Irrationalities and their p-modular reductions

Common Irrationalities in Characteristic 19

C1  =  X + 17
C2  =  X2 + 18X + 2
C3  =  X3 + 4X + 17
C4  =  X4 + 2X2 + 11X + 2
C6  =  X6 + 17X3 + 17X2 + 6X + 2


ξ f Cn
b5 4 C1
b5∗ 14 C1
b11 11X + 13 C2
b11∗∗ 8X + 5 C2
b15 10 C1
b15∗∗ 8 C1
b17 12 C1
b17∗ 6 C1
b27 3 C1
b27∗∗ 15 C1
b31 5 C1
b31∗∗ 13 C1
b35 10X + 4 C2
b35∗∗ 9X + 14 C2
b39 7X + 15 C2
b39∗∗ 12X + 3 C2
b59 12 C1
b59∗∗ 6 C1
b119 13X + 12 C2
b119∗∗ 6X + 6 C2
i2 6 C1
i3 15 C1
i5 12X + 13 C2
i6 13X + 3 C2
i10 16 C1
i11 3X + 8 C2
i14 10 C1
i15 2 C1
i26 17X + 1 C2
i35 X + 9 C2
k56 10X + 14 C2
k56∗3 9X + 5 C2
k56∗5 2X + 18 C2
k56∗15 17X + 1 C2
m16 14X3 + 12X2 + 17X + 4 C4
m16∗3 14X3 + 7X2 + 15X + 18 C4
m16∗9 5X3 + 7X2 + 2X + 15 C4
m16∗11 5X3 + 12X2 + 4X + 1 C4
r2 11X + 4 C2
r3 18X + 10 C2
r5 9 C1
r6 5 C1
r7 8 C1
r11 7 C1
r17 6 C1
y7 13X2 + 11X + 9 C3
y7∗2 2X2 + 5 C3
y7∗3 4X2 + 8X + 4 C3
y9 9 C1
y9∗2 3 C1
y9∗4 7 C1
y13 5X5 + 16X4 + 6X3 + 17X2 + 5X + 7 C6
y13∗2 X5 + 12X4 + 7X3 + 14X2 + 10X + 4 C6
y13∗3 7X5 + X4 + 9X3 + 10X2 + 18X + 15 C6
y13∗4 4X5 + 10X4 + 17X2 + 13X + 16 C6
y13∗5 6X5 + 6X4 + 17X3 + 17X2 + 7X + 8 C6
y13∗6 15X5 + 12X4 + 18X3 + X2 + 4X + 6 C6
y20 8 C1
y20∗3 13 C1
y20∗7 6 C1
y20∗9 11 C1
y36 12X + 13 C2
y36∗5 14X + 12 C2
y36∗7 17X + 1 C2
y36∗11 2X + 18 C2
y36∗13 5X + 7 C2
y36∗17 7X + 6 C2
y40 4X + 17 C2
y40∗3 9X + 5 C2
y40∗7 3X + 8 C2
y40∗9 13X + 3 C2
y40∗11 6X + 16 C2
y40∗13 16X + 11 C2
y40∗17 10X + 14 C2
y40∗19 15X + 2 C2
y'189 5X2 + 18X + 1 C3
y'189∗2 12X2 + 3X + 16 C3
y'189∗4 9X2 + 7X C3
y'189∗5 13X2 + 8X + 11 C3
y'189∗8 2X2 + 12X + 9 C3
y'189∗10 7X2 + 16X C3
y'189∗11 14X2 + X + 15 C3
y'189∗13 11X2 + 13X + 6 C3
y'189∗16 5X2 + 11X C3
y'189∗17 13X2 + 5X + 18 C3
y'189∗19 7X2 + 4X C3
y'189∗20 12X2 + 15X + 16 C3
y'189∗22 X2 + 15X + 4 C3
y'189∗23 10X2 + 12X + 7 C3
y'189∗25 17X2 + 9X C3
y'189∗26 14X2 + 13X + 6 C3
y'189∗29 8X2 + 10X + 17 C3
y'189∗32 18X2 + 4X + 3 C3
y'189∗34 6X2 + 14X + 5 C3
y'189∗37 X2 + 6X C3
y'189∗40 9X2 + 16X C3
