K12a634
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+3 q-6+12 q^{-1} -17 q^{-2} +20 q^{-3} -21 q^{-4} +20 q^{-5} -15 q^{-6} +11 q^{-7} -6 q^{-8} +2 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-15 t^2+30 t-37+30 t^{-1} -15 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+9 z^4+6 z^2+1 }[/math] |
| Determinant | 135 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-3 z^2 a^8-3 a^8+z^6 a^6+3 z^4 a^6+5 z^2 a^6+4 a^6+2 z^6 a^4+6 z^4 a^4+5 z^2 a^4+z^6 a^2+2 z^4 a^2+z^2 a^2-z^4-2 z^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-5 z^5 a^{11}+8 z^3 a^{11}-4 z a^{11}+2 z^8 a^{10}-7 z^6 a^{10}+6 z^4 a^{10}+3 z^9 a^9-9 z^7 a^9+7 z^5 a^9-2 z^3 a^9+z a^9+3 z^{10} a^8-9 z^8 a^8+17 z^6 a^8-31 z^4 a^8+22 z^2 a^8-3 a^8+z^{11} a^7+5 z^9 a^7-24 z^7 a^7+40 z^5 a^7-39 z^3 a^7+11 z a^7+7 z^{10} a^6-22 z^8 a^6+39 z^6 a^6-46 z^4 a^6+23 z^2 a^6-4 a^6+z^{11} a^5+9 z^9 a^5-37 z^7 a^5+63 z^5 a^5-47 z^3 a^5+9 z a^5+4 z^{10} a^4-4 z^8 a^4-4 z^6 a^4+13 z^4 a^4-4 z^2 a^4+7 z^9 a^3-18 z^7 a^3+25 z^5 a^3-12 z^3 a^3+3 z a^3+7 z^8 a^2-16 z^6 a^2+16 z^4 a^2-3 z^2 a^2+5 z^7 a-9 z^5 a+4 z^3 a+3 z^6-6 z^4+2 z^2+z^5 a^{-1} -2 z^3 a^{-1} }[/math] |
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