LMFDB - $p$-adic family 2.1.16.56l

Defining polynomial

$x^{16} + 8 b_{47} x^{15} + 8 b_{46} x^{14} + 8 b_{45} x^{13} + 4 b_{28} x^{12} + 8 b_{43} x^{11} + 8 b_{42} x^{10} + 8 a_{41} x^{9} + 2 a_{8} x^{8} + 8 b_{38} x^{6} + 4 a_{20} x^{4} + 8 b_{34} x^{2} + 4 c_{16} + 8 c_{32} + 16 c_{48} + 2$

Invariants

Residue field characteristic:	$2$
Degree:	$16$
Base field:	$\Q_{2}$
Ramification index $e$:	$16$
Residue field degree $f$:	$1$
Discriminant exponent $c$:	$56$
Artin slopes:	$[2,3,4,4]$
Swan slopes:	$[1,2,3,3]$
Means:	$\langle\frac{1}{2},\frac{5}{4},\frac{17}{8},\frac{41}{16}\rangle$
Rams:	$(1,3,7,7)$
Field count:	$384$ (complete)
Ambiguity:	$8$
Mass:	$256$
Absolute Mass:	$256$

Diagrams

Varying

Indices of inseparability:	$[41,34,20,8,0]$ (show 128), $[41,36,20,8,0]$ (show 256)
Associated inertia:	$[1,1,2]$ (show 256), $[1,1,3]$ (show 128)
Jump Set:	$[1,2,4,8,32]$ (show 192), $[1,2,4,32,48]$ (show 48), $[1,2,25,41,57]$ (show 8), $[1,7,15,31,47]$ (show 96), $[1,9,18,34,50]$ (show 2), $[1,9,27,43,59]$ (show 16), $[1,9,29,45,61]$ (show 8), $[1,9,31,47,63]$ (show 4), $[1,9,32,48,64]$ (show 2), $[1,11,25,41,57]$ (show 8)

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
		$C_2^4.C_2^3$ (as 16T229)	$C_2^4.C_2^3$ (as 16T231)	$C_2^4.D_4$ (as 16T268)	$C_2^4.D_4$ (as 16T284)	$C_2^4.C_2^3$ (as 16T316)	$C_2^4.D_4$ (as 16T318)	$C_2^4.D_4$ (as 16T326)	$C_2^4:Q_8$ (as 16T354)	$C_2^4:Q_8$ (as 16T368)	$C_2^4.C_2^3$ (as 16T383)	$C_2^4:Q_8$ (as 16T384)	Total
hidden slopes	$[3,\frac{7}{2}]^{2}$	16	8	8	8	8	8	8	8	16	32	8	128

		Galois groups of order 256
		$C_2^4.D_8$ (as 16T686)	$C_2^4.Q_{16}$ (as 16T691)	$C_2^4.Q_{16}$ (as 16T698)	$C_2^4.D_8$ (as 16T705)	Total
hidden slopes	$[3,\frac{7}{2}]^{4}$	16	16	16	16	64

		Galois groups of order 512
		$C_2^6.D_4$ (as 16T900)	$C_2^6.D_4$ (as 16T921)	Total
hidden slopes	$[2,3,\frac{7}{2}]^{4}$	32	32	64

		Galois groups of order 3072
		$C_2^8:(C_2\times C_6)$ (as 16T1516)
hidden slopes	$[2,2,3,3,\frac{7}{2},\frac{7}{2}]^{3}$	64

		Galois groups of order 6144
		$C_2^6.(D_4\times A_4)$ (as 16T1655)
hidden slopes	$[2,2,3,3,\frac{7}{2},\frac{7}{2}]^{6}$	8

