K12a413
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+5 q^7-14 q^6+24 q^5-34 q^4+43 q^3-44 q^2+41 q-33+22 q^{-1} -12 q^{-2} +5 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-29 t^2+62 t-79+62 t^{-1} -29 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-z^4+2 z^2+1 }[/math] |
| Determinant | 279 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -4 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-9 z^4 a^{-2} +5 z^4 a^{-4} -z^4 a^{-6} +5 z^4-a^2 z^2-8 z^2 a^{-2} +7 z^2 a^{-4} -z^2 a^{-6} +5 z^2-2 a^{-2} +4 a^{-4} -2 a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-1} +3 z^{11} a^{-3} +22 z^{10} a^{-2} +13 z^{10} a^{-4} +9 z^{10}+10 a z^9+27 z^9 a^{-1} +40 z^9 a^{-3} +23 z^9 a^{-5} +5 a^2 z^8-22 z^8 a^{-2} +13 z^8 a^{-4} +23 z^8 a^{-6} -7 z^8+a^3 z^7-26 a z^7-89 z^7 a^{-1} -103 z^7 a^{-3} -27 z^7 a^{-5} +14 z^7 a^{-7} -13 a^2 z^6-47 z^6 a^{-2} -69 z^6 a^{-4} -33 z^6 a^{-6} +5 z^6 a^{-8} -29 z^6-2 a^3 z^5+22 a z^5+81 z^5 a^{-1} +73 z^5 a^{-3} +z^5 a^{-5} -14 z^5 a^{-7} +z^5 a^{-9} +11 a^2 z^4+61 z^4 a^{-2} +52 z^4 a^{-4} +19 z^4 a^{-6} -z^4 a^{-8} +40 z^4+a^3 z^3-6 a z^3-25 z^3 a^{-1} -20 z^3 a^{-3} +5 z^3 a^{-5} +7 z^3 a^{-7} -3 a^2 z^2-19 z^2 a^{-2} -15 z^2 a^{-4} -6 z^2 a^{-6} -13 z^2+z a^{-1} +z a^{-3} -3 z a^{-5} -3 z a^{-7} +2 a^{-2} +4 a^{-4} +2 a^{-6} +1 }[/math] |
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