K12a298
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+4 q^3-8 q^2+14 q-21+25 q^{-1} -26 q^{-2} +26 q^{-3} -20 q^{-4} +14 q^{-5} -8 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+7 t^3-20 t^2+36 t-43+36 t^{-1} -20 t^{-2} +7 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^6+2 z^4+3 z^2+1 }[/math] |
| Determinant | 171 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+2 a^4 z^6-5 a^2 z^6+2 z^6-a^6 z^4+8 a^4 z^4-11 a^2 z^4-z^4 a^{-2} +7 z^4-3 a^6 z^2+12 a^4 z^2-11 a^2 z^2-2 z^2 a^{-2} +7 z^2-3 a^6+6 a^4-3 a^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+4 a^4 z^{10}+8 a^2 z^{10}+4 z^{10}+7 a^5 z^9+14 a^3 z^9+13 a z^9+6 z^9 a^{-1} +8 a^6 z^8+7 a^4 z^8-7 a^2 z^8+4 z^8 a^{-2} -2 z^8+6 a^7 z^7-4 a^5 z^7-34 a^3 z^7-44 a z^7-19 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6-12 a^6 z^6-27 a^4 z^6-19 a^2 z^6-14 z^6 a^{-2} -21 z^6+a^9 z^5-9 a^7 z^5-8 a^5 z^5+25 a^3 z^5+44 a z^5+18 z^5 a^{-1} -3 z^5 a^{-3} -4 a^8 z^4+12 a^6 z^4+28 a^4 z^4+24 a^2 z^4+14 z^4 a^{-2} +26 z^4-2 a^9 z^3+7 a^7 z^3+14 a^5 z^3-6 a^3 z^3-19 a z^3-6 z^3 a^{-1} +2 z^3 a^{-3} +a^8 z^2-8 a^6 z^2-15 a^4 z^2-11 a^2 z^2-3 z^2 a^{-2} -8 z^2+a^9 z-3 a^7 z-6 a^5 z-2 a^3 z+3 a^6+6 a^4+3 a^2+1 }[/math] |
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