K12a397
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-4 q^{11}+9 q^{10}-17 q^9+24 q^8-30 q^7+33 q^6-30 q^5+25 q^4-17 q^3+10 q^2-4 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+20 t^2-48 t+63-48 t^{-1} +20 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6+2 z^4+5 z^2+1 }[/math] |
| Determinant | 205 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -2 z^6 a^{-6} +z^4 a^{-2} -4 z^4 a^{-6} +5 z^4 a^{-8} +z^2 a^{-2} +3 z^2 a^{-4} -4 z^2 a^{-6} +9 z^2 a^{-8} -4 z^2 a^{-10} +2 a^{-4} -2 a^{-6} +4 a^{-8} -4 a^{-10} + a^{-12} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-7} +2 z^{11} a^{-9} +7 z^{10} a^{-6} +13 z^{10} a^{-8} +6 z^{10} a^{-10} +10 z^9 a^{-5} +17 z^9 a^{-7} +15 z^9 a^{-9} +8 z^9 a^{-11} +8 z^8 a^{-4} -4 z^8 a^{-6} -19 z^8 a^{-8} +7 z^8 a^{-12} +4 z^7 a^{-3} -21 z^7 a^{-5} -55 z^7 a^{-7} -44 z^7 a^{-9} -10 z^7 a^{-11} +4 z^7 a^{-13} +z^6 a^{-2} -17 z^6 a^{-4} -19 z^6 a^{-6} -10 z^6 a^{-8} -23 z^6 a^{-10} -13 z^6 a^{-12} +z^6 a^{-14} -8 z^5 a^{-3} +16 z^5 a^{-5} +62 z^5 a^{-7} +40 z^5 a^{-9} -7 z^5 a^{-11} -9 z^5 a^{-13} -2 z^4 a^{-2} +11 z^4 a^{-4} +30 z^4 a^{-6} +40 z^4 a^{-8} +30 z^4 a^{-10} +5 z^4 a^{-12} -2 z^4 a^{-14} +3 z^3 a^{-3} -9 z^3 a^{-5} -26 z^3 a^{-7} -7 z^3 a^{-9} +13 z^3 a^{-11} +6 z^3 a^{-13} +z^2 a^{-2} -7 z^2 a^{-4} -16 z^2 a^{-6} -22 z^2 a^{-8} -17 z^2 a^{-10} -2 z^2 a^{-12} +z^2 a^{-14} +z a^{-5} +4 z a^{-7} -2 z a^{-9} -7 z a^{-11} -2 z a^{-13} +2 a^{-4} +2 a^{-6} +4 a^{-8} +4 a^{-10} + a^{-12} }[/math] |
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