# 9 33 (KnotPlot image) See the full Rolfsen Knot Table. Visit 9 33's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 9 33 at Knotilus!

### Knot presentations

 Planar diagram presentation X4251 X12,8,13,7 X8394 X2,9,3,10 X18,13,1,14 X14,5,15,6 X6,17,7,18 X16,12,17,11 X10,16,11,15 Gauss code 1, -4, 3, -1, 6, -7, 2, -3, 4, -9, 8, -2, 5, -6, 9, -8, 7, -5 Dowker-Thistlethwaite code 4 8 14 12 2 16 18 10 6 Conway Notation [.21.2]

### Three dimensional invariants

 Symmetry type Chiral Unknotting number 1 3-genus 3 Bridge index 3 Super bridge index $\{4,6\}$ Nakanishi index 1 Maximal Thurston-Bennequin number [-6][-5] Hyperbolic Volume 13.2805 A-Polynomial See Data:9 33/A-polynomial

### Four dimensional invariants

 Smooth 4 genus $1$ Topological 4 genus $1$ Concordance genus $3$ Rasmussen s-Invariant 0

### Polynomial invariants

 Alexander polynomial $-t^3+6 t^2-14 t+19-14 t^{-1} +6 t^{-2} - t^{-3}$ Conway polynomial $-z^6+z^2+1$ 2nd Alexander ideal (db, data sources) $\{1\}$ Determinant and Signature { 61, 0 } Jones polynomial $q^4-4 q^3+7 q^2-9 q+11-10 q^{-1} +9 q^{-2} -6 q^{-3} +3 q^{-4} - q^{-5}$ HOMFLY-PT polynomial (db, data sources) $-z^6+2 a^2 z^4+z^4 a^{-2} -3 z^4-a^4 z^2+4 a^2 z^2+z^2 a^{-2} -3 z^2-a^4+2 a^2$ Kauffman polynomial (db, data sources) $2 a^2 z^8+2 z^8+4 a^3 z^7+10 a z^7+6 z^7 a^{-1} +3 a^4 z^6+5 a^2 z^6+7 z^6 a^{-2} +9 z^6+a^5 z^5-6 a^3 z^5-16 a z^5-5 z^5 a^{-1} +4 z^5 a^{-3} -6 a^4 z^4-16 a^2 z^4-9 z^4 a^{-2} +z^4 a^{-4} -20 z^4-2 a^5 z^3+a^3 z^3+5 a z^3-z^3 a^{-1} -3 z^3 a^{-3} +4 a^4 z^2+10 a^2 z^2+3 z^2 a^{-2} +9 z^2+a^5 z+a^3 z-a^4-2 a^2$ The A2 invariant $-q^{16}+q^{12}-2 q^{10}+2 q^8+3 q^2-1+3 q^{-2} -2 q^{-4} + q^{-8} -2 q^{-10} + q^{-12}$ The G2 invariant $q^{80}-2 q^{78}+5 q^{76}-8 q^{74}+8 q^{72}-7 q^{70}-2 q^{68}+17 q^{66}-35 q^{64}+50 q^{62}-52 q^{60}+28 q^{58}+13 q^{56}-67 q^{54}+113 q^{52}-123 q^{50}+92 q^{48}-23 q^{46}-64 q^{44}+129 q^{42}-148 q^{40}+111 q^{38}-31 q^{36}-54 q^{34}+104 q^{32}-98 q^{30}+43 q^{28}+39 q^{26}-101 q^{24}+121 q^{22}-81 q^{20}-5 q^{18}+102 q^{16}-171 q^{14}+188 q^{12}-138 q^{10}+43 q^8+71 q^6-159 q^4+198 q^2-170+88 q^{-2} +17 q^{-4} -101 q^{-6} +132 q^{-8} -101 q^{-10} +29 q^{-12} +54 q^{-14} -99 q^{-16} +89 q^{-18} -33 q^{-20} -51 q^{-22} +119 q^{-24} -142 q^{-26} +110 q^{-28} -38 q^{-30} -44 q^{-32} +103 q^{-34} -124 q^{-36} +105 q^{-38} -58 q^{-40} +6 q^{-42} +31 q^{-44} -54 q^{-46} +53 q^{-48} -36 q^{-50} +20 q^{-52} -2 q^{-54} -6 q^{-56} +9 q^{-58} -10 q^{-60} +6 q^{-62} -3 q^{-64} + q^{-66}$