Irrationalities and Conway polynomials

Irrationalities and their p-modular reductions

Common Irrationalities in Characteristic 17

C₁	=	X + 14
C₂	=	X² + 16X + 3
C₃	=	X³ + X + 14
C₄	=	X⁴ + 7X² + 10X + 3
C₆	=	X⁶ + 2X⁴ + 10X² + 3X + 3

ξ	f	C_n
b5	10X + 3	C₂
b5∗	7X + 13	C₂
b7	8X + 4	C₂
b7∗∗	9X + 12	C₂
b11	X + 16	C₂
b11∗∗	16X	C₂
b13	12	C₁
b13∗	4	C₁
b15	11	C₁
b15∗∗	5	C₁
b19	3	C₁
b19∗∗	13	C₁
b21	9	C₁
b21∗	7	C₁
b27	2X + 7	C₂
b27∗∗	15X + 9	C₂
b29	6X + 5	C₂
b29∗	11X + 11	C₂
b31	3X + 15	C₂
b31∗∗	14X + 1	C₂
b33	6	C₁
b33∗	10	C₁
b35	10	C₁
b35∗∗	6	C₁
b39	11X + 11	C₂
b39∗∗	6X + 5	C₂
b45	13X + 10	C₂
b45∗	4X + 6	C₂
b47	9	C₁
b47∗∗	7	C₁
b59	15	C₁
b59∗∗	1	C₁
b71	5X + 14	C₂
b71∗∗	12X + 2	C₂
b87	3	C₁
b87∗∗	13	C₁
b117	3	C₁
b117∗	13	C₁
c31	10X² + 6X + 12	C₃
c31∗3	15X² + 6X + 4	C₃
c31∗5	9X² + 5X	C₃
f31	X⁵ + 14X⁴ + 9X³ + 10X² + 8X + 10	C₆
f31∗3	4X⁵ + 14X⁴ + 4X³ + 8X² + 16X + 2	C₆
f31∗5	3X⁵ + 2X⁴ + 5X³ + 1	C₆
f31∗7	5X⁵ + X⁴ + 14X³ + 3X² + 9X + 14	C₆
f31∗11	9X⁵ + 9X⁴ + 10X³ + 8X² + 3X + 2	C₆
f31∗15	12X⁵ + 11X⁴ + 9X³ + 5X² + 15X + 4	C₆
i	13	C₁
i2	7	C₁
i3	7X + 5	C₂
i5	5X + 6	C₂
i7	16X + 9	C₂
i11	2X + 16	C₂
i14	6X + 14	C₂
i15	6	C₁
i19	7	C₁
i26	5	C₁
i35	4	C₁
r2	11	C₁
r3	11X + 3	C₂
r5	3X + 7	C₂
r6	2X + 16	C₂
r7	13X + 2	C₂
r10	16X + 9	C₂
r13	8	C₁
r21	2	C₁
v33	14X + 5	C₂
v33∗2	3X + 2	C₂
v33∗5	2X + 13	C₂
v33∗7	15X + 15	C₂
y9	14	C₁
y9∗2	7	C₁
y9∗4	13	C₁
y15	8X³ + 9X² + 14X + 11	C₄
y15∗2	4X³ + X² + 14X + 4	C₄
y15∗4	14X³ + X² + 10X + 11	C₄
y15∗7	8X³ + 6X² + 13X + 9	C₄
y16	9	C₁
y16∗3	5	C₁
y16∗5	12	C₁
y16∗7	8	C₁
y32	9X + 4	C₂
y32∗3	4X + 15	C₂
y32∗5	10X + 12	C₂
y32∗7	X + 8	C₂
y32∗9	16X + 9	C₂
y32∗11	7X + 5	C₂
y32∗13	13X + 2	C₂
y32∗15	8X + 13	C₂
y36	15X + 1	C₂
y36∗5	12X + 11	C₂
y36∗7	3X + 7	C₂
y36∗11	14X + 10	C₂
y36∗13	5X + 6	C₂
y36∗17	2X + 16	C₂
z3	12X + 2	C₂
z3∗∗	5X + 14	C₂

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