Irrationalities and Conway polynomials

Irrationalities and their p-modular reductions

Common Irrationalities in Characteristic 11

C₁	=	X + 9
C₂	=	X² + 7X + 2
C₃	=	X³ + 2X + 9
C₄	=	X⁴ + 8X² + 10X + 2
C₅	=	X⁵ + 10X² + 9
C₆	=	X⁶ + 3X⁴ + 4X³ + 6X² + 7X + 2
C₁₅	=	X¹⁵ + 10X⁶ + 7X⁵ + 5X³ + 9

ξ	f	C_n
b5	7	C₁
b5∗	3	C₁
b7	4	C₁
b7∗∗	6	C₁
b13	5X + 6	C₂
b13∗	6X + 4	C₂
b15	7X + 2	C₂
b15∗∗	4X + 8	C₂
b17	3X + 10	C₂
b17∗	8X	C₂
b19	2	C₁
b19∗∗	8	C₁
b21	9X + 9	C₂
b21∗	2X + 1	C₂
b23	2X + 1	C₂
b23∗∗	9X + 9	C₂
b27	8X	C₂
b27∗∗	3X + 10	C₂
b31	5X + 6	C₂
b31∗∗	6X + 4	C₂
b35	1	C₁
b35∗∗	9	C₁
b37	6	C₁
b37∗	4	C₁
b39	7	C₁
b39∗∗	3	C₁
b45	0	C₁
b45∗	10	C₁
b95	4	C₁
b95∗∗	6	C₁
b117	4X + 8	C₂
b117∗	7X + 2	C₂
c19	6	C₁
c19∗2	1	C₁
c19∗4	3	C₁
c31	2X² + 2X + 6	C₃
c31∗3	9X² + 7X + 8	C₃
c31∗5	2X + 7	C₃
c37	0	C₁
c37∗2	3	C₁
c37∗3	7	C₁
c43	10	C₁
c43∗3	6	C₁
c43∗7	5	C₁
e31	8X⁴ + 6X³ + X² + 4X + 5	C₅
e31∗2	7X⁴ + 3X³ + 9X² + 4X + 9	C₅
e31∗3	3X⁴ + X³ + 7X² + X + 8	C₅
e31∗4	2X⁴ + X³ + 3X² + 8	C₅
e31∗8	2X⁴ + 2X² + 2X + 2	C₅
f31	2X⁵ + 2X⁴ + 3X³ + 3X² + 9X + 8	C₆
f31∗3	5X⁵ + 4X⁴ + 5X³ + 7X² + 6X	C₆
f31∗5	4X⁵ + 3X⁴ + 10X³ + 9X² + 6X + 6	C₆
f31∗7	8X⁵ + 2X⁴ + X³ + 5X² + 5X + 3	C₆
f31∗11	8X⁵ + 2X⁴ + 6X³ + 3X² + 3X	C₆
f31∗15	6X⁵ + 9X⁴ + 8X³ + 6X² + 4X + 4	C₆
i	7X + 8	C₂
i2	3	C₁
i3	9X + 4	C₂
i5	6X + 10	C₂
i6	7	C₁
i7	9	C₁
i8	6	C₁
i10	1	C₁
i14	9X + 4	C₂
i15	3X + 5	C₂
i19	5	C₁
i21	10	C₁
i26	8X + 6	C₂
i35	3	C₁
k56	5X + 4	C₂
k56∗3	6X + 7	C₂
k56∗5	6X + 2	C₂
k56∗15	5X + 9	C₂
m5	1	C₁
m5∗2	7	C₁
m5∗3	4	C₁
m5∗4	10	C₁
m20	5X + 1	C₂
m20∗3	X + 9	C₂
m20∗11	6X + 10	C₂
m20∗13	10X + 2	C₂
m'40	2X + 2	C₂
m'40∗3	6X + 3	C₂
m'40∗9	9X + 9	C₂
m'40∗11	9X + 10	C₂
m'40∗13	6X + 6	C₂
m'40∗19	2X + 1	C₂
m'40∗23	5X + 8	C₂
m'40∗33	5X + 5	C₂
r2	X + 9	C₂
