Irrationalities and Conway polynomials

Irrationalities and their p-modular reductions

Common Irrationalities in Characteristic 7

C₁	=	X + 4
C₂	=	X² + 6X + 3
C₃	=	X³ + 6X² + 4
C₄	=	X⁴ + 5X² + 4X + 3
C₅	=	X⁵ + X + 4
C₆	=	X⁶ + X⁴ + 5X³ + 4X² + 6X + 3
C₈	=	X⁸ + 4X³ + 6X² + 2X + 3
C₉	=	X⁹ + 6X⁴ + X³ + 6X + 4
C₁₂	=	X¹² + 2X⁸ + 5X⁷ + 3X⁶ + 2X⁵ + 4X⁴ + 5X² + 3

ξ	f	C_n
b5	2X + 2	C₂
b5∗	5X + 4	C₂
b11	6X	C₂
b11∗∗	X + 6	C₂
b13	4X + 1	C₂
b13∗	3X + 5	C₂
b15	3X + 5	C₂
b15∗∗	4X + 1	C₂
b17	X + 6	C₂
b17∗	6X	C₂
b19	5	C₁
b19∗∗	1	C₁
b23	5X + 4	C₂
b23∗∗	2X + 2	C₂
b27	0	C₁
b27∗∗	6	C₁
b29	0	C₁
b29∗	6	C₁
b31	2	C₁
b31∗∗	4	C₁
b33	5X + 4	C₂
b33∗	2X + 2	C₂
b37	5	C₁
b37∗	1	C₁
b39	6X	C₂
b39∗∗	X + 6	C₂
b45	6X	C₂
b45∗	X + 6	C₂
b47	5	C₁
b47∗∗	1	C₁
b59	2	C₁
b59∗∗	4	C₁
b87	2	C₁
b87∗∗	4	C₁
b95	X + 6	C₂
b95∗∗	6X	C₂
b117	5X + 4	C₂
b117∗	2X + 2	C₂
c13	2X² + 5X + 2	C₃
c13∗2	2X² + 6	C₃
c13∗4	3X² + 2X + 5	C₃
c19	0	C₁
c19∗2	4	C₁
c19∗4	2	C₁
c31	4X² + 3	C₃
c31∗3	4X² + 3X + 2	C₃
c31∗5	6X² + 4X + 1	C₃
c37	4X + 3	C₃
c37∗2	2X² + 4X	C₃
c37∗3	5X² + 6X + 3	C₃
c43	3X² + 5X + 4	C₃
c43∗3	X + 4	C₃
c43∗7	4X² + X + 5	C₃
d17	4X³ + 2X² + 2X + 1	C₄
d17∗2	6X³ + X + 2	C₄
d17∗3	3X³ + 3X	C₄
d17∗6	X³ + 5X² + X + 3	C₄
e31	5X⁴ + 4X³ + 3X² + 1	C₅
e31∗2	6X⁴ + 6X³ + 4X + 6	C₅
e31∗3	4X⁴ + 3X³ + 3X² + 6X + 3	C₅
e31∗4	3X⁴ + 4X³ + 2X² + 6X + 5	C₅
e31∗8	3X⁴ + 4X³ + 6X² + 5X + 5	C₅
f31	6X² + X + 3	C₃
f31∗3	2X² + 4X + 4	C₃
f31∗5	6X² + 1	C₃
f31∗7	2X² + 6X + 5	C₃
f31∗11	4X	C₃
f31∗15	5X² + 6X	C₃
f37	X² + 4X	C₃
f37∗2	2X² + 6X	C₃
f37∗3	6X² + 5X + 5	C₃
f37∗5	6X² + X + 5	C₃
f37∗6	6X² + 3	C₃
f37∗9	5X	C₃
i	6X + 4	C₂
i2	4X + 5	C₂
i3	5	C₁
i5	4	C₁
i6	1	C₁
i8	X + 3	C₂
i10	5	C₁
i11	5X + 1	C₂
i15	6X + 4	C₂
i19	4	C₁
