K12a530
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+5 q^6-11 q^5+19 q^4-27 q^3+32 q^2-34 q+32-25 q^{-1} +17 q^{-2} -9 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+19 t^2-51 t+71-51 t^{-1} +19 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6+z^4-2 z^2+1 }[/math] |
| Determinant | 217 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -2 z^6 a^{-2} -z^6+2 a^2 z^4-5 z^4 a^{-2} +3 z^4 a^{-4} +z^4-a^4 z^2+a^2 z^2-8 z^2 a^{-2} +4 z^2 a^{-4} -z^2 a^{-6} +3 z^2-4 a^{-2} +2 a^{-4} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +15 z^{10} a^{-2} +7 z^{10} a^{-4} +8 z^{10}+13 a z^9+25 z^9 a^{-1} +21 z^9 a^{-3} +9 z^9 a^{-5} +12 a^2 z^8-19 z^8 a^{-2} -5 z^8 a^{-4} +5 z^8 a^{-6} +3 z^8+8 a^3 z^7-22 a z^7-80 z^7 a^{-1} -76 z^7 a^{-3} -25 z^7 a^{-5} +z^7 a^{-7} +4 a^4 z^6-19 a^2 z^6-35 z^6 a^{-2} -31 z^6 a^{-4} -14 z^6 a^{-6} -41 z^6+a^5 z^5-10 a^3 z^5+18 a z^5+84 z^5 a^{-1} +76 z^5 a^{-3} +19 z^5 a^{-5} -2 z^5 a^{-7} -5 a^4 z^4+14 a^2 z^4+64 z^4 a^{-2} +40 z^4 a^{-4} +11 z^4 a^{-6} +54 z^4-a^5 z^3+3 a^3 z^3-7 a z^3-36 z^3 a^{-1} -31 z^3 a^{-3} -5 z^3 a^{-5} +z^3 a^{-7} +a^4 z^2-5 a^2 z^2-31 z^2 a^{-2} -16 z^2 a^{-4} -2 z^2 a^{-6} -23 z^2+2 a z+6 z a^{-1} +4 z a^{-3} +4 a^{-2} +2 a^{-4} +3 }[/math] |
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