The knots page explains the above terms and the notation used in the table.
Number Conway b Braid notation
L(4)10(1) 4,2,2,2 = 4:ABccccBaBccB
= 4:AbbbbACbbC
= 4:AbbcbbabbCbbbb
= 4:aBccBABccccB
= 5:ABccBaDccbCdCBD
= 5:aBccdCbCBABDccB
= 5:aBccBAdCbCBDccB
= 6:abCdeDDCBACBCdCbCEDD
L(4)10(2) 31,2,2,2 = 5:ABcDcbadCbCddCBCd
= 5:AbCbacBDccBDc
= 5:AbbccdcbbabbCbDCb
= 5:abCddCBACbcDcBddC
= 4:AbbACCCbbC
= 4:aBccBABBBccB
= 4:aBccBBBABccB
= 5:abCDDDDCBACBCdCbC
L(4)10(3) 2,2,2,2++ = 5:ABCddcBaBccBd
= 5:abCbbAcBDccBD
= 4:AbbCbbaBccbbbc
= 5:abCddCBACbcDccBdC
= 5:AbbAcDccbDC
= 5:aBccBABdCddCbcD
= 5:abcDccBAdCBCddCbC
= 6:abcDeDCBADCBDCDeDcbDcD
L(4)10(4) (2,2,2)(2,2) = 5:ABcDcbacbccddccBc
= 6:aBcdcedcBABcDcEDcB
= 4:AbCCbabbCCbb
= 5:AbCCbaBBCCDCbCd
= 4:AbbCCbbabCCb
= 5:aBCCBABBcDcBBcd
= 4:aaBBaacBBc
= 5:abCDDCBACCbdCCb
L(4)10(5) (2,2)2(2,2) = 4:ABccBaccBccB
= 4:AbbCbbAbbC
= 4:AbbCbbabbCbb
= 5:AbbCdCbbaBBCDCb
= 4:AbbACbbCbb
= 4:aBccBABccBcc
= 5:AbbCbbadCBBCDCb
= 6:ACbCdCedCBBaBBCDCbED
L(4)10(6) (2,2)11(2,2) = 5:ABcDcbacbdCddCBdc
= 5:AbCbabcDccDcb
= 4:AbCCbaCbbCbb
= 5:aBCCdCCBABcBd
= 4:AbbACCbCCb
= 4:aBccBABBcBBc
= 4:aaBaacBBcB
= 5:abcDDcBADDCBCdCbC
L(4)10(7) .(2,2)1 = 4:AbCbCbabCCbC
= 4:aBcBcBacBB
= 4:ABcBcBaBBcBB
= 5:abCbAbcDcDcbD
= 4:aBBaBcBcBc
= 4:abCbCbAbCCbC
= 4:AbCbAACbAC
= 5:abcDcBAcBdCdCdCbc
L(4)10(8) .(2,2):2 = 5:ABcDcbbacbccdccBc
= 5:aBccdCBABcdCdcB
= 4:ABcBBcBaBccB
= 4:AbCCbACbbC
= 4:aaBcBaaBcB
= 5:abCDDCBACbCdCbC
= 4:AbbACbCCbC
= 4:aBccBABcBBcB
L(4)10(9) 10*** = 4:aBcBacBaBc
= 4:AbCbCbabCbCb
= 4:abCbCbAbCbCb
= 4:aBacBcBacB
= 4:AbACbCbACb
= 4:ABcBcBaBcBcB
= 4:aBcBcBABcBcB
= 4:AbCbACbAbC
L(4)10(10) 4,2,2,2- = 4:ABccccBaBCCB
= 4:abbaCbbbbC
= 4:ABBcbbabbCbbbb
= 4:aBccBAbccccb
= 5:ABCCBaDccbCdCBD
= 5:aBccdCbCBAbDccb
= 5:aBccBAdCbCBDCCB
5 6:abCdeDDCBAcBCdCbcEDD
L(4)10(11) 31,2,2,2- = 5:ABcDcbadCbCDDCBCd
= 5:AbCbacBdccBdc
= 5:ABBccdcbbabbCbDCb