Fields

Galois group	Galois Artin	Indices

Assoc. Inertia	Jump Set

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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
2.1.16.56l1.65	16	$x^{16} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$	$C_2^4.D_8$ (as 16T705)	$256$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,2,2,\frac{5}{2},3,3]^{4}$	$[3,\frac{7}{2}]^{4}$	$[2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.66	16	$x^{16} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 18$	$C_2^4.D_8$ (as 16T705)	$256$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,2,2,\frac{5}{2},3,3]^{4}$	$[3,\frac{7}{2}]^{4}$	$[2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.67	16	$x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$	$C_2^4.D_8$ (as 16T705)	$256$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,2,2,\frac{5}{2},3,3]^{4}$	$[3,\frac{7}{2}]^{4}$	$[2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.68	16	$x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 18$	$C_2^4.D_8$ (as 16T705)	$256$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,2,2,\frac{5}{2},3,3]^{4}$	$[3,\frac{7}{2}]^{4}$	$[2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.69	16	$x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$	$C_2^4.D_8$ (as 16T705)	$256$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,2,2,\frac{5}{2},3,3]^{4}$	$[3,\frac{7}{2}]^{4}$	$[2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.70	16	$x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 18$	$C_2^4.D_8$ (as 16T705)	$256$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,2,2,\frac{5}{2},3,3]^{4}$	$[3,\frac{7}{2}]^{4}$	$[2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.71	16	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$	$C_2^4.D_8$ (as 16T705)	$256$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,2,2,\frac{5}{2},3,3]^{4}$	$[3,\frac{7}{2}]^{4}$	$[2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.72	16	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 18$	$C_2^4.D_8$ (as 16T705)	$256$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,2,2,\frac{5}{2},3,3]^{4}$	$[3,\frac{7}{2}]^{4}$	$[2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.73	16	$x^{16} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$	$C_2^4.D_8$ (as 16T686)	$256$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,2,2,\frac{5}{2},3,3]^{4}$	$[3,\frac{7}{2}]^{4}$	$[2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.74	16	$x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$	$C_2^4.D_8$ (as 16T686)	$256$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,2,2,\frac{5}{2},3,3]^{4}$	$[3,\frac{7}{2}]^{4}$	$[2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.75	16	$x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$	$C_2^4.D_8$ (as 16T686)	$256$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,2,2,\frac{5}{2},3,3]^{4}$	$[3,\frac{7}{2}]^{4}$	$[2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.76	16	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$	$C_2^4.D_8$ (as 16T686)	$256$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,2,2,\frac{5}{2},3,3]^{4}$	$[3,\frac{7}{2}]^{4}$	$[2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.77	32	$x^{16} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$	$C_2^6.D_4$ (as 16T921)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,1,2,2,\frac{5}{2},3,3]^{4}$	$[2,3,\frac{7}{2}]^{4}$	$[1,2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.78	32	$x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$	$C_2^6.D_4$ (as 16T921)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,1,2,2,\frac{5}{2},3,3]^{4}$	$[2,3,\frac{7}{2}]^{4}$	$[1,2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.79	32	$x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$	$C_2^6.D_4$ (as 16T921)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,1,2,2,\frac{5}{2},3,3]^{4}$	$[2,3,\frac{7}{2}]^{4}$	$[1,2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.80	32	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$	$C_2^6.D_4$ (as 16T921)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,1,2,2,\frac{5}{2},3,3]^{4}$	$[2,3,\frac{7}{2}]^{4}$	$[1,2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.81	32	$x^{16} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$	$C_2^6.D_4$ (as 16T900)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,1,2,2,\frac{5}{2},3,3]^{4}$	$[2,3,\frac{7}{2}]^{4}$	$[1,2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.82	32	$x^{16} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 18$	$C_2^6.D_4$ (as 16T900)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,1,2,2,\frac{5}{2},3,3]^{4}$	$[2,3,\frac{7}{2}]^{4}$	$[1,2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.83	32	$x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$	$C_2^6.D_4$ (as 16T900)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,1,2,2,\frac{5}{2},3,3]^{4}$	$[2,3,\frac{7}{2}]^{4}$	$[1,2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.84	32	$x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 18$	$C_2^6.D_4$ (as 16T900)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,1,2,2,\frac{5}{2},3,3]^{4}$	$[2,3,\frac{7}{2}]^{4}$	$[1,2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.85	32	$x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$	$C_2^6.D_4$ (as 16T900)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,1,2,2,\frac{5}{2},3,3]^{4}$	$[2,3,\frac{7}{2}]^{4}$	$[1,2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.86	32	$x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 18$	$C_2^6.D_4$ (as 16T900)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,1,2,2,\frac{5}{2},3,3]^{4}$	$[2,3,\frac{7}{2}]^{4}$	$[1,2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.87	32	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$	$C_2^6.D_4$ (as 16T900)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,1,2,2,\frac{5}{2},3,3]^{4}$	$[2,3,\frac{7}{2}]^{4}$	$[1,2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.88	32	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 18$	$C_2^6.D_4$ (as 16T900)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,1,2,2,\frac{5}{2},3,3]^{4}$	$[2,3,\frac{7}{2}]^{4}$	$[1,2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.89	16	$x^{16} + 4 x^{12} + 8 x^{10} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$	$C_2^4.D_8$ (as 16T686)	$256$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,2,2,\frac{5}{2},3,3]^{4}$	$[3,\frac{7}{2}]^{4}$	$[2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.90	16	$x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{10} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$	$C_2^4.D_8$ (as 16T686)	