LMFDB - $p$-adic family 2.1.16.60j

Defining polynomial

$x^{16} + 8 b_{47} x^{15} + 8 b_{46} x^{14} + 8 a_{45} x^{13} + 8 b_{44} x^{12} + 8 b_{42} x^{10} + 4 b_{24} x^{8} + 8 b_{36} x^{4} + 16 b_{49} x + 8 c_{32} + 16 c_{48} + 2$

Invariants

Residue field characteristic:	$2$
Degree:	$16$
Base field:	$\Q_{2}$
Ramification index $e$:	$16$
Residue field degree $f$:	$1$
Discriminant exponent $c$:	$60$
Artin slopes:	$[3,4,\frac{49}{12},\frac{49}{12}]$
Swan slopes:	$[2,3,\frac{37}{12},\frac{37}{12}]$
Means:	$\langle1,2,\frac{61}{24},\frac{45}{16}\rangle$
Rams:	$(2,4,\frac{13}{3},\frac{13}{3})$
Field count:	$128$ (complete)
Ambiguity:	$4$
Mass:	$128$
Absolute Mass:	$128$

Diagrams

Varying

Indices of inseparability:	$[45,42,32,16,0]$ (show 64), $[45,45,32,16,0]$ (show 64)
Associated inertia:	$[1,1,1]$
Jump Set:	$[1,3,7,15,31]$

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 1536
		$C_2^6:(C_4\times S_3)$ (as 16T1300)	$C_2^6:D_{12}$ (as 16T1313)	Total
hidden slopes	$[\frac{4}{3},\frac{4}{3},\frac{19}{6},\frac{19}{6}]^{2}_{3}$	28	32	60

		Galois groups of order 3072
		$C_2^6:(C_2\times S_4)$ (as 16T1519)
hidden slopes	$[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6}]^{2}_{3}$	64

