z^4 a^4+7 z^2 a^4+2 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+2 }[/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}+12 a^7 z^9+25 a^5 z^9+29 a^3 z^9+16 a z^9+9 a^8 z^8+2 a^6 z^8-21 a^4 z^8-2 a^2 z^8+12 z^8+4 a^9 z^7-19 a^7 z^7-66 a^5 z^7-79 a^3 z^7-31 a z^7+5 z^7 a^{-1} +a^{10} z^6-17 a^8 z^6-34 a^6 z^6-26 a^4 z^6-34 a^2 z^6+z^6 a^{-2} -23 z^6-7 a^9 z^5+11 a^7 z^5+56 a^5 z^5+66 a^3 z^5+21 a z^5-7 z^5 a^{-1} -2 a^{10} z^4+14 a^8 z^4+38 a^6 z^4+44 a^4 z^4+37 a^2 z^4-z^4 a^{-2} +14 z^4+4 a^9 z^3-5 a^7 z^3-20 a^5 z^3-19 a^3 z^3-7 a z^3+z^3 a^{-1} +a^{10} z^2-7 a^8 z^2-17 a^6 z^2-18 a^4 z^2-14 a^2 z^2-5 z^2-a^9 z+a^7 z+3 a^5 z+a^3 z+a^8+2 a^6+2 a^4+2 a^2+2 }[/math] |
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