# 9 27 (KnotPlot image) See the full Rolfsen Knot Table. Visit 9 27's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 9 27 at Knotilus!

### Knot presentations

 Planar diagram presentation X1425 X3,10,4,11 X11,1,12,18 X5,13,6,12 X13,17,14,16 X7,14,8,15 X15,6,16,7 X17,9,18,8 X9,2,10,3 Gauss code -1, 9, -2, 1, -4, 7, -6, 8, -9, 2, -3, 4, -5, 6, -7, 5, -8, 3 Dowker-Thistlethwaite code 4 10 12 14 2 18 16 6 8 Conway Notation 

### Three dimensional invariants

 Symmetry type Reversible Unknotting number 1 3-genus 3 Bridge index 2 Super bridge index $\{4,6\}$ Nakanishi index 1 Maximal Thurston-Bennequin number [-6][-5] Hyperbolic Volume 11. A-Polynomial See Data:9 27/A-polynomial

### Four dimensional invariants

 Smooth 4 genus $0$ Topological 4 genus $0$ Concordance genus $0$ Rasmussen s-Invariant 0

### Polynomial invariants

 Alexander polynomial $-t^3+5 t^2-11 t+15-11 t^{-1} +5 t^{-2} - t^{-3}$ Conway polynomial $-z^6-z^4+1$ 2nd Alexander ideal (db, data sources) $\{1\}$ Determinant and Signature { 49, 0 } Jones polynomial $q^4-3 q^3+5 q^2-7 q+9-8 q^{-1} +7 q^{-2} -5 q^{-3} +3 q^{-4} - q^{-5}$ HOMFLY-PT polynomial (db, data sources) $-z^6+2 a^2 z^4+z^4 a^{-2} -4 z^4-a^4 z^2+5 a^2 z^2+2 z^2 a^{-2} -6 z^2-a^4+3 a^2+ a^{-2} -2$ Kauffman polynomial (db, data sources) $a^2 z^8+z^8+3 a^3 z^7+6 a z^7+3 z^7 a^{-1} +3 a^4 z^6+6 a^2 z^6+4 z^6 a^{-2} +7 z^6+a^5 z^5-4 a^3 z^5-8 a z^5+3 z^5 a^{-3} -7 a^4 z^4-17 a^2 z^4-5 z^4 a^{-2} +z^4 a^{-4} -16 z^4-2 a^5 z^3-2 a^3 z^3-4 z^3 a^{-1} -4 z^3 a^{-3} +4 a^4 z^2+12 a^2 z^2+3 z^2 a^{-2} -z^2 a^{-4} +12 z^2+a^5 z+2 a^3 z+2 a z+2 z a^{-1} +z a^{-3} -a^4-3 a^2- a^{-2} -2$ The A2 invariant $-q^{16}+q^{12}-q^{10}+2 q^8+2 q^2-1+2 q^{-2} -2 q^{-4} + q^{-8} - q^{-10} + q^{-12}$ The G2 invariant $q^{80}-2 q^{78}+5 q^{76}-8 q^{74}+7 q^{72}-4 q^{70}-6 q^{68}+19 q^{66}-29 q^{64}+33 q^{62}-29 q^{60}+6 q^{58}+22 q^{56}-50 q^{54}+65 q^{52}-56 q^{50}+32 q^{48}+6 q^{46}-42 q^{44}+61 q^{42}-58 q^{40}+33 q^{38}+3 q^{36}-32 q^{34}+41 q^{32}-25 q^{30}-q^{28}+36 q^{26}-53 q^{24}+50 q^{22}-24 q^{20}-20 q^{18}+64 q^{16}-89 q^{14}+88 q^{12}-53 q^{10}+8 q^8+45 q^6-81 q^4+87 q^2-67+26 q^{-2} +16 q^{-4} -47 q^{-6} +48 q^{-8} -25 q^{-10} -5 q^{-12} +31 q^{-14} -41 q^{-16} +24 q^{-18} + q^{-20} -35 q^{-22} +58 q^{-24} -59 q^{-26} +43 q^{-28} -9 q^{-30} -22 q^{-32} +45 q^{-34} -51 q^{-36} +45 q^{-38} -28 q^{-40} +7 q^{-42} +11 q^{-44} -23 q^{-46} +24 q^{-48} -18 q^{-50} +13 q^{-52} -4 q^{-54} -2 q^{-56} +4 q^{-58} -6 q^{-60} +4 q^{-62} -2 q^{-64} + q^{-66}$