K12a45
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+3 q^3-8 q^2+15 q-21+27 q^{-1} -28 q^{-2} +27 q^{-3} -22 q^{-4} +15 q^{-5} -8 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-22 t^2+37 t-43+37 t^{-1} -22 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+6 z^4+5 z^2+1 }[/math] |
| Determinant | 179 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^2 z^8+2 a^4 z^6-4 a^2 z^6+2 z^6-a^6 z^4+7 a^4 z^4-6 a^2 z^4-z^4 a^{-2} +7 z^4-3 a^6 z^2+8 a^4 z^2-5 a^2 z^2-3 z^2 a^{-2} +8 z^2-2 a^6+3 a^4-2 a^2-2 a^{-2} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+5 a^4 z^{10}+9 a^2 z^{10}+4 z^{10}+9 a^5 z^9+19 a^3 z^9+15 a z^9+5 z^9 a^{-1} +9 a^6 z^8+7 a^4 z^8-7 a^2 z^8+3 z^8 a^{-2} -2 z^8+6 a^7 z^7-12 a^5 z^7-55 a^3 z^7-52 a z^7-14 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6-15 a^6 z^6-37 a^4 z^6-29 a^2 z^6-10 z^6 a^{-2} -20 z^6+a^9 z^5-8 a^7 z^5+6 a^5 z^5+58 a^3 z^5+58 a z^5+11 z^5 a^{-1} -4 z^5 a^{-3} -4 a^8 z^4+16 a^6 z^4+45 a^4 z^4+42 a^2 z^4+11 z^4 a^{-2} +28 z^4-2 a^9 z^3+5 a^7 z^3+2 a^5 z^3-30 a^3 z^3-33 a z^3-3 z^3 a^{-1} +5 z^3 a^{-3} +a^8 z^2-9 a^6 z^2-20 a^4 z^2-20 a^2 z^2-6 z^2 a^{-2} -16 z^2+a^9 z-2 a^7 z-a^5 z+7 a^3 z+7 a z-2 z a^{-3} +2 a^6+3 a^4+2 a^2+2 a^{-2} +4 }[/math] |
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