K13a1012
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Polynomial invariants
| Jones polynomial | Data:K13a1012/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-14 t^3+42 t^2-78 t+97-78 t^{-1} +42 t^{-2} -14 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | Data:K13a1012/Conway Polynomial |
| Determinant | 369 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +z^8-2 a^2 z^6+3 z^6 a^{-2} -z^6 a^{-4} +2 z^6+a^4 z^4-5 a^2 z^4+4 z^4 a^{-2} -2 z^4 a^{-4} +2 a^4 z^2-4 a^2 z^2+2 z^2 a^{-2} -z^2 a^{-4} -3 z^2+a^4+ a^{-4} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{12} a^{-2} +3 z^{12}+10 a z^{11}+20 z^{11} a^{-1} +10 z^{11} a^{-3} +15 a^2 z^{10}+26 z^{10} a^{-2} +14 z^{10} a^{-4} +27 z^{10}+14 a^3 z^9+2 a z^9-25 z^9 a^{-1} -2 z^9 a^{-3} +11 z^9 a^{-5} +9 a^4 z^8-23 a^2 z^8-77 z^8 a^{-2} -27 z^8 a^{-4} +5 z^8 a^{-6} -77 z^8+4 a^5 z^7-26 a^3 z^7-38 a z^7-21 z^7 a^{-1} -40 z^7 a^{-3} -26 z^7 a^{-5} +z^7 a^{-7} +a^6 z^6-16 a^4 z^6+13 a^2 z^6+66 z^6 a^{-2} +6 z^6 a^{-4} -12 z^6 a^{-6} +78 z^6-7 a^5 z^5+23 a^3 z^5+50 a z^5+44 z^5 a^{-1} +44 z^5 a^{-3} +18 z^5 a^{-5} -2 z^5 a^{-7} -2 a^6 z^4+11 a^4 z^4+a^2 z^4-24 z^4 a^{-2} +9 z^4 a^{-4} +9 z^4 a^{-6} -36 z^4+3 a^5 z^3-12 a^3 z^3-22 a z^3-22 z^3 a^{-1} -21 z^3 a^{-3} -5 z^3 a^{-5} +z^3 a^{-7} +a^6 z^2-5 a^4 z^2-3 a^2 z^2+2 z^2 a^{-2} -7 z^2 a^{-4} -2 z^2 a^{-6} +10 z^2+2 a^3 z+3 a z+5 z a^{-1} +5 z a^{-3} +z a^{-5} +a^4+ a^{-4} -1 }[/math] |
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