LMFDB - $p$-adic family 2.1.8.31a

Defining polynomial

$x^{8} + 16 b_{31} x^{7} + 8 b_{22} x^{6} + 16 b_{29} x^{5} + 4 b_{12} x^{4} + 16 b_{27} x^{3} + 8 b_{18} x^{2} + 16 b_{25} x + 8 c_{16} + 16 c_{24} + 32 c_{32} + 2$

Invariants

Residue field characteristic:	$2$
Degree:	$8$
Base field:	$\Q_{2}$
Ramification index $e$:	$8$
Residue field degree $f$:	$1$
Discriminant exponent $c$:	$31$
Artin slopes:	$[3,4,5]$
Swan slopes:	$[2,3,4]$
Means:	$\langle1,2,3\rangle$
Rams:	$(2,4,8)$
Field count:	$296$ (complete)
Ambiguity:	$8$
Mass:	$128$
Absolute Mass:	$128$

Diagrams

Varying

Indices of inseparability:	$[24,16,8,0]$
Associated inertia:	$[1,1,1]$
Jump Set:	$[1,3,7,15]$

Galois groups and Hidden Artin slopes

Select desired size of Galois group.

		Galois groups of order 8
		$C_8$ (as 8T1)
hidden slopes	$[\ ]$	16

		Galois groups of order 16
		$D_8$ (as 8T6)	$\OD_{16}$ (as 8T7)	$\SD_{16}$ (as 8T8)	Total
hidden slopes	$[2]$	8	16	8	32

$[\ ]^{2}$	4	8	4	16

Total	12	24	12	48

		Galois groups of order 32
		$D_8:C_2$ (as 8T15)	$\OD_{16}:C_2$ (as 8T16)	$C_4\wr C_2$ (as 8T17)	Total
hidden slopes	$[2,\frac{7}{2}]$		16	32	48

$[2]^{2}$	24			24

Total	24	16	32	72

		Galois groups of order 64
		$D_4:D_4$ (as 8T26)	$C_2\wr C_4$ (as 8T27)	$C_2\wr C_4$ (as 8T28)	Total
hidden slopes	$[2,\frac{7}{2},\frac{17}{4}]$		32	32	64

$[2,\frac{7}{2}]^{2}$	32			32

Total	32	32	32	96

		Galois groups of order 128
		$C_2\wr D_4$ (as 8T35)
hidden slopes	$[2,\frac{7}{2},\frac{17}{4}]^{2}$	64