r3	6	C₁
r5	4	C₁
r6	6X + 10	C₂
r7	3X + 5	C₂
r10	4X + 3	C₂
r13	10X + 2	C₂
r14	6	C₁
r15	2	C₁
r17	6X + 10	C₂
r21	7X + 8	C₂
r30	2X + 7	C₂
s51	3X³ + 6X² + 3X	C₄
s51∗5	9X³ + 3X + 10	C₄
s51∗11	5X³ + 10X² + 4X + 9	C₄
s51∗19	5X³ + 6X² + X + 4	C₄
u'63	X⁵ + X⁴ + 10X³ + 3X² + 7X + 7	C₆
u'63∗2	3X⁵ + 9X⁴ + 4X² + 6X + 6	C₆
u'63∗5	3X⁵ + 6X⁴ + 6X³ + 2X² + 7X + 2	C₆
u'63∗10	8X⁵ + X⁴ + X³ + 8X² + 8X + 7	C₆
u'63∗11	5X⁵ + 7X⁴ + 5X³ + 5X² + 9X + 3	C₆
u'63∗13	2X⁵ + 9X⁴ + 7X + 8	C₆
u''52	8X³ + 5X² + 7X + 3	C₄
u''52∗3	3X³ + 6X² + 4X + 8	C₄
u''52∗5	10X³ + 5X² + 5X + 7	C₄
u''52∗15	X³ + 6X² + 6X + 4	C₄
x37	2X + 5	C₂
x37∗2	7X + 2	C₂
x37∗3	7X	C₂
x37∗5	8X + 1	C₂
x37∗6	X	C₂
x37∗7	4X + 6	C₂
x37∗9	6X + 1	C₂
x37∗11	9X + 2	C₂
x37∗14	10X + 4	C₂
x37∗17	4X + 8	C₂
x37∗18	3X	C₂
x37∗21	5X + 3	C₂
x111	X + 9	C₂
x111∗2	2X + 9	C₂
x111∗4	X + 6	C₂
x111∗5	8X + 3	C₂
x111∗7	3X + 10	C₂
x111∗8	7X + 3	C₂
x111∗11	10X + 2	C₂
x111∗13	4X + 4	C₂
x111∗14	3X + 5	C₂
x111∗16	10X + 3	C₂
x111∗17	10X + 5	C₂
x111∗22	9X + 6	C₂
x111∗25	6X + 6	C₂
x111∗26	5X + 10	C₂
x111∗31	4X + 9	C₂
x111∗32	7X + 9	C₂
x111∗41	8X	C₂
x111∗43	8X + 6	C₂
x111∗44	10X + 10	C₂
x111∗52	X + 1	C₂
x111∗53	5X + 8	C₂
x111∗55	3X + 2	C₂
x111∗62	X + 10	C₂
x111∗64	6X + 8	C₂
x'333	6X + 4	C₂
x'333∗2	9X + 5	C₂
x'333∗4	7X + 10	C₂
x'333∗5	10X + 10	C₂
x'333∗7	9X + 9	C₂
x'333∗8	3X + 4	C₂
x'333∗10	2X	C₂
x'333∗11	5X + 6	C₂
x'333∗13	5X + 3	C₂
x'333∗14	3X + 7	C₂
x'333∗16	4X	C₂
x'333∗17	10X + 6	C₂
x'333∗19	X + 9	C₂
x'333∗20	9	C₁
x'333∗22	2X + 8	C₂
x'333∗23	5X + 1	C₂
x'333∗25	5X + 4	C₂
x'333∗26	8X + 9	C₂
x'333∗31	8X + 5	C₂
x'333∗32	10X + 2	C₂
x'333∗34	7X + 4	C₂
x'333∗35	10X + 9	C₂
x'333∗38	10X	C₂
x'333∗40	4X + 5	C₂
x'333∗41	4X + 10	C₂
x'333∗43	9X + 8	C₂
x'333∗44	4X + 5	C₂