= 5:abCddCBAcbcDcBddc
= 4:ABBACCCbbC
= 4:abccbABBBccB
= 4:aBCCBBBABccB
4 5:abCDDDDCBACBcdcbC
L(4)10(12) 4,2,2,2-- = 4:ABccccBabCCb
= 4:aBBaCbbbbC
= 4:ABBcBBabbCbbbb
= 4:abccbAbccccb
= 5:AbCCbaDccbCdCBD
= 5:aBccdCbCBAbDCCb
= 5:aBCCBAdCbCBDCCB
5 6:abCdeDDCBAcBcdcbcEDD
L(4)10(13) (2,2,2)(2,2-) = 5:ABcDcbacbCCddccBc
5 6:aBcdcedcBAbcDcEDcb
= 4:AbCCbabbCCBB
4 5:AbCCbaBBCCDcbcd
= 4:ABBCCbbabCCb
4 5:abCCbABBcDcBBcd
= 4:aaBBAAcBBc
4 5:abcDDcBACCbdCCb
L(4)10(14) (2,2,2-)(2,2) 4 5:ABcDcbaCbccddccBC
5 6:aBCdcedcBABcDcEDCB
= 4:AbCCbabbccbb
= 5:AbCCbaBBccDCbCd
= 4:AbbCCbbaBCCB
= 5:aBCCBABBcDCBBCd
= 4:aabbaacBBc
= 5:abCDDCBACCbdccb
L(4)10(15) (2,2,2-)(2,2-) 4 5:ABcDcbaCbCCddccBC
4 6:aBCdcedcBAbcDcEDCb
= 4:AbCCbabbccBB
4 5:AbCCbaBBccDcbcd
= 4:ABBCCbbaBCCB
4 5:abCCbABBcDCBBCd
= 4:aabbAAcBBc
4 5:abcDDcBACCbdccb
L(4)10(16) (2,2,2--)(2,2) = 4:Abccbabbccbb
= 5:AbccbaBBccDCbCd
4 5:ABCDCbaCbccddccBC
5 6:aBCdCedcBABcDCEDCB
= 4:aabbaaCBBC
= 5:abCDDCBACCBdccB
= 4:AbbCCbbaBccB
= 5:aBCCBABBcDCbbCd
L(4)10(17) (2,2,2)-(2,2) = 5:ABcDcbacbCCddCCBc
5 6:abcdcedcbAbcDcEDcb
= 4:AbCCbaBBCCBB
= 5:ABCCDcbbacbdCCb
= 4:ABBCCBBabCCb
= 5:ABcDCCbbabCCbdc
= 4:AABBAAcBBc
= 5:abcDcBACCbddCCb
L(4)10(18) .(2,2-)1 = 4:AbCbCbabccbC
= 4:ABBABcBcBc
= 4:ABcBcBabbcBB
4 5:aBCBAbcDcDcbD
= 4:abbaBcBcBc
= 4:abCbCbABCCBC
= 4:AbCbaaCbAC
4 5:abCDCBAcBdCdCdCbc
L(4)10(19) .(2,2-):2 = 5:ABcDcbbacbccdCCBc
= 5:aBccdCBAbcdCdcb
= 4:ABcBBcBaBCCB
= 4:abbaCbCCbC
= 4:aaBcBAABcB
4 5:abcDDcBACbCdCbC
= 4:ABBACbCCbC
= 4:abccbABcBBcB
L(4)10(20) .-(2,2):2 = 4:ABcBBcBabCCb
= 5:ABcDcbbacbCCdCCBc
= 4:aBBaCbCCbC
= 5:abccdCbAbcdCdcb
= 4:abCCbaCBBC
= 4:AABcBAABcB
= 4:abCCbABcBBcB
= 5:abcDcBACbCddCbC
L(4)10(21) 10***-1.-1.-1.-1.-1 = 4:abCbCbABcBcB
= 4:aBaCbCbaCB
= 4:AbAbAcBcBc
= 4:ABcBcBabCbCb
= 4:abCbCbABcBcB
= 4:aBaBaCbCbC
= 4:AbAcBcBAcb
= 4:AbCbCbaBcBcB
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