K12a978
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-3 q^{11}+6 q^{10}-11 q^9+15 q^8-19 q^7+21 q^6-19 q^5+16 q^4-11 q^3+7 q^2-3 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+15 t^2-30 t+37-30 t^{-1} +15 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6-3 z^4+3 z^2+1 }[/math] |
| Determinant | 133 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} -2 z^4 a^{-4} -3 z^4 a^{-8} +z^4 a^{-10} +2 z^2 a^{-2} -z^2 a^{-4} +5 z^2 a^{-6} -5 z^2 a^{-8} +2 z^2 a^{-10} + a^{-2} - a^{-4} +4 a^{-6} -4 a^{-8} + a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-7} +2 z^{11} a^{-9} +4 z^{10} a^{-6} +10 z^{10} a^{-8} +6 z^{10} a^{-10} +4 z^9 a^{-5} +3 z^9 a^{-9} +7 z^9 a^{-11} +4 z^8 a^{-4} -10 z^8 a^{-6} -42 z^8 a^{-8} -23 z^8 a^{-10} +5 z^8 a^{-12} +3 z^7 a^{-3} -5 z^7 a^{-5} -15 z^7 a^{-7} -37 z^7 a^{-9} -27 z^7 a^{-11} +3 z^7 a^{-13} +z^6 a^{-2} -7 z^6 a^{-4} +15 z^6 a^{-6} +73 z^6 a^{-8} +34 z^6 a^{-10} -15 z^6 a^{-12} +z^6 a^{-14} -8 z^5 a^{-3} -6 z^5 a^{-5} +35 z^5 a^{-7} +80 z^5 a^{-9} +38 z^5 a^{-11} -9 z^5 a^{-13} -3 z^4 a^{-2} -3 z^4 a^{-4} -20 z^4 a^{-6} -51 z^4 a^{-8} -19 z^4 a^{-10} +9 z^4 a^{-12} -3 z^4 a^{-14} +5 z^3 a^{-3} +5 z^3 a^{-5} -27 z^3 a^{-7} -55 z^3 a^{-9} -24 z^3 a^{-11} +4 z^3 a^{-13} +3 z^2 a^{-2} +4 z^2 a^{-4} +14 z^2 a^{-6} +20 z^2 a^{-8} +5 z^2 a^{-10} -z^2 a^{-12} +z^2 a^{-14} -z a^{-3} -z a^{-5} +8 z a^{-7} +12 z a^{-9} +4 z a^{-11} - a^{-2} - a^{-4} -4 a^{-6} -4 a^{-8} - a^{-10} }[/math] |
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