i26	3	C₁
k13	5X³ + X² + 2X	C₄
k13∗2	X³ + 2X² + 1	C₄
k13∗4	2X³ + 6X² + 5X	C₄
k13∗7	6X³ + 5X² + 6	C₄
k'52	X³ + X² + X + 2	C₄
k'52∗3	6X³ + 6X² + 6X + 5	C₄
k'52∗5	6X³ + X² + 4X + 3	C₄
k'52∗15	X³ + 6X² + 3X + 4	C₄
m5	X³ + 4X² + 5X + 6	C₄
m5∗2	3X³ + X² + 5X + 1	C₄
m5∗3	4X³ + 6X² + 2X + 6	C₄
m5∗4	6X³ + 3X² + 2X + 1	C₄
m16	6	C₁
m16∗3	3	C₁
m16∗9	1	C₁
m16∗11	4	C₁
m20	4X	C₂
m20∗3	3X + 4	C₂
m20∗11	3X	C₂
m20∗13	4X + 3	C₂
r2	3	C₁
r3	5X + 1	C₂
r5	4X + 5	C₂
r6	X + 3	C₂
r10	5X + 1	C₂
r11	2	C₁
r13	X + 3	C₂
r15	1	C₁
r17	2X + 6	C₂
r30	3	C₁
s51	3X³ + 6X² + 3X + 5	C₄
s51∗5	4X³ + 4X² + X + 3	C₄
s51∗11	X² + 3X + 1	C₄
s51∗19	3X² + 6	C₄
u''52	X³ + X² + X + 2	C₄
u''52∗3	6X³ + 6X² + 6X + 5	C₄
u''52∗5	6X³ + X² + 4X + 3	C₄
u''52∗15	X³ + 6X² + 3X + 4	C₄
v33	3X	C₂
v33∗2	2X + 5	C₂
v33∗5	5X	C₂
v33∗7	4X + 3	C₂
w'40	6X + 3	C₂
w'40∗3	6X + 5	C₂
w'40∗7	X + 2	C₂
w'40∗17	X + 4	C₂
w'80	3X³ + 6X² + 3	C₄
w'80∗3	4X³ + 4X² + 4X + 1	C₄
w'80∗7	X³ + 3X² + 6X	C₄
w'80∗11	6X³ + 4X² + X	C₄
w'80∗13	4X³ + X² + 4	C₄
w'80∗17	3X³ + 4X² + 2X + 5	C₄
w'80∗31	3X³ + 3X² + 3X + 6	C₄
w'80∗33	4X³ + 3X² + 5X + 2	C₄
x13	5X³ + X² + 5	C₄
x13∗2	5X³ + 4X² + X + 2	C₄
x13∗4	5X + 5	C₄
x13∗7	4X³ + 2X² + X + 1	C₄
x19	4	C₁
x19∗2	3	C₁
x19∗4	0	C₁
x19∗5	1	C₁
x19∗8	3	C₁
x19∗10	2	C₁
x43	X	C₂
x43∗2	3X + 2	C₂
x43∗3	5X + 5	C₂
x43∗4	6X + 2	C₂
x43∗5	2X + 6	C₂
x43∗7	6X + 1	C₂
x43∗9	3X + 3	C₂
x43∗10	4X + 1	C₂
x43∗13	5X + 1	C₂
x43∗14	4X + 5	C₂
x43∗19	X + 1	C₂
x43∗20	4X + 6	C₂
x43∗21	2X + 3	C₂
x43∗26	3X + 5	C₂
x57	4	C₁
x57∗2	2	C₁
x57∗4	6	C₁
x57∗5	5	C₁
x57∗8	0	C₁
x57∗10	2	C₁
x57∗11	1	C₁
x57∗16	6	C₁
x57∗22	1	C₁
x57∗23	5	C₁
x57∗29	4	C₁
x57∗31	0	C₁
x73	3X⁷ + 3X⁶ + 4X⁵ + 4X⁴ + 3X³ + X² + 4X	C₈
x73∗2	X⁷ + 3X⁶ + 2X⁴ + 3X³ + 5X² + 2X + 6	C₈
