LMFDB - $p$-adic family 3.1.9.22a

Defining polynomial

$x^{9} + 9 b_{17} x^{8} + 9 b_{16} x^{7} + 3 a_{6} x^{6} + 9 a_{14} x^{5} + 9 c_{9} + 27 c_{18} + 3$

Invariants

Residue field characteristic:	$3$
Degree:	$9$
Base field:	$\Q_{3}$
Ramification index $e$:	$9$
Residue field degree $f$:	$1$
Discriminant exponent $c$:	$22$
Artin slopes:	$[2,3]$
Swan slopes:	$[1,2]$
Means:	$\langle\frac{2}{3},\frac{14}{9}\rangle$
Rams:	$(1,4)$
Field count:	$78$ (complete)
Ambiguity:	$9$
Mass:	$36$
Absolute Mass:	$36$

Diagrams

Varying

Indices of inseparability:	$[14,6,0]$
Associated inertia:	$[1,1]$ (show 33), $[1,2]$ (show 9), $[2,1]$ (show 27), $[2,2]$ (show 9)
Jump Set:	undefined

Galois groups and Hidden Artin slopes

Select desired size of Galois group.

		Galois groups of order 9
		$C_9$ (as 9T1)
hidden slopes	$[\ ]$	9

		Galois groups of order 18
		$D_9$ (as 9T3)
hidden slopes	$[\ ]^{2}$	1

		Galois groups of order 27
		$C_9:C_3$ (as 9T6)
hidden slopes	$[\ ]^{3}$	6

		Galois groups of order 54
		$C_9:C_6$ (as 9T10)
hidden slopes	$[2]^{2}$	6

$[\ ]^{6}$	2

Total	8

		Galois groups of order 81
		$C_3\wr C_3$ (as 9T17)
hidden slopes	$[2]^{3}$	18

		Galois groups of order 162
		$C_3\wr S_3$ (as 9T20)	$C_3^3:C_6$ (as 9T22)	Total
hidden slopes	$[2,\frac{7}{3}]^{2}$	27	9	36

