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 Cn
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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