x73∗3	3X⁷ + 2X⁶ + 5X³ + 4X² + 2X + 3	C₈
x73∗4	6X⁷ + 2X⁶ + 4X⁵ + 3X⁴ + 2X³ + 5X² + 2X	C₈
x73∗5	5X⁵ + 6X⁴ + 6X³ + 3X² + X + 4	C₈
x73∗6	3X⁷ + 6X⁶ + 2X⁵ + X⁴ + 2X³ + 6X² + 2X	C₈
x73∗7	4X⁷ + X⁶ + 5X⁵ + 6X⁴ + 6X³ + X² + 6X + 4	C₈
x73∗9	3X⁶ + X⁴ + 5X³ + 4X + 4	C₈
x73∗11	X⁷ + 2X⁶ + X⁵ + X⁴ + 5X³ + 5X² + 3	C₈
x73∗12	X⁷ + 3X⁶ + 3X³ + 3X² + 5X + 5	C₈
x73∗13	2X⁷ + X⁶ + 2X⁵ + 3X⁴ + 4X³ + 4X² + 4X + 2	C₈
x73∗14	X⁷ + 4X⁶ + 6X⁵ + 6X⁴ + 2X² + 5X + 1	C₈
x73∗17	2X⁶ + 5X⁵ + X⁴ + 5X³ + 2X² + 4X + 5	C₈
x73∗18	6X⁷ + 3X⁶ + 4X⁴ + 6X³ + 2X + 6	C₈
x73∗21	X⁷ + 5X⁶ + 6X⁵ + 5X⁴ + X³ + 6X	C₈
x73∗25	5X⁷ + 2X⁶ + 4X⁵ + 4X⁴ + 4X³ + 4X² + X + 1	C₈
x73∗26	5X⁷ + 3X⁶ + 2X⁴ + 4X³ + 4X² + 2X + 5	C₈
x73∗27	4X⁷ + 6X⁶ + 4X³ + 5X² + 4X	C₈
x73∗33	2X⁶ + 2X⁵ + X⁴ + 5X³ + X² + 4X + 2	C₈
x73∗34	X⁷ + 4X⁶ + 6X⁵ + 4X⁴ + 3X³ + 2X² + 2X + 1	C₈
x73∗35	6X⁷ + 5X⁶ + 4X⁴ + 4X³ + 6X² + 3X	C₈
x73∗36	2X⁷ + 4X⁶ + 2X⁵ + 4X⁴ + 6X³ + X² + 4X + 4	C₈
x73∗42	2X⁷ + 5X⁶ + X⁵ + 4X⁴ + 6X³ + 5X² + 3X	C₈
x73∗43	6X⁷ + 6X⁶ + X⁵ + 4X⁴ + 6X³ + X² + 5X + 6	C₈
x171	1	C₁
x171∗2	6	C₁
x171∗4	0	C₁
x171∗5	1	C₁
x171∗8	1	C₁
x171∗10	5	C₁
x171∗11	3	C₁
x171∗13	6	C₁
x171∗16	4	C₁
x171∗17	4	C₁
x171∗20	5	C₁
x171∗22	6	C₁
x171∗23	5	C₁
x171∗29	3	C₁
x171∗31	6	C₁
x171∗34	3	C₁
x171∗37	5	C₁
x171∗40	5	C₁
x171∗41	3	C₁
x171∗43	2	C₁
x171∗44	6	C₁
x171∗47	3	C₁
x171∗58	2	C₁
x171∗59	5	C₁
x171∗61	0	C₁
x171∗62	2	C₁
x171∗65	2	C₁
x171∗68	6	C₁
x171∗73	1	C₁
x171∗86	6	C₁
x171∗94	3	C₁
x171∗97	3	C₁
x171∗115	4	C₁
x171∗118	0	C₁
x171∗122	4	C₁
x171∗143	5	C₁
y9	5X² + 3X + 2	C₃
y9∗2	3X + 6	C₃
y9∗4	2X² + X + 6	C₃
y13	X⁵ + 4X⁴ + 6X³ + 6X² + 6X + 6	C₆
y13∗2	3X⁵ + 3X⁴ + 2X³ + 2X² + 5X + 1	C₆
y13∗3	2X⁵ + 4X³ + 2X² + 4X + 4	C₆
