K12a576
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -1+2 q^{-1} -3 q^{-2} +6 q^{-3} -6 q^{-4} +8 q^{-5} -9 q^{-6} +8 q^{-7} -7 q^{-8} +6 q^{-9} -4 q^{-10} +2 q^{-11} - q^{-12} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^5-3 t^4+6 t^3-8 t^2+9 t-9+9 t^{-1} -8 t^{-2} +6 t^{-3} -3 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^{10}+7 z^8+17 z^6+18 z^4+8 z^2+1 }[/math] |
| Determinant | 63 |
| Signature | -6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^6 z^{10}-a^8 z^8+9 a^6 z^8-a^4 z^8-7 a^8 z^6+31 a^6 z^6-7 a^4 z^6-17 a^8 z^4+51 a^6 z^4-16 a^4 z^4-17 a^8 z^2+38 a^6 z^2-13 a^4 z^2-5 a^8+8 a^6-2 a^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^3 a^{15}-z a^{15}+2 z^4 a^{14}-z^2 a^{14}+3 z^5 a^{13}-2 z^3 a^{13}+z a^{13}+4 z^6 a^{12}-6 z^4 a^{12}+4 z^2 a^{12}+4 z^7 a^{11}-7 z^5 a^{11}+2 z^3 a^{11}+4 z^8 a^{10}-10 z^6 a^{10}+5 z^4 a^{10}-2 z^2 a^{10}+4 z^9 a^9-15 z^7 a^9+18 z^5 a^9-13 z^3 a^9+2 z a^9+3 z^{10} a^8-13 z^8 a^8+19 z^6 a^8-21 z^4 a^8+17 z^2 a^8-5 a^8+z^{11} a^7-20 z^7 a^7+44 z^5 a^7-32 z^3 a^7+7 z a^7+5 z^{10} a^6-31 z^8 a^6+67 z^6 a^6-70 z^4 a^6+41 z^2 a^6-8 a^6+z^{11} a^5-3 z^9 a^5-8 z^7 a^5+32 z^5 a^5-27 z^3 a^5+5 z a^5+2 z^{10} a^4-14 z^8 a^4+34 z^6 a^4-36 z^4 a^4+17 z^2 a^4-2 a^4+z^9 a^3-7 z^7 a^3+16 z^5 a^3-13 z^3 a^3+2 z a^3 }[/math] |
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