Irrationalities and their p-modular reductions

Common Irrationalities in Characteristic 73

C1  =  X + 68
C2  =  X2 + 70X + 5
C3  =  X3 + 2X + 68
C4  =  X4 + 16X2 + 56X + 5
C6  =  X6 + 45X3 + 23X2 + 48X + 5


ξ f Cn
b5 51X + 69 C2
b5∗ 22X + 3 C2
b7 40X + 49 C2
b7∗∗ 33X + 23 C2
i 27 C1
m5 17X3 + 26X2 + 3X + 46 C4
m5∗2 56X3 + 18X2 + 4X + 14 C4
m5∗3 17X3 + 55X2 + 69X + 59 C4
m5∗4 56X3 + 47X2 + 70X + 27 C4
m16 70X + 41 C2
m16∗3 47X + 39 C2
m16∗9 3X + 32 C2
m16∗11 26X + 34 C2
r2 32 C1
y7 49X2 + 66X + 65 C3
y7∗2 11X2 + 57X + 63 C3
y7∗3 13X2 + 23X + 17 C3
y9 39 C1
y9∗2 59 C1
y9∗4 48 C1
y'24 9 C1
y'24∗7 24 C1
y'24∗13 64 C1
y'24∗19 49 C1
y'63 17X5 + 17X4 + 30X3 + 29X2 + 54X + 26 C6
y'63∗2 26X5 + 14X4 + 59X3 + 11X2 + 72X + 45 C6
y'63∗4 9X5 + 51X4 + 28X3 + 41X2 + 33X + 71 C6
y'63∗5 18X5 + 6X4 + 71X3 + 17X2 + 41X + 15 C6
y'63∗10 62X5 + 18X4 + 37X3 + 19X2 + 33X + 40 C6
y'63∗11 X5 + 30X4 + 68X3 + 37X2 + 28X + 16 C6
y'63∗13 51X5 + 31X4 + 7X3 + 3X2 + 6X + 35 C6
y'63∗19 53X5 + 42X4 + 59X3 + 46X2 + 68X + 32 C6
y'63∗20 30X5 + 44X4 + 17X3 + 49X2 + 25X + 12 C6
y'63∗22 65X5 + 65X4 + 46X3 + 25X2 + 39X + 35 C6
y'63∗23 15X5 + 53X4 + 20X3 + 26X2 + 64X + 40 C6
y'63∗29 64X5 + 64X4 + 70X3 + 19X2 + 53X + 12 C6
y'63∗31 61X5 + 13X4 + 47X3 + 34X2 + 36X + 37 C6
y'63∗37 32X5 + 6X4 + 67X3 + 36X2 + 10X + 61 C6
y'63∗38 23X5 + 42X4 + 62X3 + 20X2 + 4X + 69 C6
y'63∗46 63X5 + 65X4 + 50X3 + 68X2 + 12X + 59 C6
y'63∗47 2X5 + 25X4 + 16X3 + 10X2 + 37X + 26 C6
y'63∗55 65X5 + 71X4 + 49X3 + 21X2 + 42X + 26 C6
y''40 71X3 + 27X2 + 51X + 67 C4
y''40∗3 71X3 + X2 + 17X + 62 C4
y''40∗7 35X3 + 28X2 + 6X + 23 C4
y''40∗9 38X3 + 19X2 + 33X + 4 C4
y''40∗11 2X3 + 46X2 + 22X + 6 C4
y''40∗19 35X3 + 54X2 + 40X + 69 C4
y''40∗23 2X3 + 72X2 + 56X + 11 C4
y''40∗27 38X3 + 45X2 + 67X + 50 C4
y''80 X3 + 10X2 + 67X + 69 C4
y''80∗3 6X3 + 65X2 + 52X + 5 C4
y''80∗7 34X3 + 5X2 + 68X + 61 C4
y''80∗9 19X3 + 33X2 + 36X + 20 C4
y''80∗11 31X3 + 18X2 + 33X + 22 C4
y''80∗13 67X3 + 8X2 + 21X + 68 C4
y''80∗19 5X3 + X2 + 21X + 36 C4
y''80∗21 42X3 + 55X2 + 40X + 51 C4
y''80∗23 21X3 + 45X2 + 36X + 54 C4
y''80∗27 32X3 + 9X2 + 64X + 66 C4
y''80∗29 68X3 + 72X2 + 52X + 37 C4
y''80∗31 72X3 + 63X2 + 6X + 4 C4
y''80∗37 41X3 + 64X2 + 9X + 7 C4
y''80∗39 54X3 + 40X2 + 37X + 53 C4
y''80∗47 39X3 + 68X2 + 5X + 12 C4
y''80∗63 52X3 + 28X2 + 37X + 19 C4
z5 41X3 + 16X2 + 53X + 43 C4
z5∗2 32X3 + 6X2 + 60X + 23 C4
z5∗3 49X3 + 61X2 + 56X + 9 C4
z5∗4 24X3 + 63X2 + 50X + 70 C4
z7 25X5 + 64X4 + 9X3 + 19X2 + 58X + 18 C6
z7∗2 15X5 + 12X4 + 71X3 + 44X2 + 55X + 21 C6
z7∗3 12X5 + 3X4 + 36X3 + 5X2 + 10X + 34 C6
z7∗4 11X5 + 11X4 + 28X3 + 66X2 + 65X + 34 C6
z7∗5 53X5 + 46X4 + 54X3 + 8X2 + 60X + 13 C6
z7∗6 30X5 + 10X4 + 21X3 + 4X2 + 44X + 25 C6




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