y13∗4	2X⁵ + X⁴ + 3X³ + 2	C₆
y13∗5	4X⁵ + 2X⁴ + 2X³ + X² + 4X + 5	C₆
y13∗6	2X⁵ + 4X⁴ + 4X³ + 3X² + 2X + 2	C₆
y15	6X³ + 3X² + X + 3	C₄
y15∗2	5X³ + 2X² + 2X + 1	C₄
y15∗4	X² + 5X + 1	C₄
y15∗7	3X³ + X² + 6X + 3	C₄
y16	3X + 2	C₂
y16∗3	6X + 4	C₂
y16∗5	X + 3	C₂
y16∗7	4X + 5	C₂
y20	5X² + 2X + 2	C₄
y20∗3	5X³ + 3X + 1	C₄
y20∗7	2X³ + 4X + 6	C₄
y20∗9	2X² + 5X + 5	C₄
y24	4X + 3	C₂
y24∗5	4X	C₂
y24∗7	3X	C₂
y24∗11	3X + 4	C₂
y25	3X + 3	C₂
y25∗2	6X + 1	C₂
y25∗3	X + 2	C₂
y25∗4	6X + 3	C₂
y25∗6	5X + 6	C₂
y25∗7	4X + 6	C₂
y25∗8	2X + 4	C₂
y25∗9	6X + 2	C₂
y25∗11	X	C₂
y25∗12	X + 1	C₂
y32	4X³ + 2X² + 6X + 3	C₄
y32∗3	3X³ + 2X² + 4X	C₄
y32∗5	2X³ + 4X² + 2	C₄
y32∗7	5X³ + 4X² + 6X + 4	C₄
y32∗9	2X³ + 3X² + X + 3	C₄
y32∗11	5X³ + 3X² + 5	C₄
y32∗13	4X³ + 5X² + 3X	C₄
y32∗15	3X³ + 5X² + X + 4	C₄
y48	3X + 5	C₂
y48∗5	5X	C₂
y48∗7	4X + 1	C₂
y48∗11	5X + 2	C₂
y48∗13	2X + 5	C₂
y48∗17	3X + 6	C₂
y48∗19	2X	C₂
y48∗23	4X + 2	C₂
y52	4X¹¹ + 4X¹⁰ + X⁹ + 4X⁷ + 4X⁶ + 4X⁴ + X³ + 4X² + 2X + 2	C₁₂
y52∗3	X¹¹ + 2X¹⁰ + 3X⁹ + 5X⁸ + 3X⁷ + 6X⁶ + 3X⁵ + 5X⁴ + 6X³ + 2X² + 4X + 6	C₁₂
y52∗5	6X¹¹ + 4X¹⁰ + X⁹ + 3X⁸ + 6X⁷ + 4X⁶ + X⁵ + X³ + 5X + 5	C₁₂
y52∗7	2X¹¹ + 2X¹⁰ + 2X⁹ + 2X⁸ + 6X⁷ + 6X⁶ + 5X⁵ + 4X⁴ + 4X³ + X² + X + 2	C₁₂
y52∗9	3X¹¹ + 3X¹⁰ + 3X⁹ + 5X⁸ + 2X⁶ + 5X⁵ + 5X⁴ + X³ + 3X² + 2X + 3	C₁₂
y52∗11	6X¹¹ + X¹⁰ + 2X⁹ + 6X⁸ + 3X⁶ + 4X⁵ + X⁴ + X³ + 5X² + 5X + 1	C₁₂
y52∗15	X¹¹ + 6X¹⁰ + 5X⁹ + X⁸ + 4X⁶ + 3X⁵ + 6X⁴ + 6X³ + 2X² + 2X + 6	C₁₂
y52∗17	4X¹¹ + 4X¹⁰ + 4X⁹ + 2X⁸ + 5X⁶ + 2X⁵ + 2X⁴ + 6X³ + 4X² + 5X + 4	C₁₂
y52∗19	5X¹¹ + 5X¹⁰ + 5X⁹ + 5X⁸ + X⁷ + X⁶ + 2X⁵ + 3X⁴ + 3X³ + 6X² + 6X + 5	C₁₂
y52∗21	X¹¹ + 3X¹⁰ + 6X⁹ + 4X⁸ + X⁷ + 3X⁶ + 6X⁵ + 6X³ + 2X + 2	C₁₂
y52∗23	6X¹¹ + 5X¹⁰ + 4X⁹ + 2X⁸ + 4X⁷ + X⁶ + 4X⁵ + 2X⁴ + X³ + 5X² + 3X + 1	C₁₂