Fields

Galois group	Galois Artin	Indices

Assoc. Inertia	Jump Set	Fields per packet

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Showing 1-50 of 296

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Label	Packet size	Polynomial	Galois group	Galois degree	$\#\Aut(K/\Q_p)$	Artin slope content	Swan slope content	Hidden Artin slopes	Hidden Swan slopes	Ind. of Insep.	Assoc. Inertia	Resid. Poly	Jump Set
2.1.8.31a1.1	8	$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 34$	$D_{8}$ (as 8T6)	$16$	$2$	$[2, 3, 4, 5]$	$[1,2,3,4]$	$[2]$	$[1]$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.2	24	$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 2$	$Z_8 : Z_8^\times$ (as 8T15)	$32$	$2$	$[2, 3, 4, 5]^{2}$	$[1,2,3,4]^{2}$	$[2]^{2}$	$[1]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.3	24	$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 34$	$Z_8 : Z_8^\times$ (as 8T15)	$32$	$2$	$[2, 3, 4, 5]^{2}$	$[1,2,3,4]^{2}$	$[2]^{2}$	$[1]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.4	32	$x^{8} + 16 x^{7} + 8 x^{6} + 34$	$C_4\wr C_2$ (as 8T17)	$32$	$4$	$[2, 3, \frac{7}{2}, 4, 5]$	$[1,2,\frac{5}{2},3,4]$	$[2,\frac{7}{2}]$	$[1,\frac{5}{2}]$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.5	32	$x^{8} + 8 x^{6} + 34$	$C_4\wr C_2$ (as 8T17)	$32$	$4$	$[2, 3, \frac{7}{2}, 4, 5]$	$[1,2,\frac{5}{2},3,4]$	$[2,\frac{7}{2}]$	$[1,\frac{5}{2}]$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.6	64	$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x + 34$	$C_2 \wr C_2\wr C_2$ (as 8T35)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{13}{4}]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.7	64	$x^{8} + 8 x^{6} + 16 x^{5} + 16 x + 34$	$C_2 \wr C_2\wr C_2$ (as 8T35)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{13}{4}]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.8	64	$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 16 x + 2$	$C_2 \wr C_2\wr C_2$ (as 8T35)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{13}{4}]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.9	64	$x^{8} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 16 x + 2$	$C_2 \wr C_2\wr C_2$ (as 8T35)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{13}{4}]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.10	64	$x^{8} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 16 x + 34$	$C_2 \wr C_2\wr C_2$ (as 8T35)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{13}{4}]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.11	64	$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 16 x + 34$	$C_2 \wr C_2\wr C_2$ (as 8T35)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{13}{4}]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.12	8	$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 50$	$D_{8}$ (as 8T6)	$16$	$2$	$[2, 3, 4, 5]$	$[1,2,3,4]$	$[2]$	$[1]$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.13	24	$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 18$	$Z_8 : Z_8^\times$ (as 8T15)	$32$	$2$	$[2, 3, 4, 5]^{2}$	$[1,2,3,4]^{2}$	$[2]^{2}$	$[1]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.14	24	$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 50$	$Z_8 : Z_8^\times$ (as 8T15)	$32$	$2$	$[2, 3, 4, 5]^{2}$	$[1,2,3,4]^{2}$	$[2]^{2}$	$[1]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.15	32	$x^{8} + 16 x^{7} + 8 x^{6} + 50$	$C_4\wr C_2$ (as 8T17)	$32$	$4$	$[2, 3, \frac{7}{2}, 4, 5]$	$[1,2,\frac{5}{2},3,4]$	$[2,\frac{7}{2}]$	$[1,\frac{5}{2}]$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.16	32	$x^{8} + 8 x^{6} + 50$	$C_4\wr C_2$ (as 8T17)	$32$	$4$	$[2, 3, \frac{7}{2}, 4, 5]$	$[1,2,\frac{5}{2},3,4]$	$[2,\frac{7}{2}]$	$[1,\frac{5}{2}]$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.17	64	$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x + 50$	$C_2 \wr C_2\wr C_2$ (as 8T35)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{13}{4}]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.18	64	$x^{8} + 8 x^{6} + 16 x^{5} + 16 x + 50$	$C_2 \wr C_2\wr C_2$ (as 8T35)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{13}{4}]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.19	64	$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 16 x + 18$	$C_2 \wr C_2\wr C_2$ (as 8T35)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{13}{4}]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.20	64	$x^{8} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 16 x + 18$	$C_2 \wr C_2\wr C_2$ (as 8T35)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{13}{4}]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.21	64	$x^{8} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 16 x + 50$	$C_2 \wr C_2\wr C_2$ (as 8T35)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{13}{4}]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.22	64	$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 16 x + 50$	$C_2 \wr C_2\wr C_2$ (as 8T35)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{13}{4}]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.23	32	$x^{8} + 8 x^{6} + 2$	$C_4\wr C_2$ (as 8T17)	$32$	$4$	$[2, 3, \frac{7}{2}, 4, 5]$	$[1,2,\frac{5}{2},3,4]$	$[2,\frac{7}{2}]$	$[1,\frac{5}{2}]$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.24	32	$x^{8} + 16 x^{7} + 8 x^{6} + 2$	$C_4\wr C_2$ (as 8T17)	$32$	$4$	$[2, 3, \frac{7}{2}, 4, 5]$	$[1,2,\frac{5}{2},3,4]$	$[2,\frac{7}{2}]$	$[1,\frac{5}{2}]$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.25	32	$x^{8} + 8 x^{6} + 16 x^{5} + 2$	$C_4\wr C_2$ (as 8T17)	$32$	$4$	$[2, 3, \frac{7}{2}, 4, 5]$	