Irrationalities and their p-modular reductions

Common Irrationalities in Characteristic 37

C1  =  X + 35
C2  =  X2 + 33X + 2
C3  =  X3 + 6X + 35
C4  =  X4 + 6X2 + 24X + 2
C6  =  X6 + 35X3 + 4X2 + 30X + 2


ξ f Cn
b5 12X + 31 C2
b5∗ 25X + 5 C2
b7 28 C1
b7∗∗ 8 C1
b11 13 C1
b11∗∗ 23 C1
b21 6 C1
b21∗ 30 C1
b27 5 C1
b27∗∗ 31 C1
b33 24 C1
b33∗ 12 C1
c19 29 C1
c19∗2 14 C1
c19∗4 30 C1
c31 29X2 + 20X + 17 C3
c31∗3 24X2 + 22X + 34 C3
c31∗5 21X2 + 32X + 22 C3
c43 9X2 + 23X + 11 C3
c43∗3 14X2 + 10X + 31 C3
c43∗7 14X2 + 4X + 31 C3
c67 16X2 + 36X + 2 C3
c67∗2 3X2 + 36X + 24 C3
c67∗4 18X2 + 2X + 10 C3
e31 19 C1
e31∗2 4 C1
e31∗3 17 C1
e31∗4 27 C1
e31∗8 6 C1
i 31 C1
i3 16 C1
i11 27 C1
m20 2X + 36 C2
m20∗3 2X + 30 C2
m20∗11 35X + 1 C2
m20∗13 35X + 7 C2
m'40 19X3 + 28X2 + X + 19 C4
m'40∗3 17X3 + 2X2 + X + 16 C4
m'40∗9 18X3 + 9X2 + 36X + 18 C4
m'40∗11 34X3 + 17X2 + 31X + 34 C4
m'40∗13 9X3 + 25X2 + 31X + 15 C4
m'40∗19 3X3 + 20X2 + 6X + 3 C4
m'40∗23 20X3 + 35X2 + 36X + 21 C4
m'40∗33 28X3 + 12X2 + 6X + 22 C4
r3 22 C1
r5 24X + 26 C2
r6 15X + 7 C2
r10 26 C1
y7 3X2 + 15X + 24 C3
y7∗2 19X2 + 13X + 14 C3
y7∗3 15X2 + 9X + 35 C3
y9 23 C1
y9∗2 9 C1
y9∗4 5 C1
y13 X5 + 4X4 + 32X3 + 26X2 + 20X + 22 C6
y13∗2 5X5 + 7X4 + 28X3 + 9X2 + 35X + 23 C6
y13∗3 11X5 + 36X4 + 17X3 + 4X2 + 8X + 27 C6
y13∗4 X5 + 35X4 + 2X3 + 23X2 + 26X + 36 C6
y13∗5 25X5 + 26X4 + X3 + 13X2 + 13X + 21 C6
y13∗6 31X5 + 3X4 + 31X3 + 36X2 + 9X + 18 C6
z3 26 C1
z3∗∗ 10 C1
z9 16 C1
z9∗2 34 C1
z9∗4 9 C1
z9∗5 33 C1
z9∗7 12 C1
z9∗8 7 C1
z12 8 C1
z12∗5 23 C1
z12∗7 29 C1
z12∗11 14 C1




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