y52∗25	3X¹¹ + 3X¹⁰ + 6X⁹ + 3X⁷ + 3X⁶ + 3X⁴ + 6X³ + 3X² + 5X + 5	C₁₂
y60	X³ + 6X² + 6	C₄
y60∗7	5X³ + 6X + 3	C₄
y60∗11	3X³ + 6X² + 4X + 5	C₄
y60∗13	2X³ + 5X² + 3X + 6	C₄
y60∗17	5X³ + 2X² + 4X + 1	C₄
y60∗19	4X³ + X² + 3X + 2	C₄
y60∗23	2X³ + X + 4	C₄
y60∗29	6X³ + X² + 1	C₄
y96	6X³ + 5X + 4	C₄
y96∗5	6X³ + 3X² + 2X + 1	C₄
y96∗7	6X² + X + 1	C₄
y96∗11	X³ + 6X² + 3X + 4	C₄
y96∗13	3X³ + X² + 5X + 1	C₄
y96∗17	4X³ + 3X² + 5X + 2	C₄
y96∗19	X³ + X² + X + 2	C₄
y96∗23	4X³ + 4X² + 4X + 1	C₄
y96∗25	3X³ + 3X² + 3X + 6	C₄
y96∗29	6X³ + 6X² + 6X + 5	C₄
y96∗31	3X³ + 4X² + 2X + 5	C₄
y96∗35	4X³ + 6X² + 2X + 6	C₄
y96∗37	6X³ + X² + 4X + 3	C₄
y96∗41	X² + 6X + 6	C₄
y96∗43	X³ + 4X² + 5X + 6	C₄
y96∗47	X³ + 2X + 3	C₄
y100	2X³ + X² + 3X + 5	C₄
y100∗3	2X³ + 5X² + 6X + 1	C₄
y100∗7	6X³ + 2X² + 3X + 2	C₄
y100∗9	2X³ + 6X² + 5X	C₄
y100∗11	6X³ + 4X² + X	C₄
y100∗13	6X³ + 5X² + 6	C₄
y100∗17	3X² + 4X + 4	C₄
y100∗19	4X³ + X + 5	C₄
y100∗21	2X³ + 2X² + 2X + 4	C₄
y100∗23	3X³ + 6X² + 3	C₄
y100∗27	4X³ + X² + 4	C₄
y100∗29	5X³ + 5X² + 5X + 3	C₄
y100∗31	3X³ + 6X + 2	C₄
y100∗33	4X² + 3X + 3	C₄
y100∗37	X³ + 2X² + 1	C₄
y100∗39	X³ + 3X² + 6X	C₄
y100∗41	5X³ + X² + 2X	C₄
y100∗43	X³ + 5X² + 4X + 5	C₄
y100∗47	5X³ + 2X² + X + 6	C₄
y100∗49	5X³ + 6X² + 4X + 2	C₄
y'40	4X	C₂
y'40∗3	4X + 3	C₂
y'40∗7	3X + 4	C₂
y'40∗11	5X + 5	C₂
y'40∗13	2X + 3	C₂
y'40∗17	5X + 4	C₂
y'40∗21	3X	C₂
y'40∗31	2X + 2	C₂
y'48	1	C₁
y'48∗5	3	C₁
y'48∗11	4	C₁
y'48∗13	2	C₁
y'48∗17	2	C₁
y'48∗19	5	C₁
y'48∗25	6	C₁
y'48∗41	5	C₁
y'80	2X³ + 2X² + 2X + 4	C₄
y'80∗3	2X³ + 4X² + 2	C₄
y'80∗7	5X³ + 2X² + X + 6	C₄
y'80∗11	4X³ + 6X² + 2X + 6	C₄
y'80∗13	6X³ + 3X² + 2X + 1	C₄
y'80∗17	2X² + 5X + 5	C₄
y'80∗21	3X³ + 2X² + 4X	C₄
