7 6

[[Image:7_5.{{{ext}}}|80px|link=7_5]] 7_5

[[Image:7_7.{{{ext}}}|80px|link=7_7]] 7_7

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Knot presentations

Planar diagram presentation	X1425 X3849 X5,12,6,13 X9,1,10,14 X13,11,14,10 X11,6,12,7 X7283
Gauss code	-1, 7, -2, 1, -3, 6, -7, 2, -4, 5, -6, 3, -5, 4
Dowker-Thistlethwaite code	4 8 12 2 14 6 10
Conway Notation	[2212]

Three dimensional invariants

Symmetry type Reversible Unknotting number 1 3-genus 2 Bridge index 2 Super bridge index 4 Nakanishi index 1 Maximal Thurston-Bennequin number [-8][-1] Hyperbolic Volume 7.08493 A-Polynomial See Data:7 6/A-polynomial

[edit Notes for 7 6's three dimensional invariants]

Polynomial invariants

Jones polynomial	$q-2+3q^{-1}-3q^{-2}+4q^{-3}-3q^{-4}+2q^{-5}-q^{-6}$
Alexander polynomial	$-t^{2}-t^{-2}+5t+5t^{-1}-7$
Conway polynomial	$-z^{4}+z^{2}+1$
Determinant	19
Signature	-2
HOMFLY-PT polynomial	$-a^{6}+2a^{4}z^{2}+2a^{4}-a^{2}z^{4}-2a^{2}z^{2}-a^{2}+z^{2}+1$
Kauffman polynomial	$a^{7}z^{3}-a^{7}z+2a^{6}z^{4}-2a^{6}z^{2}+a^{6}+2a^{5}z^{5}-a^{5}z^{3}+a^{4}z^{6}+2a^{4}z^{4}-4a^{4}z^{2}+2a^{4}+4a^{3}z^{5}-6a^{3}z^{3}+2a^{3}z+a^{2}z^{6}+a^{2}z^{4}-4a^{2}z^{2}+a^{2}+2az^{5}-4az^{3}+az+z^{4}-2z^{2}+1$
(other formats)

Vassiliev invariants

V2 and V3:

(1, -2)

V2,1 through V6,9:

V2,1 V3,1 V4,1 V4,2 V4,3 V5,1 V5,2 V5,3 V5,4 V6,1 V6,2 V6,3 V6,4 V6,5 V6,6 V6,7 V6,8 V6,9 $4$ $-16$ $8$ ${\frac {158}{3}}$ ${\frac {34}{3}}$ $-64$ $-{\frac {544}{3}}$ $-{\frac {64}{3}}$ $-48$ ${\frac {32}{3}}$ $128$ ${\frac {632}{3}}$ ${\frac {136}{3}}$ ${\frac {19471}{30}}$ $-{\frac {474}{5}}$ ${\frac {17342}{45}}$ ${\frac {401}{18}}$ ${\frac {1711}{30}}$

V_2,1 through V_6,9 were provided by Petr Dunin-Barkowski <barkovs@itep.ru>, Andrey Smirnov <asmirnov@itep.ru>, and Alexei Sleptsov <sleptsov@itep.ru> and uploaded on October 2010 by User:Drorbn. Note that they are normalized differently than V₂ and V₃.