K12a621
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+4 q^3-9 q^2+15 q-21+26 q^{-1} -27 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+8 t^3-22 t^2+36 t-41+36 t^{-1} -22 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+6 z^4+4 z^2+1 }[/math] |
| Determinant | 175 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+2 a^4 z^6-4 a^2 z^6+2 z^6-a^6 z^4+7 a^4 z^4-5 a^2 z^4-z^4 a^{-2} +6 z^4-3 a^6 z^2+7 a^4 z^2-a^2 z^2-2 z^2 a^{-2} +3 z^2-2 a^6+2 a^4+2 a^2-1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+6 a^4 z^{10}+12 a^2 z^{10}+6 z^{10}+8 a^5 z^9+11 a^3 z^9+10 a z^9+7 z^9 a^{-1} +8 a^6 z^8-6 a^4 z^8-31 a^2 z^8+4 z^8 a^{-2} -13 z^8+6 a^7 z^7-11 a^5 z^7-42 a^3 z^7-49 a z^7-23 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6-12 a^6 z^6+27 a^2 z^6-13 z^6 a^{-2} -z^6+a^9 z^5-9 a^7 z^5+7 a^5 z^5+55 a^3 z^5+63 a z^5+22 z^5 a^{-1} -3 z^5 a^{-3} -4 a^8 z^4+10 a^6 z^4+3 a^4 z^4-14 a^2 z^4+11 z^4 a^{-2} +8 z^4-2 a^9 z^3+6 a^7 z^3-a^5 z^3-33 a^3 z^3-36 a z^3-10 z^3 a^{-1} +2 z^3 a^{-3} +a^8 z^2-6 a^6 z^2-3 a^4 z^2+7 a^2 z^2-3 z^2 a^{-2} +a^9 z-2 a^7 z-a^5 z+7 a^3 z+8 a z+3 z a^{-1} +2 a^6+2 a^4-2 a^2-1 }[/math] |
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