x'333∗46	6X + 3	C₂
x'333∗49	X + 8	C₂
x'333∗50	9X + 2	C₂
x'333∗52	X + 5	C₂
x'333∗53	5X + 4	C₂
x'333∗55	X + 6	C₂
x'333∗62	7X + 5	C₂
x'333∗64	X + 7	C₂
x'333∗65	10X + 1	C₂
x'333∗67	7	C₁
x'333∗68	6X + 4	C₂
x'333∗70	6X + 9	C₂
x'333∗71	7	C₁
x'333∗73	7X + 7	C₂
x'333∗76	9X + 4	C₂
x'333∗77	2X + 1	C₂
x'333∗79	5X + 10	C₂
x'333∗82	5X + 6	C₂
x'333∗92	6X + 1	C₂
x'333∗95	5X + 5	C₂
x'333∗98	6X + 8	C₂
x'333∗100	3X + 7	C₂
x'333∗101	8X + 8	C₂
x'333∗103	8X + 7	C₂
x'333∗104	5X	C₂
x'333∗106	8X	C₂
x'333∗107	7X + 10	C₂
x'333∗109	9X + 5	C₂
x'333∗110	9X + 8	C₂
x'333∗125	2X	C₂
x'333∗128	2X + 7	C₂
x'333∗131	2X + 8	C₂
x'333∗134	3X + 6	C₂
x'333∗136	5	C₁
x'333∗137	4X + 2	C₂
x'333∗154	8X + 8	C₂
x'333∗161	3X + 10	C₂
x'333∗164	5	C₁
x'333∗184	3X + 8	C₂
x'333∗187	X + 2	C₂
x'333∗214	6X + 10	C₂
x'333∗217	2X + 5	C₂
x'333∗220	9	C₁
x'333∗247	6X + 2	C₂
x'333∗275	6X + 2	C₂
y16	8X² + 2X + 10	C₄
y16∗3	3X³ + 5X² + X + 4	C₄
y16∗5	8X³ + 6X² + 10X + 7	C₄
y16∗7	3X² + 9X + 1	C₄
y20	4X + 3	C₂
y20∗3	6X + 10	C₂
y20∗7	5X + 1	C₂
y20∗9	7X + 8	C₂
y24	9X + 4	C₂
y24∗5	8X + 6	C₂
y24∗7	3X + 5	C₂
y24∗11	2X + 7	C₂
y31	8X¹⁴ + X¹³ + 5X¹² + 8X¹¹ + 9X¹⁰ + 10X⁹ + 2X⁸ + 5X⁷ + 8X⁶ + 7X⁵ + 6X⁴ + 7X³ + 2X² + 4X + 9	C₁₅
y31∗2	5X¹⁴ + 9X¹³ + 10X¹² + 5X¹¹ + X¹⁰ + 8X⁹ + 4X⁸ + 7X⁷ + 2X⁶ + 9X⁵ + 5X⁴ + X³ + 3X² + X + 9	C₁₅
y31∗3	8X¹⁴ + 2X¹³ + 2X¹² + X¹¹ + 5X⁹ + 3X⁸ + 5X⁷ + 6X⁶ + 2X⁵ + 2X⁴ + 6X³ + 2X² + 8X + 2	C₁₅
y31∗4	6X¹⁴ + 7X¹³ + 9X¹² + 4X¹¹ + 7X¹⁰ + 2X⁸ + 8X⁷ + 8X⁶ + 2X⁵ + 3X⁴ + 8X³ + X² + 7X + 7	C₁₅
y31∗5	4X¹⁴ + 4X¹³ + 3X¹² + 6X¹¹ + 4X¹⁰ + 10X⁹ + 7X⁷ + X⁶ + 7X⁵ + 10X⁴ + 2X³ + 7X² + 9X + 7	C₁₅
y31∗6	2X¹⁴ + 10X¹³ + 3X¹² + X¹¹ + 9X¹⁰ + X⁹ + 3X⁸ + 5X⁶ + 4X⁵ + 8X⁴ + 5X³ + 4X² + 4X + 2	C₁₅
y31∗7	2X¹³ + 10X¹² + 5X¹¹ + 6X¹⁰ + 8X⁹ + 5X⁸ + 10X⁷ + X⁵ + 7X⁴ + 9X³ + 5X² + 8X + 3	C₁₅