$[1,2,\frac{5}{2},3,4]$	$[2,\frac{7}{2}]$	$[1,\frac{5}{2}]$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.26	32	$x^{8} + 8 x^{6} + 16 x^{5} + 34$	$C_4\wr C_2$ (as 8T17)	$32$	$4$	$[2, 3, \frac{7}{2}, 4, 5]$	$[1,2,\frac{5}{2},3,4]$	$[2,\frac{7}{2}]$	$[1,\frac{5}{2}]$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.27	32	$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 2$	$C_4\wr C_2$ (as 8T17)	$32$	$4$	$[2, 3, \frac{7}{2}, 4, 5]$	$[1,2,\frac{5}{2},3,4]$	$[2,\frac{7}{2}]$	$[1,\frac{5}{2}]$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.28	32	$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 34$	$C_4\wr C_2$ (as 8T17)	$32$	$4$	$[2, 3, \frac{7}{2}, 4, 5]$	$[1,2,\frac{5}{2},3,4]$	$[2,\frac{7}{2}]$	$[1,\frac{5}{2}]$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.29	8	$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 2$	$D_{8}$ (as 8T6)	$16$	$2$	$[2, 3, 4, 5]$	$[1,2,3,4]$	$[2]$	$[1]$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.30	64	$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x + 2$	$C_2 \wr C_2\wr C_2$ (as 8T35)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{13}{4}]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.31	64	$x^{8} + 8 x^{6} + 16 x^{5} + 16 x + 2$	$C_2 \wr C_2\wr C_2$ (as 8T35)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{13}{4}]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.32	32	$x^{8} + 8 x^{6} + 18$	$C_4\wr C_2$ (as 8T17)	$32$	$4$	$[2, 3, \frac{7}{2}, 4, 5]$	$[1,2,\frac{5}{2},3,4]$	$[2,\frac{7}{2}]$	$[1,\frac{5}{2}]$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.33	32	$x^{8} + 16 x^{7} + 8 x^{6} + 18$	$C_4\wr C_2$ (as 8T17)	$32$	$4$	$[2, 3, \frac{7}{2}, 4, 5]$	$[1,2,\frac{5}{2},3,4]$	$[2,\frac{7}{2}]$	$[1,\frac{5}{2}]$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.34	32	$x^{8} + 8 x^{6} + 16 x^{5} + 18$	$C_4\wr C_2$ (as 8T17)	$32$	$4$	$[2, 3, \frac{7}{2}, 4, 5]$	$[1,2,\frac{5}{2},3,4]$	$[2,\frac{7}{2}]$	$[1,\frac{5}{2}]$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.35	32	$x^{8} + 8 x^{6} + 16 x^{5} + 50$	$C_4\wr C_2$ (as 8T17)	$32$	$4$	$[2, 3, \frac{7}{2}, 4, 5]$	$[1,2,\frac{5}{2},3,4]$	$[2,\frac{7}{2}]$	$[1,\frac{5}{2}]$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.36	32	$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 18$	$C_4\wr C_2$ (as 8T17)	$32$	$4$	$[2, 3, \frac{7}{2}, 4, 5]$	$[1,2,\frac{5}{2},3,4]$	$[2,\frac{7}{2}]$	$[1,\frac{5}{2}]$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.37	32	$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 50$	$C_4\wr C_2$ (as 8T17)	$32$	$4$	$[2, 3, \frac{7}{2}, 4, 5]$	$[1,2,\frac{5}{2},3,4]$	$[2,\frac{7}{2}]$	$[1,\frac{5}{2}]$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.38	8	$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 18$	$D_{8}$ (as 8T6)	$16$	$2$	$[2, 3, 4, 5]$	$[1,2,3,4]$	$[2]$	$[1]$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.39	64	$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x + 18$	$C_2 \wr C_2\wr C_2$ (as 8T35)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{13}{4}]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.40	64	$x^{8} + 8 x^{6} + 16 x^{5} + 16 x + 18$	$C_2 \wr C_2\wr C_2$ (as 8T35)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{13}{4}]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.41	64	$x^{8} + 16 x^{5} + 16 x^{3} + 8 x^{2} + 18$	$C_2 \wr C_2\wr C_2$ (as 8T35)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{13}{4}]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.42	64	$x^{8} + 16 x^{5} + 16 x^{3} + 8 x^{2} + 50$	$C_2 \wr C_2\wr C_2$ (as 8T35)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{13}{4}]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.43	64	$x^{8} + 16 x^{7} + 16 x^{5} + 16 x^{3} + 8 x^{2} + 18$	$C_2 \wr C_2\wr C_2$ (as 8T35)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{13}{4}]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.44	64	$x^{8} + 16 x^{7} + 16 x^{5} + 16 x^{3} + 8 x^{2} + 50$	$C_2 \wr C_2\wr C_2$ (as 8T35)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{13}{4}]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.45	64	$x^{8} + 16 x^{7} + 16 x^{5} + 8 x^{2} + 18$	$C_2 \wr C_2\wr C_2$ (as 8T35)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{13}{4}]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.46	64	$x^{8} + 16 x^{5} + 8 x^{2} + 18$	$C_2 \wr C_2\wr C_2$ (as 8T35)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{13}{4}]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.47	64	$x^{8} + 16 x^{5} + 8 x^{2} + 50$	$C_2 \wr C_2\wr C_2$ (as 8T35)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{13}{4}]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.48	64	$x^{8} + 16 x^{7} + 16 x^{5} + 8 x^{2} + 50$	$C_2 \wr C_2\wr C_2$ (as 8T35)	$128$	$2$	$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$	$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$	$[2,\frac{7}{2},\frac{17}{4}]^{2}$	$[1,\frac{5}{2},\frac{13}{4}]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.49	4	$x^{8} + 16 x^{7} + 8 x^{2} + 16 x + 50$	$D_{8}$ (as 8T6)	$16$	$2$	$[3, 4, 5]^{2}$	$[2,3,4]^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$
2.1.8.31a1.50	4	$x^{8} + 8 x^{2} + 16 x + 50$	$D_{8}$ (as 8T6)	$16$	$2$	$[3, 4, 5]^{2}$	$[2,3,4]^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$[24, 16, 8, 0]$	$[1, 1, 1]$	$z^4 + 1,z^2 + 1,z + 1$	$[1, 3, 7, 15]$

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Label	2.1.8.31a
Base	2.1.1.0a1.1
Degree	\(8\)
e	\(8\)
f	\(1\)
c	\(31\)

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