K12a964
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+5 q^3-12 q^2+22 q-31+38 q^{-1} -41 q^{-2} +38 q^{-3} -30 q^{-4} +21 q^{-5} -11 q^{-6} +4 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+9 t^3-30 t^2+55 t-65+55 t^{-1} -30 t^{-2} +9 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+z^6+4 z^4+1 }[/math] |
| Determinant | 255 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+2 a^4 z^6-3 a^2 z^6+2 z^6-a^6 z^4+5 a^4 z^4-3 a^2 z^4-z^4 a^{-2} +4 z^4-2 a^6 z^2+4 a^4 z^2-a^2 z^2-z^2 a^{-2} -a^6+2 a^4+ a^{-2} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 a^3 z^{11}+4 a z^{11}+13 a^4 z^{10}+23 a^2 z^{10}+10 z^{10}+19 a^5 z^9+25 a^3 z^9+16 a z^9+10 z^9 a^{-1} +17 a^6 z^8-8 a^4 z^8-47 a^2 z^8+5 z^8 a^{-2} -17 z^8+10 a^7 z^7-33 a^5 z^7-80 a^3 z^7-64 a z^7-26 z^7 a^{-1} +z^7 a^{-3} +4 a^8 z^6-29 a^6 z^6-22 a^4 z^6+20 a^2 z^6-13 z^6 a^{-2} -4 z^6+a^9 z^5-12 a^7 z^5+26 a^5 z^5+77 a^3 z^5+59 a z^5+19 z^5 a^{-1} -2 z^5 a^{-3} -3 a^8 z^4+26 a^6 z^4+29 a^4 z^4-a^2 z^4+10 z^4 a^{-2} +9 z^4-a^9 z^3+7 a^7 z^3-9 a^5 z^3-37 a^3 z^3-25 a z^3-4 z^3 a^{-1} +z^3 a^{-3} -10 a^6 z^2-14 a^4 z^2-a^2 z^2-z^2 a^{-2} +2 z^2-a^7 z+2 a^5 z+8 a^3 z+6 a z+z a^{-1} +a^6+2 a^4- a^{-2} -1 }[/math] |
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