LMFDB - $p$-adic family 2.1.16.42k

Defining polynomial

$x^{16} + 4 b_{31} x^{15} + 4 b_{29} x^{13} + 2 a_{12} x^{12} + 4 a_{27} x^{11} + \left(2 b_{8} + 4 c_{24}\right) x^{8} + 4 b_{22} x^{6} + 8 c_{36} x^{4} + 8 b_{35} x^{3} + 4 a_{18} x^{2} + 8 b_{33} x + 4 c_{16} + 2$

Invariants

Residue field characteristic:	$2$
Degree:	$16$
Base field:	$\Q_{2}$
Ramification index $e$:	$16$
Residue field degree $f$:	$1$
Discriminant exponent $c$:	$42$
Artin slopes:	$[2,2,\frac{5}{2},\frac{13}{4}]$
Swan slopes:	$[1,1,\frac{3}{2},\frac{9}{4}]$
Means:	$\langle\frac{1}{2},\frac{3}{4},\frac{9}{8},\frac{27}{16}\rangle$
Rams:	$(1,1,3,9)$
Field count:	$160$ (complete)
Ambiguity:	$8$
Mass:	$64$
Absolute Mass:	$64$

Diagrams

Varying

Indices of inseparability:	$[27,18,12,8,0]$ (show 80), $[27,18,12,12,0]$ (show 80)
Associated inertia:	$[2,1,1]$ (show 80), $[3,1,1]$ (show 80)
Jump Set:	$[1,2,7,15,31]$ (show 80), $[1,3,6,12,32]$ (show 40), $[1,3,9,25,41]$ (show 40)

Galois groups and Hidden Artin slopes

Select desired size of Galois group. Note that the following data has not all been computed for fields in this family, so the tables below are incomplete.

		Galois groups of order 128
		$C_2^3.\SD_{16}$ (as 16T374)
hidden slopes	$[3,3]^{2}$	8

		Galois groups of order 256
		$C_8^2:C_2^2$ (as 16T568)	$C_2^4.\SD_{16}$ (as 16T673)	$C_4^2.Q_{16}$ (as 16T697)	Total
hidden slopes	$[3,3]^{4}$	16	16	8	40

		Galois groups of order 1024
		$C_2^6.\SD_{16}$ (as 16T1250)	$C_2^6.\SD_{16}$ (as 16T1264)	Total
hidden slopes	$[2,2,3,3]_{4}$	16	16	32

		Galois groups of order 6144
		$C_4^4:(C_2\times A_4)$ (as 16T1657)
hidden slopes	$[2,2,2,2,3,3]^{6}$	16

