K13a2172
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Polynomial invariants
| Jones polynomial | Data:K13a2172/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ t^5-6 t^4+18 t^3-36 t^2+55 t-63+55 t^{-1} -36 t^{-2} +18 t^{-3} -6 t^{-4} + t^{-5} }[/math] |
| Conway polynomial | Data:K13a2172/Conway Polynomial |
| Determinant | 295 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^{10} a^{-2} +7 z^8 a^{-2} -2 z^8 a^{-4} -z^8+20 z^6 a^{-2} -11 z^6 a^{-4} +z^6 a^{-6} -5 z^6+29 z^4 a^{-2} -22 z^4 a^{-4} +4 z^4 a^{-6} -9 z^4+22 z^2 a^{-2} -18 z^2 a^{-4} +5 z^2 a^{-6} -7 z^2+7 a^{-2} -5 a^{-4} + a^{-6} -2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{12} a^{-2} +2 z^{12} a^{-4} +6 z^{11} a^{-1} +14 z^{11} a^{-3} +8 z^{11} a^{-5} +15 z^{10} a^{-2} +21 z^{10} a^{-4} +14 z^{10} a^{-6} +8 z^{10}+7 a z^9-4 z^9 a^{-1} -28 z^9 a^{-3} -3 z^9 a^{-5} +14 z^9 a^{-7} +4 a^2 z^8-55 z^8 a^{-2} -80 z^8 a^{-4} -35 z^8 a^{-6} +9 z^8 a^{-8} -15 z^8+a^3 z^7-17 a z^7-12 z^7 a^{-1} +13 z^7 a^{-3} -34 z^7 a^{-5} -37 z^7 a^{-7} +4 z^7 a^{-9} -12 a^2 z^6+83 z^6 a^{-2} +129 z^6 a^{-4} +40 z^6 a^{-6} -20 z^6 a^{-8} +z^6 a^{-10} +3 z^6-3 a^3 z^5+8 a z^5+10 z^5 a^{-1} +24 z^5 a^{-3} +73 z^5 a^{-5} +40 z^5 a^{-7} -8 z^5 a^{-9} +11 a^2 z^4-78 z^4 a^{-2} -100 z^4 a^{-4} -21 z^4 a^{-6} +12 z^4 a^{-8} -2 z^4 a^{-10} -2 z^4+3 a^3 z^3+3 a z^3-7 z^3 a^{-1} -36 z^3 a^{-3} -50 z^3 a^{-5} -19 z^3 a^{-7} +2 z^3 a^{-9} -3 a^2 z^2+36 z^2 a^{-2} +36 z^2 a^{-4} +8 z^2 a^{-6} -2 z^2 a^{-8} +7 z^2-a^3 z-a z+4 z a^{-1} +12 z a^{-3} +11 z a^{-5} +3 z a^{-7} -7 a^{-2} -5 a^{-4} - a^{-6} -2 }[/math] |
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