y'80∗23	2X³ + 5X² + 6X + 1	C₄
y'80∗31	5X³ + 3X + 1	C₄
y'80∗33	5X² + 2X + 2	C₄
y'80∗41	5X³ + 5X² + 5X + 3	C₄
y'80∗43	5X³ + 3X² + 5	C₄
y'80∗51	3X³ + X² + 5X + 1	C₄
y'80∗53	X³ + 4X² + 5X + 6	C₄
y'80∗61	4X³ + 5X² + 3X	C₄
y'80∗71	2X³ + 4X + 6	C₄
y''48	6X	C₂
y''48∗5	4X + 4	C₂
y''48∗7	X + 6	C₂
y''48∗11	4X + 6	C₂
y''48∗17	X	C₂
y''48∗23	6X + 1	C₂
y''48∗29	3X + 3	C₂
y''48∗35	3X + 1	C₂
y'''24	2	C₁
y'''24∗5	6	C₁
y'''24∗13	5	C₁
y'''24∗17	1	C₁
z3	2	C₁
z3∗∗	4	C₁
z8	2X + 4	C₂
z8∗3	2X + 1	C₂
z8∗5	5X + 3	C₂
z8∗7	5X + 6	C₂
z9	2X² + 2X + 1	C₃
z9∗2	6X² + 2X + 2	C₃
z9∗4	4X² + 4X + 2	C₃
z9∗5	5X² + 4X + 4	C₃
z9∗7	X² + X + 4	C₃
z9∗8	3X² + X + 1	C₃
z27	6X⁸ + 3X⁷ + 6X⁵ + X⁴ + 5X³ + 5X² + 3X + 3	C₉
z27∗2	4X⁸ + 5X⁷ + 4X⁶ + 5X⁵ + 5X⁴ + 3X³ + 2X² + 6X + 1	C₉
z27∗4	3X⁸ + 5X⁷ + 4X⁶ + 2X⁵ + 4X³ + 5X² + 2X + 2	C₉
z27∗5	5X⁸ + 6X⁷ + 6X⁶ + 5X⁵ + 3X⁴ + 6X³ + 2X² + 4X + 3	C₉
z27∗7	2X⁸ + 6X⁷ + 4X⁶ + 6X⁵ + 6X⁴ + 5X³ + 5X² + 4X + 3	C₉
z27∗8	2X⁸ + 6X⁷ + 3X⁶ + 6X⁵ + 6X⁴ + 3X³	C₉
z27∗10	5X⁸ + 6X⁷ + 5X⁵ + 2X⁴ + 3X³ + 3X² + 6X + 6	C₉
z27∗11	X⁸ + 3X⁷ + X⁶ + 3X⁵ + 3X⁴ + 6X³ + 4X² + 5X + 2	C₉
z27∗13	6X⁸ + 3X⁷ + X⁶ + 4X⁵ + X³ + 3X² + 4X + 4	C₉
z27∗14	3X⁸ + 5X⁷ + 5X⁶ + 3X⁵ + 6X⁴ + 5X³ + 4X² + X + 6	C₉
z27∗16	4X⁸ + 5X⁷ + X⁶ + 5X⁵ + 5X⁴ + 3X³ + 3X² + X + 6	C₉
z27∗17	4X⁸ + 5X⁷ + 6X⁶ + 5X⁵ + 5X⁴ + 6X³	C₉
z27∗19	3X⁸ + 5X⁷ + 3X⁵ + 4X⁴ + 6X³ + 6X² + 5X + 5	C₉
z27∗20	2X⁸ + 6X⁷ + 2X⁶ + 6X⁵ + 6X⁴ + 5X³ + X² + 3X + 4	C₉
z27∗22	5X⁸ + 6X⁷ + 2X⁶ + X⁵ + 2X³ + 6X² + X + 1	C₉
z27∗23	6X⁸ + 3X⁷ + 3X⁶ + 6X⁵ + 5X⁴ + 3X³ + X² + 2X + 5	C₉
z27∗25	X⁸ + 3X⁷ + 2X⁶ + 3X⁵ + 3X⁴ + 6X³ + 6X² + 2X + 5	C₉
z27∗26	X⁸ + 3X⁷ + 5X⁶ + 3X⁵ + 3X⁴ + 5X³	C₉

File created automatically by GAP on 20-Oct-2010.