K12a245
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+5 q^6-11 q^5+19 q^4-28 q^3+33 q^2-35 q+34-26 q^{-1} +18 q^{-2} -10 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+24 t^2-49 t+63-49 t^{-1} +24 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6+2 z^4+1 }[/math] |
| Determinant | 225 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-a^2 z^6-3 z^6 a^{-2} +5 z^6-3 a^2 z^4-10 z^4 a^{-2} +3 z^4 a^{-4} +12 z^4-4 a^2 z^2-13 z^2 a^{-2} +5 z^2 a^{-4} -z^2 a^{-6} +13 z^2-2 a^2-6 a^{-2} +2 a^{-4} +7 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +15 z^{10} a^{-2} +7 z^{10} a^{-4} +8 z^{10}+14 a z^9+26 z^9 a^{-1} +21 z^9 a^{-3} +9 z^9 a^{-5} +14 a^2 z^8-15 z^8 a^{-2} -5 z^8 a^{-4} +5 z^8 a^{-6} +9 z^8+9 a^3 z^7-20 a z^7-73 z^7 a^{-1} -70 z^7 a^{-3} -25 z^7 a^{-5} +z^7 a^{-7} +4 a^4 z^6-25 a^2 z^6-41 z^6 a^{-2} -27 z^6 a^{-4} -14 z^6 a^{-6} -57 z^6+a^5 z^5-12 a^3 z^5+7 a z^5+58 z^5 a^{-1} +60 z^5 a^{-3} +20 z^5 a^{-5} -2 z^5 a^{-7} -4 a^4 z^4+24 a^2 z^4+62 z^4 a^{-2} +32 z^4 a^{-4} +11 z^4 a^{-6} +69 z^4-a^5 z^3+6 a^3 z^3+7 a z^3-10 z^3 a^{-1} -15 z^3 a^{-3} -4 z^3 a^{-5} +z^3 a^{-7} -12 a^2 z^2-29 z^2 a^{-2} -11 z^2 a^{-4} -z^2 a^{-6} -31 z^2-2 a^3 z-4 a z-4 z a^{-1} -4 z a^{-3} -2 z a^{-5} +2 a^2+6 a^{-2} +2 a^{-4} +7 }[/math] |
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