y31∗8	2X¹² + 6X¹¹ + 6X¹⁰ + 9X⁹ + 3X⁸ + 7X⁷ + 6X⁶ + 2X⁵ + 9X⁴ + 4X³ + 4X + 10	C₁₅
y31∗9	7X¹⁴ + 8X¹³ + 2X¹² + 6X¹⁰ + 5X⁹ + X⁸ + 4X⁷ + 2X⁶ + 5X⁵ + 3X⁴ + 10X³ + 7X² + X + 8	C₁₅
y31∗10	8X¹⁴ + 3X¹³ + 6X¹² + 8X¹¹ + 9X¹⁰ + 2X⁹ + 9X⁸ + 7X⁷ + 8X⁶ + 3X⁵ + 7X⁴ + 4X³ + 3X² + 3X + 9	C₁₅
y31∗11	7X¹⁴ + 9X¹³ + 4X¹² + 3X¹¹ + 3X¹⁰ + 10X⁹ + X⁷ + X⁵ + 9X⁴ + 3X³ + 3X² + 10	C₁₅
y31∗12	7X¹⁴ + 10X¹² + 6X¹¹ + X¹⁰ + 10X⁹ + 5X⁸ + 5X⁷ + 10X⁶ + 8X⁵ + 4X⁴ + 10X³ + 4X² + 2X + 10	C₁₅
y31∗13	X¹⁴ + 5X¹³ + 9X¹² + 4X¹⁰ + 9X⁹ + 9X⁸ + 10X⁷ + 6X⁶ + 5X⁵ + 2X⁴ + X³ + 9X² + 6X + 3	C₁₅
y31∗14	5X¹⁴ + X¹³ + X¹² + 6X¹¹ + 3X¹⁰ + 3X⁹ + 4X⁸ + 2X⁷ + 7X⁶ + 7X⁵ + 8X³ + 4X²	C₁₅
y31∗15	9X¹⁴ + 5X¹³ + X¹² + 7X¹¹ + 9X¹⁰ + 9X⁹ + 5X⁸ + 10X⁷ + 8X⁶ + 3X⁵ + 2X⁴ + 10X³ + X² + 9X + 9	C₁₅
y48	7X³ + 10X² + X + 10	C₄
y48∗5	9X³ + 8X² + 4X + 6	C₄
y48∗7	4X³ + 5X² + 6	C₄
y48∗11	2X³ + 9X + 4	C₄
y48∗13	9X³ + 2X + 7	C₄
y48∗17	7X³ + 6X² + 5	C₄
y48∗19	2X³ + 3X² + 7X + 5	C₄
y48∗23	4X³ + X² + 10X + 1	C₄
y'15	3X + 9	C₂
y'15∗2	4X + 5	C₂
y'15∗7	7X + 10	C₂
y'15∗11	8X + 10	C₂
y''60	5X + 3	C₂
y''60∗7	3X + 4	C₂
y''60∗11	6X + 1	C₂
y''60∗13	8X + 7	C₂
y''60∗17	8X + 5	C₂
y''60∗19	6X + 8	C₂
y''60∗23	3X + 6	C₂
y''60∗29	5X + 10	C₂
y''120	7X	C₂
y''120∗7	4X + 7	C₂
y''120∗11	4X + 6	C₂
y''120∗13	5X	C₂
y''120∗17	4X + 10	C₂
y''120∗19	10X + 1	C₂
y''120∗23	6X + 9	C₂
y''120∗29	10X + 3	C₂
y''120∗37	6X	C₂
y''120∗47	5X + 2	C₂
y''120∗49	4X	C₂
y''120∗59	7X + 5	C₂
y''120∗67	7X + 4	C₂
y''120∗77	7X + 1	C₂
y''120∗79	X + 10	C₂
y''120∗89	X + 8	C₂
z3	10X + 7	C₂
z3∗∗	X + 3	C₂
z8	6X + 6	C₂
z8∗3	5X + 8	C₂
z8∗5	5X + 5	C₂
z8∗7	6X + 3	C₂
z12	9X + 7	C₂
z12∗5	9X + 1	C₂
z12∗7	2X + 4	C₂
z12∗11	2X + 10	C₂

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