K12a365
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^5-4 q^4+7 q^3-11 q^2+16 q-18+20 q^{-1} -18 q^{-2} +15 q^{-3} -11 q^{-4} +6 q^{-5} -3 q^{-6} + q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+9 t^3-18 t^2+24 t-25+24 t^{-1} -18 t^{-2} +9 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-7 z^6-4 z^4+z^2+1 }[/math] |
| Determinant | 131 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8-z^8+a^4 z^6-5 a^2 z^6+z^6 a^{-2} -4 z^6+4 a^4 z^4-9 a^2 z^4+3 z^4 a^{-2} -2 z^4+4 a^4 z^2-9 a^2 z^2+6 z^2+a^4-4 a^2-2 a^{-2} +6 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +5 a^2 z^{10}+5 z^{10} a^{-2} +10 z^{10}+7 a^3 z^9+4 a z^9+z^9 a^{-1} +4 z^9 a^{-3} +8 a^4 z^8-7 a^2 z^8-22 z^8 a^{-2} +z^8 a^{-4} -38 z^8+7 a^5 z^7-11 a^3 z^7-30 a z^7-31 z^7 a^{-1} -19 z^7 a^{-3} +5 a^6 z^6-13 a^4 z^6-9 a^2 z^6+27 z^6 a^{-2} -4 z^6 a^{-4} +40 z^6+3 a^7 z^5-8 a^5 z^5-a^3 z^5+32 a z^5+48 z^5 a^{-1} +26 z^5 a^{-3} +a^8 z^4-4 a^6 z^4+8 a^4 z^4+15 a^2 z^4-8 z^4 a^{-2} +4 z^4 a^{-4} -10 z^4-3 a^7 z^3+3 a^5 z^3+5 a^3 z^3-9 a z^3-17 z^3 a^{-1} -9 z^3 a^{-3} -a^8 z^2+a^6 z^2-3 a^4 z^2-12 a^2 z^2-2 z^2 a^{-2} -z^2 a^{-4} -8 z^2+a^7 z+a^5 z-2 a^3 z-3 a z-2 z a^{-1} -z a^{-3} +a^4+4 a^2+2 a^{-2} +6 }[/math] |
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