y'189∗41 10X2 + 3X + 7 C3
y'189∗43 4X2 + 3X + 16 C3
y'189∗44 2X2 + 10X + 9 C3
y'189∗46 11X2 + 17X C3
y'189∗47 18X2 + 14X + 5 C3
y'189∗50 13X2 + 2X + 11 C3
y'189∗53 15X2 + 16X + 12 C3
y'189∗58 4X2 + 5X C3
y'189∗61 17X2 + 7X C3
y'189∗64 16X2 + 12X + 7 C3
y'189∗65 8X2 + 2X + 17 C3
y'189∗67 6X2 + 11X C3
y'189∗68 15X2 + 18X + 1 C3
y'189∗71 14X2 + 8X + 6 C3
y'189∗74 3X2 + 7X + 10 C3
y'189∗79 16X2 + X C3
y'189∗82 11X2 + 9X C3
y'189∗85 7X2 + 10X + 9 C3
y'189∗88 5X2 + 6X C3
y'189∗89 3X2 + 15X + 4 C3
y'189∗92 18X2 + 13X + 5 C3
y'189∗95 12X2 + 9X + 2 C3
y'189∗103 6X2 + 17X C3
y'189∗106 9X2 + 2X + 17 C3
y'189∗109 X2 + 5X C3
y'189∗113 15X2 + 14X + 1 C3
y'189∗116 10X2 + 17X + 8 C3
y'189∗127 17X2 + 8X + 11 C3
y'189∗130 4X2 + X C3
y'189∗134 3X2 + 18X + 4 C3
y'189∗137 2X2 + 11X + 13 C3
y'189∗151 16X2 + 4X C3
y'189∗158 8X2 + 6X + 14 C3
y''21 14X2 + 16 C3
y''21∗2 6X2 + 12X + 6 C3
y''21∗4 15X2 + X + 6 C3
y''21∗8 3X2 + 17 C3
y''21∗11 10X2 + 7X + 4 C3
y''21∗16 9X2 + 18X + 9 C3
y''63 17X2 + 15X + 17 C3
y''63∗2 8X2 + 17X + 7 C3
y''63∗4 12X2 + 11 C3
y''63∗5 18X2 + 5X + 11 C3
y''63∗8 11X2 + 3X + 11 C3
y''63∗10 18X2 + 7 C3
y''63∗11 10X2 + 6 C3
y''63∗13 5X2 + 10X + 5 C3
y''63∗16 14X2 + 6X + 17 C3
y''63∗17 15X2 + 9 C3
y''63∗19 3X2 + 4X + 5 C3
y''63∗20 X2 + 2X + 1 C3
y''63∗25 8X2 + 1 C3
y''63∗26 12X2 + 16X + 1 C3
y''63∗32 13X2 + 4 C3
y''63∗34 16X2 + 13X + 16 C3
y''63∗40 2X2 + 9X + 16 C3
y''63∗41 7X2 + 14X + 7 C3
z3 7 C1
z3∗∗ 11 C1
z9 4 C1
z9∗2 16 C1
z9∗4 9 C1
z9∗5 17 C1
z9∗7 6 C1
z9∗8 5 C1
z27 10X2 + 11X + 14 C3
z27∗2 X2 + 8X + 9 C3
z27∗4 2X2 + 6X + 18 C3
z27∗5 4X2 + 13X + 17 C3
z27∗7 8X2 + 5X + 15 C3
z27∗8 16X2 + 14X + 11 C3
z27∗10 13X2 + X + 3 C3
z27∗11 7X2 + 18X + 6 C3
z27∗13 14X2 + 4X + 12 C3
z27∗14 9X2 + 15X + 5 C3
z27∗16 18X2 + 16X + 10 C3
z27∗17 17X2 + 3X + 1 C3
z27∗19 15X2 + 7X + 2 C3
z27∗20 11X2 + 12X + 4 C3
z27∗22 3X2 + 9X + 8 C3
z27∗23 6X2 + 10X + 16 C3
z27∗25 12X2 + 17X + 13 C3
z27∗26 5X2 + 2X + 7 C3



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