# 10 97 (KnotPlot image) See the full Rolfsen Knot Table. Visit 10 97's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 10 97 at Knotilus!

### Knot presentations

 Planar diagram presentation X4251 X12,6,13,5 X8394 X2,9,3,10 X16,12,17,11 X10,18,11,17 X18,8,19,7 X20,14,1,13 X14,20,15,19 X6,16,7,15 Gauss code 1, -4, 3, -1, 2, -10, 7, -3, 4, -6, 5, -2, 8, -9, 10, -5, 6, -7, 9, -8 Dowker-Thistlethwaite code 4 8 12 18 2 16 20 6 10 14 Conway Notation [.2.210.2]

### Three dimensional invariants

 Symmetry type Reversible Unknotting number 2 3-genus 2 Bridge index 3 Super bridge index Missing Nakanishi index 1 Maximal Thurston-Bennequin number [-1][-11] Hyperbolic Volume 14.8527 A-Polynomial See Data:10 97/A-polynomial

### Four dimensional invariants

 Smooth 4 genus $1$ Topological 4 genus $1$ Concordance genus $2$ Rasmussen s-Invariant -2

### Polynomial invariants

 Alexander polynomial $-5 t^2+22 t-33+22 t^{-1} -5 t^{-2}$ Conway polynomial $-5 z^4+2 z^2+1$ 2nd Alexander ideal (db, data sources) $\{1\}$ Determinant and Signature { 87, 2 } Jones polynomial $q^9-4 q^8+7 q^7-11 q^6+14 q^5-14 q^4+14 q^3-11 q^2+7 q-3+ q^{-1}$ HOMFLY-PT polynomial (db, data sources) $-z^4 a^{-2} -3 z^4 a^{-4} -z^4 a^{-6} +2 z^2 a^{-2} -4 z^2 a^{-4} +2 z^2 a^{-6} +z^2 a^{-8} +z^2+2 a^{-2} -2 a^{-4} +2 a^{-6} - a^{-8}$ Kauffman polynomial (db, data sources) $2 z^9 a^{-5} +2 z^9 a^{-7} +6 z^8 a^{-4} +11 z^8 a^{-6} +5 z^8 a^{-8} +8 z^7 a^{-3} +11 z^7 a^{-5} +7 z^7 a^{-7} +4 z^7 a^{-9} +6 z^6 a^{-2} -3 z^6 a^{-4} -21 z^6 a^{-6} -11 z^6 a^{-8} +z^6 a^{-10} +3 z^5 a^{-1} -12 z^5 a^{-3} -32 z^5 a^{-5} -28 z^5 a^{-7} -11 z^5 a^{-9} -7 z^4 a^{-2} -9 z^4 a^{-4} +5 z^4 a^{-6} +4 z^4 a^{-8} -2 z^4 a^{-10} +z^4-2 z^3 a^{-1} +10 z^3 a^{-3} +24 z^3 a^{-5} +20 z^3 a^{-7} +8 z^3 a^{-9} +6 z^2 a^{-2} +10 z^2 a^{-4} +3 z^2 a^{-6} +z^2 a^{-8} +z^2 a^{-10} -z^2-2 z a^{-3} -6 z a^{-5} -4 z a^{-7} -2 a^{-2} -2 a^{-4} -2 a^{-6} - a^{-8}$ The A2 invariant $q^4-q^2-1+4 q^{-2} -2 q^{-4} + q^{-6} +2 q^{-8} -2 q^{-10} +2 q^{-12} -2 q^{-14} +2 q^{-16} + q^{-18} -2 q^{-20} +3 q^{-22} -2 q^{-24} -2 q^{-26} + q^{-28}$ The G2 invariant $q^{18}-2 q^{16}+4 q^{14}-6 q^{12}+6 q^{10}-5 q^8+10 q^4-19 q^2+31-39 q^{-2} +37 q^{-4} -22 q^{-6} -8 q^{-8} +53 q^{-10} -94 q^{-12} +123 q^{-14} -126 q^{-16} +82 q^{-18} - q^{-20} -105 q^{-22} +205 q^{-24} -241 q^{-26} +205 q^{-28} -91 q^{-30} -61 q^{-32} +196 q^{-34} -257 q^{-36} +214 q^{-38} -82 q^{-40} -83 q^{-42} +199 q^{-44} -208 q^{-46} +106 q^{-48} +71 q^{-50} -229 q^{-52} +296 q^{-54} -241 q^{-56} +68 q^{-58} +148 q^{-60} -329 q^{-62} +404 q^{-64} -336 q^{-66} +158 q^{-68} +73 q^{-70} -266 q^{-72} +359 q^{-74} -328 q^{-76} +186 q^{-78} +3 q^{-80} -172 q^{-82} +252 q^{-84} -210 q^{-86} +77 q^{-88} +98 q^{-90} -221 q^{-92} +231 q^{-94} -136 q^{-96} -38 q^{-98} +207 q^{-100} -299 q^{-102} +277 q^{-104} -150 q^{-106} -24 q^{-108} +177 q^{-110} -251 q^{-112} +231 q^{-114} -142 q^{-116} +28 q^{-118} +61 q^{-120} -111 q^{-122} +108 q^{-124} -71 q^{-126} +33 q^{-128} +2 q^{-130} -19 q^{-132} +20 q^{-134} -16 q^{-136} +8 q^{-138} -3 q^{-140} + q^{-142}$