$256$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,2,2,\frac{5}{2},3,3]^{4}$	$[3,\frac{7}{2}]^{4}$	$[2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.91	16	$x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{10} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$	$C_2^4.D_8$ (as 16T686)	$256$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,2,2,\frac{5}{2},3,3]^{4}$	$[3,\frac{7}{2}]^{4}$	$[2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.92	16	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{10} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$	$C_2^4.D_8$ (as 16T686)	$256$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,2,2,\frac{5}{2},3,3]^{4}$	$[3,\frac{7}{2}]^{4}$	$[2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.93	32	$x^{16} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$	$C_2^6.D_4$ (as 16T921)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,1,2,2,\frac{5}{2},3,3]^{4}$	$[2,3,\frac{7}{2}]^{4}$	$[1,2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.94	32	$x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$	$C_2^6.D_4$ (as 16T921)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,1,2,2,\frac{5}{2},3,3]^{4}$	$[2,3,\frac{7}{2}]^{4}$	$[1,2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.95	32	$x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$	$C_2^6.D_4$ (as 16T921)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,1,2,2,\frac{5}{2},3,3]^{4}$	$[2,3,\frac{7}{2}]^{4}$	$[1,2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.96	32	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{10} + 8 x^{9} + 2 x^{8} + 4 x^{4} + 2$	$C_2^6.D_4$ (as 16T921)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,1,2,2,\frac{5}{2},3,3]^{4}$	$[2,3,\frac{7}{2}]^{4}$	$[1,2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.97	32	$x^{16} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 2$	$C_2^6.D_4$ (as 16T921)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,1,2,2,\frac{5}{2},3,3]^{4}$	$[2,3,\frac{7}{2}]^{4}$	$[1,2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.98	32	$x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 2$	$C_2^6.D_4$ (as 16T921)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,1,2,2,\frac{5}{2},3,3]^{4}$	$[2,3,\frac{7}{2}]^{4}$	$[1,2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.99	32	$x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 2$	$C_2^6.D_4$ (as 16T921)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,1,2,2,\frac{5}{2},3,3]^{4}$	$[2,3,\frac{7}{2}]^{4}$	$[1,2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.100	32	$x^{16} + 8 x^{15} + 8 x^{14} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 2$	$C_2^6.D_4$ (as 16T921)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,1,2,2,\frac{5}{2},3,3]^{4}$	$[2,3,\frac{7}{2}]^{4}$	$[1,2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.101	32	$x^{16} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 2$	$C_2^6.D_4$ (as 16T900)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,1,2,2,\frac{5}{2},3,3]^{4}$	$[2,3,\frac{7}{2}]^{4}$	$[1,2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.102	32	$x^{16} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 18$	$C_2^6.D_4$ (as 16T900)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,1,2,2,\frac{5}{2},3,3]^{4}$	$[2,3,\frac{7}{2}]^{4}$	$[1,2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.103	32	$x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 2$	$C_2^6.D_4$ (as 16T900)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,1,2,2,\frac{5}{2},3,3]^{4}$	$[2,3,\frac{7}{2}]^{4}$	$[1,2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.104	32	$x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 18$	$C_2^6.D_4$ (as 16T900)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,1,2,2,\frac{5}{2},3,3]^{4}$	$[2,3,\frac{7}{2}]^{4}$	$[1,2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.105	32	$x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 2$	$C_2^6.D_4$ (as 16T900)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,1,2,2,\frac{5}{2},3,3]^{4}$	$[2,3,\frac{7}{2}]^{4}$	$[1,2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.106	32	$x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 18$	$C_2^6.D_4$ (as 16T900)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,1,2,2,\frac{5}{2},3,3]^{4}$	$[2,3,\frac{7}{2}]^{4}$	$[1,2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.107	32	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 2$	$C_2^6.D_4$ (as 16T900)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,1,2,2,\frac{5}{2},3,3]^{4}$	$[2,3,\frac{7}{2}]^{4}$	$[1,2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.108	32	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 18$	$C_2^6.D_4$ (as 16T900)	$512$	$2$	$[2, 2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,1,2,2,\frac{5}{2},3,3]^{4}$	$[2,3,\frac{7}{2}]^{4}$	$[1,2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.109	16	$x^{16} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 2$	$C_2^4.D_8$ (as 16T705)	$256$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,2,2,\frac{5}{2},3,3]^{4}$	$[3,\frac{7}{2}]^{4}$	$[2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.110	16	$x^{16} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 18$	$C_2^4.D_8$ (as 16T705)	$256$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,2,2,\frac{5}{2},3,3]^{4}$	$[3,\frac{7}{2}]^{4}$	$[2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.111	16	$x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 2$	$C_2^4.D_8$ (as 16T705)	$256$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,2,2,\frac{5}{2},3,3]^{4}$	$[3,\frac{7}{2}]^{4}$	$[2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.112	16	$x^{16} + 8 x^{15} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 18$	$C_2^4.D_8$ (as 16T705)	$256$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,2,2,\frac{5}{2},3,3]^{4}$	$[3,\frac{7}{2}]^{4}$	$[2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.113	16	$x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 2$	$C_2^4.D_8$ (as 16T705)	$256$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,2,2,\frac{5}{2},3,3]^{4}$	$[3,\frac{7}{2}]^{4}$	$[2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$
2.1.16.56l1.114	16	$x^{16} + 8 x^{14} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 18$	$C_2^4.D_8$ (as 16T705)	$256$	$2$	$[2, 3, 3, \frac{7}{2}, 4, 4]^{4}$	$[1,2,2,\frac{5}{2},3,3]^{4}$	$[3,\frac{7}{2}]^{4}$	$[2,\frac{5}{2}]^{4}$	$[41, 36, 20, 8, 0]$	$[1, 1, 2]$	$z^8 + 1,z^4 + 1,z^3 + 1$	$[1, 7, 15, 31, 47]$

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Label	2.1.16.56l
Base	2.1.1.0a1.1
Degree	\(16\)
e	\(16\)
f	\(1\)
c	\(56\)

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