Fields

Galois group	Galois Artin	Indices

Assoc. Inertia	Jump Set

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Showing 1-50 of 160

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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
2.1.16.42k1.1	16	$x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{2} + 2$	$C_2^6.\SD_{16}$ (as 16T1264)	$1024$	$2$	$[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[2,2,3,3]_{4}$	$[1,1,2,2]_{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.2	16	$x^{16} + 2 x^{12} + 4 x^{11} + 8 x^{4} + 4 x^{2} + 2$	$C_2^6.\SD_{16}$ (as 16T1264)	$1024$	$2$	$[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[2,2,3,3]_{4}$	$[1,1,2,2]_{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.3	16	$x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{2} + 8 x + 2$	$C_2^6.\SD_{16}$ (as 16T1264)	$1024$	$2$	$[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[2,2,3,3]_{4}$	$[1,1,2,2]_{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.4	16	$x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 4 x^{2} + 2$	$C_8^2:C_2^2$ (as 16T568)	$256$	$4$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[3,3]^{4}$	$[2,2]^{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.5	16	$x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 8 x^{4} + 4 x^{2} + 2$	$C_8^2:C_2^2$ (as 16T568)	$256$	$4$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[3,3]^{4}$	$[2,2]^{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.6	16	$x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 8 x^{3} + 4 x^{2} + 2$	$C_8^2:C_2^2$ (as 16T568)	$256$	$4$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[3,3]^{4}$	$[2,2]^{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.7	16	$x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 2$	$C_8^2:C_2^2$ (as 16T568)	$256$	$4$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[3,3]^{4}$	$[2,2]^{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.8	16	$x^{16} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{2} + 8 x + 2$	$C_2^6.\SD_{16}$ (as 16T1264)	$1024$	$2$	$[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[2,2,3,3]_{4}$	$[1,1,2,2]_{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.9	8	$x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{2} + 2$	$C_4^2.Q_{16}$ (as 16T697)	$256$	$2$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[3,3]^{4}$	$[2,2]^{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.10	8	$x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 8 x^{3} + 4 x^{2} + 2$	$C_4^2.Q_{16}$ (as 16T697)	$256$	$2$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[3,3]^{4}$	$[2,2]^{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.11	16	$x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{2} + 2$	$C_2^6.\SD_{16}$ (as 16T1264)	$1024$	$2$	$[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[2,2,3,3]_{4}$	$[1,1,2,2]_{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.12	16	$x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 8 x^{4} + 4 x^{2} + 2$	$C_2^6.\SD_{16}$ (as 16T1264)	$1024$	$2$	$[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[2,2,3,3]_{4}$	$[1,1,2,2]_{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.13	16	$x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{2} + 8 x + 2$	$C_2^6.\SD_{16}$ (as 16T1264)	$1024$	$2$	$[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[2,2,3,3]_{4}$	$[1,1,2,2]_{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.14	16	$x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 8 x^{4} + 4 x^{2} + 8 x + 2$	$C_2^6.\SD_{16}$ (as 16T1264)	$1024$	$2$	$[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[2,2,3,3]_{4}$	$[1,1,2,2]_{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.15	16	$x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{2} + 2$	$C_8^2:C_2^2$ (as 16T568)	$256$	$4$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[3,3]^{4}$	$[2,2]^{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.16	16	$x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 8 x^{4} + 4 x^{2} + 2$	$C_8^2:C_2^2$ (as 16T568)	$256$	$4$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[3,3]^{4}$	$[2,2]^{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.17	16	$x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 8 x^{3} + 4 x^{2} + 2$	$C_8^2:C_2^2$ (as 16T568)	$256$	$4$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[3,3]^{4}$	$[2,2]^{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.18	16	$x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 2$	$C_8^2:C_2^2$ (as 16T568)	$256$	$4$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[3,3]^{4}$	$[2,2]^{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.19	8	$x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{2} + 2$	$C_4^2.Q_{16}$ (as 16T697)	$256$	$2$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[3,3]^{4}$	$[2,2]^{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.20	8	$x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 8 x^{3} + 4 x^{2} + 2$	$C_4^2.Q_{16}$ (as 16T697)	$256$	$2$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[3,3]^{4}$	$[2,2]^{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.21	8	$x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 4 x^{2} + 2$	$C_2^3.\SD_{16}$ (as 16T374)	$128$	$2$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{2}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{2}$	$[3,3]^{2}$	$[2,2]^{2}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.22	16	$x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 4 x^{2} + 8 x + 2$	$C_2^4.\SD_{16}$ (as 16T673)	$256$	$4$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[3,3]^{4}$	$[2,2]^{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.23	16	$x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 8 x^{3} + 4 x^{2} + 8 x + 2$	$C_2^4.\SD_{16}$ (as 16T673)	$256$	$4$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[3,3]^{4}$	$[2,2]^{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.24	16	$x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 2$	$C_2^4.\SD_{16}$ (as 16T673)	$256$	$4$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[3,3]^{4}$	$[2,2]^{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.25	16	$x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 4 x^{2} + 2$	$C_2^6.\SD_{16}$ (as 16T1250)	$1024$	$2$	$[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[2,2,3,3]_{4}$	$[1,1,2,2]_{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.26	16	$x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 8 x^{4} + 4 x^{2} + 2$	$C_2^6.\SD_{16}$ (as 16T1250)	$1024$	$2$	$[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[2,2,3,3]_{4}$	$[1,1,2,2]_{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.27	16	$x^{16} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 4 x^{2} + 2$	$C_2^6.