Irrationalities and Conway polynomials

Irrationalities and their p-modular reductions

Common Irrationalities in Characteristic 13

C₁	=	X + 11
C₂	=	X² + 12X + 2
C₃	=	X³ + 2X + 11
C₄	=	X⁴ + 3X² + 12X + 2

ξ	f	C_n
b5	9X + 8	C₂
b5∗	4X + 4	C₂
b7	12X	C₂
b7∗∗	X + 12	C₂
b11	3X + 11	C₂
b11∗∗	10X + 1	C₂
b15	11X + 7	C₂
b15∗∗	2X + 5	C₂
b17	5	C₁
b17∗	7	C₁
b19	5X + 10	C₂
b19∗∗	8X + 2	C₂
b21	7X + 9	C₂
b21∗	6X + 3	C₂
b23	8	C₁
b23∗∗	4	C₁
b27	10	C₁
b27∗∗	2	C₁
b29	4	C₁
b29∗	8	C₁
b31	7X + 9	C₂
b31∗∗	6X + 3	C₂
b33	5X + 10	C₂
b33∗	8X + 2	C₂
b35	5	C₁
b35∗∗	7	C₁
b45	X + 12	C₂
b45∗	12X	C₂
b87	5	C₁
b87∗∗	7	C₁
b119	2X + 5	C₂
b119∗∗	11X + 7	C₂
c19	X² + 12X + 1	C₃
c19∗2	12X² + 9X + 7	C₃
c19∗4	5X + 4	C₃
i	8	C₁
i2	9X + 2	C₂
i3	7	C₁
i5	X + 6	C₂
i6	3X + 5	C₂
i7	11X + 1	C₂
i8	5X + 4	C₂
i11	6X + 10	C₂
i14	8	C₁
i15	9X + 2	C₂
i19	10X + 8	C₂
i21	8X + 9	C₂
i35	11	C₁
k56	10X + 2	C₂
k56∗3	3X + 11	C₂
k56∗5	3X + 12	C₂
k56∗15	10X + 1	C₂
m20	7X + 12	C₂
m20∗3	7X + 7	C₂
m20∗11	6X + 1	C₂
m20∗13	6X + 6	C₂
r2	6X + 10	C₂
r3	9	C₁
r5	5X + 4	C₂
r6	2X + 12	C₂
r7	3X + 5	C₂
r10	6	C₁
r17	11	C₁
r21	X + 6	C₂
r30	2	C₁
u56	11X + 5	C₂
u56∗5	2X + 3	C₂
u56∗11	11X + 10	C₂
u56∗29	2X + 8	C₂
w40	11X + 4	C₂
w40∗7	2X + 9	C₂
w40∗11	11X + 11	C₂
w40∗13	2X + 2	C₂
w80	3X + 8	C₂
w80∗7	9X + 7	C₂
w80∗11	4X + 3	C₂
w80∗13	10X + 11	C₂
w80∗17	9X + 10	C₂
w80∗23	4X + 6	C₂
w80∗41	10X + 5	C₂
w80∗53	3X + 2	C₂
y7	10	C₁
y7∗2	7	C₁
y7∗3	8	C₁
y9	12X² + 2X + 3	C₃
y9∗2	9X² + 9X + 12	C₃
y9∗4	5X² + 2X + 11	C₃
y16	12X³ + 4X² + 5X + 10	C₄
y16∗3	2X³ + X² + X	C₄
y16∗5	11X³ + 12X² + 12X	C₄
y16∗7	X³ + 9X² + 8X + 3	C₄
y24	4X + 11	C₂
y24∗5	11X + 1	C₂
y24∗7	2X + 12	C₂
y24∗11	9X + 2	C₂
y28	10X + 8	C₂
y28∗3	X + 6	C₂
y28∗5	8X + 9	C₂
y28∗9	5X + 4	C₂
y28∗11	12X + 7	C₂
y28∗13	3X + 5	C₂
y48	3X³ + 12X² + 10X + 6	C₄
y48∗5	2X³ + 7X + 5	C₄
y48∗7	X³ + 11X² + 9X + 6	C₄
y48∗11	10X³ + 4X² + 11X + 5	C₄
y48∗13	3X³ + 9X² + 2X + 8	C₄
y48∗17	12X³ + 2X² + 4X + 7	C₄
y48∗19	11X³ + 6X + 8	C₄
y48∗23	10X³ + X² + 3X + 7	C₄
y56	4X + 9	C₂
y56∗3	2X + 9	C₂
y56∗5	5X + 10	C₂
y56∗9	8X + 2	C₂
y56∗11	2X + 2	C₂
y56∗13	9X	C₂
y56∗15	4X	C₂
y56∗17	11X + 11	C₂
y56∗19	5X + 11	C₂
y56∗23	8X + 3	C₂
y56∗25	11X + 4	C₂
y56∗27	9X + 4	C₂
y'40	7X + 10	C₂
y'40∗3	4X + 7	C₂
y'40∗7	9X + 6	C₂
y'40∗11	4X + 2	C₂
y'40∗13	6X + 4	C₂
y'40∗17	7X + 9	C₂
y'40∗21	6X + 3	C₂
y'40∗31	9X + 11	C₂
y'80	11X + 2	C₂
y'80∗3	5X + 6	C₂
y'80∗7	12X + 4	C₂
y'80∗11	X + 3	C₂
y'80∗13	2X	C₂
y'80∗17	10X	C₂
y'80∗21	10X + 3	C₂
y'80∗23	X + 9	C₂
y'80∗31	8X + 11	C₂
y'80∗33	3X	C₂
y'80∗41	2X + 11	C₂
y'80∗43	8X + 7	C₂
y'80∗51	12X + 10	C₂
y'80∗53	11X	C₂
y'80∗61	3X + 10	C₂
y'80∗71	5X + 2	C₂
z3	3	C₁
z3∗∗	9	C₁
z5	8X³ + 2X² + 2X	C₄
z5∗2	2X³ + 12X² + X	C₄
z5∗3	2X³ + 2X² + 9X + 11	C₄
z5∗4	X³ + 10X² + X + 1	C₄
z8	X + 6	C₂
z8∗3	8X + 9	C₂
z8∗5	12X + 7	C₂
z8∗7	5X + 4	C₂
z9	2X² + 7X + 7	C₃
z9∗2	4X² + 11X + 1	C₃
z9∗4	6X² + 8X + 8	C₃
z9∗5	12X² + 7X + 3	C₃
z9∗7	5X² + 11X + 11	C₃
z9∗8	10X² + 8X + 9	C₃

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