K12a714
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^5-3 q^4+5 q^3-8 q^2+12 q-14+16 q^{-1} -15 q^{-2} +13 q^{-3} -10 q^{-4} +6 q^{-5} -3 q^{-6} + q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+8 t^3-15 t^2+19 t-19+19 t^{-1} -15 t^{-2} +8 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-8 z^6-7 z^4-z^2+1 }[/math] |
| Determinant | 107 |
| 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} -5 z^6+4 a^4 z^4-8 a^2 z^4+4 z^4 a^{-2} -7 z^4+4 a^4 z^2-6 a^2 z^2+3 z^2 a^{-2} -2 z^2+a^4-2 a^2+2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +3 a^2 z^{10}+3 z^{10} a^{-2} +6 z^{10}+5 a^3 z^9+5 a z^9+3 z^9 a^{-1} +3 z^9 a^{-3} +6 a^4 z^8-2 a^2 z^8-13 z^8 a^{-2} +z^8 a^{-4} -22 z^8+6 a^5 z^7-8 a^3 z^7-27 a z^7-29 z^7 a^{-1} -16 z^7 a^{-3} +5 a^6 z^6-8 a^4 z^6-12 a^2 z^6+14 z^6 a^{-2} -5 z^6 a^{-4} +20 z^6+3 a^7 z^5-6 a^5 z^5+3 a^3 z^5+32 a z^5+46 z^5 a^{-1} +26 z^5 a^{-3} +a^8 z^4-5 a^6 z^4+4 a^4 z^4+16 a^2 z^4-2 z^4 a^{-2} +7 z^4 a^{-4} -3 z^4-3 a^7 z^3+a^5 z^3-2 a^3 z^3-14 a z^3-22 z^3 a^{-1} -14 z^3 a^{-3} -a^8 z^2+2 a^6 z^2-3 a^4 z^2-10 a^2 z^2-z^2 a^{-2} -3 z^2 a^{-4} -2 z^2+a^7 z+a^5 z+a z+2 z a^{-1} +z a^{-3} +a^4+2 a^2+2 }[/math] |
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