K12a913
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^7-4 q^6+10 q^5-19 q^4+27 q^3-32 q^2+35 q-32+26 q^{-1} -18 q^{-2} +10 q^{-3} -4 q^{-4} + q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-24 t^2+48 t-59+48 t^{-1} -24 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6-2 z^4-z^2+1 }[/math] |
| Determinant | 219 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +z^6 a^{-4} +3 z^6-3 a^2 z^4-12 z^4 a^{-2} +3 z^4 a^{-4} +10 z^4+a^4 z^2-6 a^2 z^2-12 z^2 a^{-2} +4 z^2 a^{-4} +12 z^2+a^4-3 a^2-3 a^{-2} + a^{-4} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +6 a^2 z^{10}+13 z^{10} a^{-2} +19 z^{10}+4 a^3 z^9+9 a z^9+29 z^9 a^{-1} +24 z^9 a^{-3} +a^4 z^8-18 a^2 z^8-4 z^8 a^{-2} +26 z^8 a^{-4} -49 z^8-16 a^3 z^7-65 a z^7-115 z^7 a^{-1} -47 z^7 a^{-3} +19 z^7 a^{-5} -4 a^4 z^6+8 a^2 z^6-66 z^6 a^{-2} -50 z^6 a^{-4} +10 z^6 a^{-6} +6 z^6+23 a^3 z^5+92 a z^5+115 z^5 a^{-1} +17 z^5 a^{-3} -25 z^5 a^{-5} +4 z^5 a^{-7} +6 a^4 z^4+17 a^2 z^4+76 z^4 a^{-2} +32 z^4 a^{-4} -5 z^4 a^{-6} +z^4 a^{-8} +49 z^4-14 a^3 z^3-44 a z^3-41 z^3 a^{-1} +z^3 a^{-3} +12 z^3 a^{-5} -4 a^4 z^2-15 a^2 z^2-30 z^2 a^{-2} -10 z^2 a^{-4} +z^2 a^{-6} -30 z^2+3 a^3 z+7 a z+5 z a^{-1} -z a^{-5} +a^4+3 a^2+3 a^{-2} + a^{-4} +5 }[/math] |
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