K12a3
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-4 q^5+9 q^4-15 q^3+21 q^2-25 q+27-24 q^{-1} +19 q^{-2} -13 q^{-3} +7 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+14 t^2-40 t+57-40 t^{-1} +14 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+2 z^4-2 z^2+1 }[/math] |
| Determinant | 169 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^6-3 z^2 a^4-2 a^4+3 z^4 a^2+3 z^2 a^2+a^2-z^6+z^2+2-z^6 a^{-2} -2 z^4 a^{-2} -4 z^2 a^{-2} -2 a^{-2} +z^4 a^{-4} +z^2 a^{-4} + a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +3 a^2 z^{10}+5 z^{10} a^{-2} +8 z^{10}+4 a^3 z^9+10 a z^9+15 z^9 a^{-1} +9 z^9 a^{-3} +4 a^4 z^8+2 a^2 z^8-z^8 a^{-2} +8 z^8 a^{-4} -11 z^8+3 a^5 z^7-a^3 z^7-26 a z^7-49 z^7 a^{-1} -23 z^7 a^{-3} +4 z^7 a^{-5} +a^6 z^6-5 a^4 z^6-6 a^2 z^6-22 z^6 a^{-2} -21 z^6 a^{-4} +z^6 a^{-6} -8 a^5 z^5-10 a^3 z^5+32 a z^5+64 z^5 a^{-1} +21 z^5 a^{-3} -9 z^5 a^{-5} -3 a^6 z^4-5 a^4 z^4-4 a^2 z^4+33 z^4 a^{-2} +16 z^4 a^{-4} -2 z^4 a^{-6} +13 z^4+7 a^5 z^3+7 a^3 z^3-22 a z^3-35 z^3 a^{-1} -10 z^3 a^{-3} +3 z^3 a^{-5} +3 a^6 z^2+8 a^4 z^2+5 a^2 z^2-15 z^2 a^{-2} -6 z^2 a^{-4} -9 z^2-2 a^5 z-a^3 z+5 a z+7 z a^{-1} +3 z a^{-3} -a^6-2 a^4-a^2+2 a^{-2} + a^{-4} +2 }[/math] |
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