K12a310
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+12 q^4-21 q^3+31 q^2-37 q+39-36 q^{-1} +29 q^{-2} -19 q^{-3} +10 q^{-4} -4 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+27 t^2-53 t+67-53 t^{-1} +27 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-z^4-z^2+1 }[/math] |
| Determinant | 245 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-2 z^6 a^{-2} +4 z^6+a^4 z^4-6 a^2 z^4-5 z^4 a^{-2} +z^4 a^{-4} +8 z^4+2 a^4 z^2-7 a^2 z^2-4 z^2 a^{-2} +z^2 a^{-4} +7 z^2+a^4-2 a^2+2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +7 a^2 z^{10}+8 z^{10} a^{-2} +15 z^{10}+10 a^3 z^9+24 a z^9+27 z^9 a^{-1} +13 z^9 a^{-3} +8 a^4 z^8+6 a^2 z^8+9 z^8 a^{-2} +11 z^8 a^{-4} -4 z^8+4 a^5 z^7-14 a^3 z^7-57 a z^7-63 z^7 a^{-1} -19 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-15 a^4 z^6-37 a^2 z^6-49 z^6 a^{-2} -21 z^6 a^{-4} +z^6 a^{-6} -48 z^6-8 a^5 z^5+4 a^3 z^5+43 a z^5+42 z^5 a^{-1} +3 z^5 a^{-3} -8 z^5 a^{-5} -2 a^6 z^4+11 a^4 z^4+41 a^2 z^4+43 z^4 a^{-2} +13 z^4 a^{-4} -z^4 a^{-6} +57 z^4+5 a^5 z^3+2 a^3 z^3-11 a z^3-9 z^3 a^{-1} +2 z^3 a^{-3} +3 z^3 a^{-5} +a^6 z^2-5 a^4 z^2-18 a^2 z^2-12 z^2 a^{-2} -3 z^2 a^{-4} -21 z^2-a^5 z-a^3 z+a^4+2 a^2+2 }[/math] |
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