K12a460
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-5 q^5+12 q^4-20 q^3+29 q^2-34 q+35-32 q^{-1} +25 q^{-2} -16 q^{-3} +8 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+17 t^2-53 t+77-53 t^{-1} +17 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+5 z^4-3 z^2+1 }[/math] |
| Determinant | 221 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^6-3 z^2 a^4-a^4+3 z^4 a^2-a^2-z^6+2 z^4+4 z^2+3-z^6 a^{-2} -z^4 a^{-2} -4 z^2 a^{-2} -2 a^{-2} +z^4 a^{-4} + a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a z^{11}+2 z^{11} a^{-1} +6 a^2 z^{10}+8 z^{10} a^{-2} +14 z^{10}+7 a^3 z^9+17 a z^9+23 z^9 a^{-1} +13 z^9 a^{-3} +5 a^4 z^8-3 a^2 z^8+3 z^8 a^{-2} +11 z^8 a^{-4} -16 z^8+3 a^5 z^7-11 a^3 z^7-51 a z^7-65 z^7 a^{-1} -23 z^7 a^{-3} +5 z^7 a^{-5} +a^6 z^6-7 a^4 z^6-7 a^2 z^6-39 z^6 a^{-2} -22 z^6 a^{-4} +z^6 a^{-6} -15 z^6-7 a^5 z^5+9 a^3 z^5+64 a z^5+65 z^5 a^{-1} +9 z^5 a^{-3} -8 z^5 a^{-5} -3 a^6 z^4-a^4 z^4+12 a^2 z^4+40 z^4 a^{-2} +12 z^4 a^{-4} -z^4 a^{-6} +37 z^4+5 a^5 z^3-7 a^3 z^3-38 a z^3-31 z^3 a^{-1} -3 z^3 a^{-3} +2 z^3 a^{-5} +3 a^6 z^2+4 a^4 z^2-8 a^2 z^2-15 z^2 a^{-2} -3 z^2 a^{-4} -21 z^2-a^5 z+3 a^3 z+8 a z+6 z a^{-1} +2 z a^{-3} -a^6-a^4+a^2+2 a^{-2} + a^{-4} +3 }[/math] |
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