Fields

Galois group	Galois Artin	Indices

Assoc. Inertia	Jump Set

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Showing 1-50 of 64

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Label	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
2.1.16.60j1.1	$x^{16} + 8 x^{13} + 2$	$C_2^6:D_{12}$ (as 16T1313)	$1536$	$1$	$[\frac{4}{3}, \frac{4}{3}, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.2	$x^{16} + 8 x^{15} + 8 x^{13} + 2$	$C_2^6:D_{12}$ (as 16T1313)	$1536$	$1$	$[\frac{4}{3}, \frac{4}{3}, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.3	$x^{16} + 8 x^{14} + 8 x^{13} + 2$	$C_2^6:D_{12}$ (as 16T1313)	$1536$	$1$	$[\frac{4}{3}, \frac{4}{3}, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.4	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 2$	$C_2^6:D_{12}$ (as 16T1313)	$1536$	$1$	$[\frac{4}{3}, \frac{4}{3}, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.5	$x^{16} + 8 x^{13} + 8 x^{12} + 2$	$C_2^6:D_{12}$ (as 16T1313)	$1536$	$1$	$[\frac{4}{3}, \frac{4}{3}, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.6	$x^{16} + 8 x^{15} + 8 x^{13} + 8 x^{12} + 2$	$C_2^6:D_{12}$ (as 16T1313)	$1536$	$1$	$[\frac{4}{3}, \frac{4}{3}, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.7	$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{12} + 2$	$C_2^6:D_{12}$ (as 16T1313)	$1536$	$1$	$[\frac{4}{3}, \frac{4}{3}, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.8	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{12} + 2$	$C_2^6:D_{12}$ (as 16T1313)	$1536$	$1$	$[\frac{4}{3}, \frac{4}{3}, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.17	$x^{16} + 8 x^{13} + 8 x^{4} + 2$	$C_2^6:(C_2\times S_4)$ (as 16T1519)	$3072$	$1$	$[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.18	$x^{16} + 8 x^{13} + 8 x^{4} + 18$	$C_2^6:(C_2\times S_4)$ (as 16T1519)	$3072$	$1$	$[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.19	$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{4} + 2$	$C_2^6:(C_2\times S_4)$ (as 16T1519)	$3072$	$1$	$[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.20	$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{4} + 18$	$C_2^6:(C_2\times S_4)$ (as 16T1519)	$3072$	$1$	$[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.21	$x^{16} + 8 x^{13} + 8 x^{12} + 8 x^{4} + 2$	$C_2^6:(C_2\times S_4)$ (as 16T1519)	$3072$	$1$	$[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.22	$x^{16} + 8 x^{13} + 8 x^{12} + 8 x^{4} + 18$	$C_2^6:(C_2\times S_4)$ (as 16T1519)	$3072$	$1$	$[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.23	$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{12} + 8 x^{4} + 2$	$C_2^6:(C_2\times S_4)$ (as 16T1519)	$3072$	$1$	$[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.24	$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{12} + 8 x^{4} + 18$	$C_2^6:(C_2\times S_4)$ (as 16T1519)	$3072$	$1$	$[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.33	$x^{16} + 8 x^{13} + 10$	$C_2^6:D_{12}$ (as 16T1313)	$1536$	$1$	$[\frac{4}{3}, \frac{4}{3}, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.34	$x^{16} + 8 x^{15} + 8 x^{13} + 10$	$C_2^6:D_{12}$ (as 16T1313)	$1536$	$1$	$[\frac{4}{3}, \frac{4}{3}, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.35	$x^{16} + 8 x^{14} + 8 x^{13} + 10$	$C_2^6:D_{12}$ (as 16T1313)	$1536$	$1$	$[\frac{4}{3}, \frac{4}{3}, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.36	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 10$	$C_2^6:D_{12}$ (as 16T1313)	$1536$	$1$	$[\frac{4}{3}, \frac{4}{3}, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.37	$x^{16} + 8 x^{13} + 8 x^{12} + 10$	$C_2^6:D_{12}$ (as 16T1313)	$1536$	$1$	$[\frac{4}{3}, \frac{4}{3}, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.38	$x^{16} + 8 x^{15} + 8 x^{13} + 8 x^{12} + 10$	$C_2^6:D_{12}$ (as 16T1313)	$1536$	$1$	$[\frac{4}{3}, \frac{4}{3}, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.39	$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{12} + 10$	$C_2^6:D_{12}$ (as 16T1313)	$1536$	$1$	$[\frac{4}{3}, \frac{4}{3}, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.40	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 8 x^{12} + 10$	$C_2^6:D_{12}$ (as 16T1313)	$1536$	$1$	$[\frac{4}{3}, \frac{4}{3}, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.49	$x^{16} + 8 x^{13} + 8 x^{4} + 10$	$C_2^6:(C_2\times S_4)$ (as 16T1519)	$3072$	$1$	$[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.50	$x^{16} + 8 x^{13} + 8 x^{4} + 26$	$C_2^6:(C_2\times S_4)$ (as 16T1519)	$3072$	$1$	$[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.51	$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{4} + 10$	$C_2^6:(C_2\times S_4)$ (as 16T1519)	$3072$	$1$	$[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.52	