\SD_{16}$ (as 16T1250)	$1024$	$2$	$[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[2,2,3,3]_{4}$	$[1,1,2,2]_{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.28	16	$x^{16} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 8 x^{4} + 4 x^{2} + 2$	$C_2^6.\SD_{16}$ (as 16T1250)	$1024$	$2$	$[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[2,2,3,3]_{4}$	$[1,1,2,2]_{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.29	8	$x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 4 x^{2} + 2$	$C_2^3.\SD_{16}$ (as 16T374)	$128$	$2$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{2}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{2}$	$[3,3]^{2}$	$[2,2]^{2}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.30	8	$x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 8 x^{3} + 4 x^{2} + 2$	$C_2^3.\SD_{16}$ (as 16T374)	$128$	$2$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{2}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{2}$	$[3,3]^{2}$	$[2,2]^{2}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.31	16	$x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 4 x^{2} + 8 x + 2$	$C_2^4.\SD_{16}$ (as 16T673)	$256$	$4$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[3,3]^{4}$	$[2,2]^{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.32	16	$x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{6} + 8 x^{4} + 4 x^{2} + 8 x + 2$	$C_2^4.\SD_{16}$ (as 16T673)	$256$	$4$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[3,3]^{4}$	$[2,2]^{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.33	16	$x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{6} + 4 x^{2} + 8 x + 2$	$C_2^4.\SD_{16}$ (as 16T673)	$256$	$4$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[3,3]^{4}$	$[2,2]^{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.34	16	$x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{6} + 8 x^{4} + 4 x^{2} + 8 x + 2$	$C_2^4.\SD_{16}$ (as 16T673)	$256$	$4$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[3,3]^{4}$	$[2,2]^{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.35	16	$x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{6} + 4 x^{2} + 2$	$C_2^6.\SD_{16}$ (as 16T1250)	$1024$	$2$	$[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[2,2,3,3]_{4}$	$[1,1,2,2]_{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.36	16	$x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{6} + 8 x^{4} + 4 x^{2} + 2$	$C_2^6.\SD_{16}$ (as 16T1250)	$1024$	$2$	$[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[2,2,3,3]_{4}$	$[1,1,2,2]_{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.37	16	$x^{16} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{6} + 4 x^{2} + 2$	$C_2^6.\SD_{16}$ (as 16T1250)	$1024$	$2$	$[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[2,2,3,3]_{4}$	$[1,1,2,2]_{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.38	16	$x^{16} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{6} + 8 x^{4} + 4 x^{2} + 2$	$C_2^6.\SD_{16}$ (as 16T1250)	$1024$	$2$	$[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[2,2,3,3]_{4}$	$[1,1,2,2]_{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.39	8	$x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{6} + 4 x^{2} + 2$	$C_2^3.\SD_{16}$ (as 16T374)	$128$	$2$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{2}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{2}$	$[3,3]^{2}$	$[2,2]^{2}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.40	16	$x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{8} + 4 x^{6} + 4 x^{2} + 8 x + 2$	$C_2^4.\SD_{16}$ (as 16T673)	$256$	$4$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[3,3]^{4}$	$[2,2]^{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 9, 25, 41]$
2.1.16.42k1.41	16	$x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{2} + 6$	$C_2^6.\SD_{16}$ (as 16T1264)	$1024$	$2$	$[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[2,2,3,3]_{4}$	$[1,1,2,2]_{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 6, 12, 32]$
2.1.16.42k1.42	16	$x^{16} + 2 x^{12} + 4 x^{11} + 4 x^{2} + 8 x + 6$	$C_2^6.\SD_{16}$ (as 16T1264)	$1024$	$2$	$[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[2,2,3,3]_{4}$	$[1,1,2,2]_{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 6, 12, 32]$
2.1.16.42k1.43	16	$x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 4 x^{2} + 6$	$C_8^2:C_2^2$ (as 16T568)	$256$	$4$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[3,3]^{4}$	$[2,2]^{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 6, 12, 32]$
2.1.16.42k1.44	16	$x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 8 x^{4} + 4 x^{2} + 6$	$C_8^2:C_2^2$ (as 16T568)	$256$	$4$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[3,3]^{4}$	$[2,2]^{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 6, 12, 32]$
2.1.16.42k1.45	16	$x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 8 x^{3} + 4 x^{2} + 6$	$C_8^2:C_2^2$ (as 16T568)	$256$	$4$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[3,3]^{4}$	$[2,2]^{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 6, 12, 32]$
2.1.16.42k1.46	16	$x^{16} + 4 x^{15} + 2 x^{12} + 4 x^{11} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 6$	$C_8^2:C_2^2$ (as 16T568)	$256$	$4$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[3,3]^{4}$	$[2,2]^{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 6, 12, 32]$
2.1.16.42k1.47	16	$x^{16} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{2} + 6$	$C_2^6.\SD_{16}$ (as 16T1264)	$1024$	$2$	$[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[2,2,3,3]_{4}$	$[1,1,2,2]_{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 6, 12, 32]$
2.1.16.42k1.48	16	$x^{16} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{2} + 8 x + 6$	$C_2^6.\SD_{16}$ (as 16T1264)	$1024$	$2$	$[2, 2, 2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[2,2,3,3]_{4}$	$[1,1,2,2]_{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 6, 12, 32]$
2.1.16.42k1.49	8	$x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 4 x^{2} + 6$	$C_4^2.Q_{16}$ (as 16T697)	$256$	$2$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[3,3]^{4}$	$[2,2]^{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 6, 12, 32]$
2.1.16.42k1.50	8	$x^{16} + 4 x^{15} + 4 x^{13} + 2 x^{12} + 4 x^{11} + 8 x^{3} + 4 x^{2} + 6$	$C_4^2.Q_{16}$ (as 16T697)	$256$	$2$	$[2, 2, \frac{5}{2}, 3, 3, \frac{13}{4}]^{4}$	$[1,1,\frac{3}{2},2,2,\frac{9}{4}]^{4}$	$[3,3]^{4}$	$[2,2]^{4}$	$[27, 18, 12, 12, 0]$	$[2, 1, 1]$	$z^{12} + 1,z^2 + 1,z + 1$	$[1, 3, 6, 12, 32]$

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
Higher genus families
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Label	2.1.16.42k
Base	2.1.1.0a1.1
Degree	\(16\)
e	\(16\)
f	\(1\)
c	\(42\)

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