$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{4} + 26$	$C_2^6:(C_2\times S_4)$ (as 16T1519)	$3072$	$1$	$[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.53	$x^{16} + 8 x^{13} + 8 x^{12} + 8 x^{4} + 10$	$C_2^6:(C_2\times S_4)$ (as 16T1519)	$3072$	$1$	$[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.54	$x^{16} + 8 x^{13} + 8 x^{12} + 8 x^{4} + 26$	$C_2^6:(C_2\times S_4)$ (as 16T1519)	$3072$	$1$	$[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.55	$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{12} + 8 x^{4} + 10$	$C_2^6:(C_2\times S_4)$ (as 16T1519)	$3072$	$1$	$[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.56	$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{12} + 8 x^{4} + 26$	$C_2^6:(C_2\times S_4)$ (as 16T1519)	$3072$	$1$	$[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.65	$x^{16} + 8 x^{13} + 4 x^{8} + 2$	$C_2^6:(C_2\times S_4)$ (as 16T1519)	$3072$	$1$	$[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.66	$x^{16} + 8 x^{13} + 4 x^{8} + 18$	$C_2^6:(C_2\times S_4)$ (as 16T1519)	$3072$	$1$	$[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.67	$x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{8} + 2$	$C_2^6:(C_2\times S_4)$ (as 16T1519)	$3072$	$1$	$[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.68	$x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{8} + 18$	$C_2^6:(C_2\times S_4)$ (as 16T1519)	$3072$	$1$	$[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.69	$x^{16} + 8 x^{13} + 8 x^{12} + 4 x^{8} + 2$	$C_2^6:(C_2\times S_4)$ (as 16T1519)	$3072$	$1$	$[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.70	$x^{16} + 8 x^{13} + 8 x^{12} + 4 x^{8} + 18$	$C_2^6:(C_2\times S_4)$ (as 16T1519)	$3072$	$1$	$[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.71	$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{12} + 4 x^{8} + 2$	$C_2^6:(C_2\times S_4)$ (as 16T1519)	$3072$	$1$	$[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.72	$x^{16} + 8 x^{14} + 8 x^{13} + 8 x^{12} + 4 x^{8} + 18$	$C_2^6:(C_2\times S_4)$ (as 16T1519)	$3072$	$1$	$[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.81	$x^{16} + 8 x^{13} + 4 x^{8} + 8 x^{4} + 2$	$C_2^6:(C_4\times S_3)$ (as 16T1300)	$1536$	$1$	$[\frac{4}{3}, \frac{4}{3}, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.82	$x^{16} + 8 x^{13} + 4 x^{8} + 8 x^{4} + 18$	$C_2^6:(C_4\times S_3)$ (as 16T1300)	$1536$	$1$	$[\frac{4}{3}, \frac{4}{3}, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.83	$x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{8} + 8 x^{4} + 2$	$C_2^6:(C_4\times S_3)$ (as 16T1300)	$1536$	$1$	$[\frac{4}{3}, \frac{4}{3}, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.84	$x^{16} + 8 x^{15} + 8 x^{13} + 4 x^{8} + 8 x^{4} + 18$	$C_2^6:(C_4\times S_3)$ (as 16T1300)	$1536$	$1$	$[\frac{4}{3}, \frac{4}{3}, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.85	$x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{8} + 8 x^{4} + 2$	$C_2^6:(C_4\times S_3)$ (as 16T1300)	$1536$	$1$	$[\frac{4}{3}, \frac{4}{3}, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.86	$x^{16} + 8 x^{14} + 8 x^{13} + 4 x^{8} + 8 x^{4} + 18$	$C_2^6:(C_4\times S_3)$ (as 16T1300)	$1536$	$1$	$[\frac{4}{3}, \frac{4}{3}, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.87	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{8} + 8 x^{4} + 2$	$C_2^6:(C_4\times S_3)$ (as 16T1300)	$1536$	$1$	$[\frac{4}{3}, \frac{4}{3}, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.88	$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{8} + 8 x^{4} + 18$	$C_2^6:(C_4\times S_3)$ (as 16T1300)	$1536$	$1$	$[\frac{4}{3}, \frac{4}{3}, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.97	$x^{16} + 8 x^{13} + 4 x^{8} + 10$	$C_2^6:(C_2\times S_4)$ (as 16T1519)	$3072$	$1$	$[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$
2.1.16.60j1.98	$x^{16} + 8 x^{13} + 4 x^{8} + 26$	$C_2^6:(C_2\times S_4)$ (as 16T1519)	$3072$	$1$	$[\frac{4}{3}, \frac{4}{3}, 2, 3, \frac{19}{6}, \frac{19}{6}, 4, \frac{49}{12}, \frac{49}{12}]_{3}^{2}$	$[\frac{1}{3},\frac{1}{3},1,2,\frac{13}{6},\frac{13}{6},3,\frac{37}{12},\frac{37}{12}]_{3}^{2}$	$[\frac{4}{3},\frac{4}{3},2,\frac{19}{6},\frac{19}{6}]^{2}_{3}$	$[\frac{1}{3},\frac{1}{3},1,\frac{13}{6},\frac{13}{6}]^{2}_{3}$	$[45, 45, 32, 16, 0]$	$[1, 1, 1]$	$z^8 + 1,z^4 + 1,z + 1$	$[1, 3, 7, 15, 31]$

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Overview	Random
Universe	Knowledge

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	2.1.16.60j
Base	2.1.1.0a1.1
Degree	\(16\)
e	\(16\)
f	\(1\)
c	\(60\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Defining polynomial

Invariants

Diagrams

Varying

Galois groups and Hidden Artin slopes

Fields

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.