Fields

Galois group	Galois Artin	Indices

Assoc. Inertia	Jump Set	Fields per packet

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Showing 1-50 of 78

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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
3.1.9.22a1.1	1	$x^{9} + 3 x^{6} + 18 x^{5} + 3$	$D_{9}$ (as 9T3)	$18$	$1$	$[2, 3]^{2}$	$[1,2]^{2}$	$[\ ]^{2}$	$[\ ]^{2}$	$[14, 6, 0]$	$[2, 2]$	$z^6 + 1,z^2 + 1$	undefined
3.1.9.22a1.2	2	$x^{9} + 9 x^{8} + 3 x^{6} + 18 x^{5} + 3$	$(C_9:C_3):C_2$ (as 9T10)	$54$	$1$	$[2, 3]^{6}$	$[1,2]^{6}$	$[\ ]^{6}$	$[\ ]^{6}$	$[14, 6, 0]$	$[2, 2]$	$z^6 + 1,z^2 + 1$	undefined
3.1.9.22a1.3	2	$x^{9} + 18 x^{8} + 3 x^{6} + 18 x^{5} + 3$	$(C_9:C_3):C_2$ (as 9T10)	$54$	$1$	$[2, 3]^{6}$	$[1,2]^{6}$	$[\ ]^{6}$	$[\ ]^{6}$	$[14, 6, 0]$	$[2, 2]$	$z^6 + 1,z^2 + 1$	undefined
3.1.9.22a1.4	6	$x^{9} + 9 x^{7} + 3 x^{6} + 18 x^{5} + 3$	$(C_9:C_3):C_2$ (as 9T10)	$54$	$1$	$[2, 2, 3]^{2}$	$[1,1,2]^{2}$	$[2]^{2}$	$[1]^{2}$	$[14, 6, 0]$	$[2, 2]$	$z^6 + 1,z^2 + 1$	undefined
3.1.9.22a1.5	6	$x^{9} + 9 x^{8} + 9 x^{7} + 3 x^{6} + 18 x^{5} + 3$	$(C_9:C_3):C_2$ (as 9T10)	$54$	$1$	$[2, 2, 3]^{2}$	$[1,1,2]^{2}$	$[2]^{2}$	$[1]^{2}$	$[14, 6, 0]$	$[2, 2]$	$z^6 + 1,z^2 + 1$	undefined
3.1.9.22a1.6	6	$x^{9} + 18 x^{8} + 9 x^{7} + 3 x^{6} + 18 x^{5} + 3$	$(C_9:C_3):C_2$ (as 9T10)	$54$	$1$	$[2, 2, 3]^{2}$	$[1,1,2]^{2}$	$[2]^{2}$	$[1]^{2}$	$[14, 6, 0]$	$[2, 2]$	$z^6 + 1,z^2 + 1$	undefined
3.1.9.22a1.7	6	$x^{9} + 18 x^{7} + 3 x^{6} + 18 x^{5} + 3$	$(C_9:C_3):C_2$ (as 9T10)	$54$	$1$	$[2, 2, 3]^{2}$	$[1,1,2]^{2}$	$[2]^{2}$	$[1]^{2}$	$[14, 6, 0]$	$[2, 2]$	$z^6 + 1,z^2 + 1$	undefined
3.1.9.22a1.8	6	$x^{9} + 9 x^{8} + 18 x^{7} + 3 x^{6} + 18 x^{5} + 3$	$(C_9:C_3):C_2$ (as 9T10)	$54$	$1$	$[2, 2, 3]^{2}$	$[1,1,2]^{2}$	$[2]^{2}$	$[1]^{2}$	$[14, 6, 0]$	$[2, 2]$	$z^6 + 1,z^2 + 1$	undefined
3.1.9.22a1.9	6	$x^{9} + 18 x^{8} + 18 x^{7} + 3 x^{6} + 18 x^{5} + 3$	$(C_9:C_3):C_2$ (as 9T10)	$54$	$1$	$[2, 2, 3]^{2}$	$[1,1,2]^{2}$	$[2]^{2}$	$[1]^{2}$	$[14, 6, 0]$	$[2, 2]$	$z^6 + 1,z^2 + 1$	undefined
3.1.9.22a2.1	27	$x^{9} + 3 x^{6} + 9 x^{5} + 3$	$C_3 \wr S_3 $ (as 9T20)	$162$	$3$	$[2, 2, \frac{7}{3}, 3]^{2}$	$[1,1,\frac{4}{3},2]^{2}$	$[2,\frac{7}{3}]^{2}$	$[1,\frac{4}{3}]^{2}$	$[14, 6, 0]$	$[2, 1]$	$z^6 + 1,z^2 + 2$	undefined
3.1.9.22a2.2	27	$x^{9} + 3 x^{6} + 9 x^{5} + 30$	$C_3 \wr S_3 $ (as 9T20)	$162$	$3$	$[2, 2, \frac{7}{3}, 3]^{2}$	$[1,1,\frac{4}{3},2]^{2}$	$[2,\frac{7}{3}]^{2}$	$[1,\frac{4}{3}]^{2}$	$[14, 6, 0]$	$[2, 1]$	$z^6 + 1,z^2 + 2$	undefined
3.1.9.22a2.3	27	$x^{9} + 3 x^{6} + 9 x^{5} + 57$	$C_3 \wr S_3 $ (as 9T20)	$162$	$3$	$[2, 2, \frac{7}{3}, 3]^{2}$	$[1,1,\frac{4}{3},2]^{2}$	$[2,\frac{7}{3}]^{2}$	$[1,\frac{4}{3}]^{2}$	$[14, 6, 0]$	$[2, 1]$	$z^6 + 1,z^2 + 2$	undefined
3.1.9.22a2.4	27	$x^{9} + 9 x^{8} + 3 x^{6} + 9 x^{5} + 3$	$C_3 \wr S_3 $ (as 9T20)	$162$	$3$	$[2, 2, \frac{7}{3}, 3]^{2}$	$[1,1,\frac{4}{3},2]^{2}$	$[2,\frac{7}{3}]^{2}$	$[1,\frac{4}{3}]^{2}$	$[14, 6, 0]$	$[2, 1]$	$z^6 + 1,z^2 + 2$	undefined
3.1.9.22a2.5	27	$x^{9} + 9 x^{8} + 3 x^{6} + 9 x^{5} + 30$	$C_3 \wr S_3 $ (as 9T20)	$162$	$3$	$[2, 2, \frac{7}{3}, 3]^{2}$	$[1,1,\frac{4}{3},2]^{2}$	$[2,\frac{7}{3}]^{2}$	$[1,\frac{4}{3}]^{2}$	$[14, 6, 0]$	$[2, 1]$	$z^6 + 1,z^2 + 2$	undefined
3.1.9.22a2.6	27	$x^{9} + 9 x^{8} + 3 x^{6} + 9 x^{5} + 57$	$C_3 \wr S_3 $ (as 9T20)	$162$	$3$	$[2, 2, \frac{7}{3}, 3]^{2}$	$[1,1,\frac{4}{3},2]^{2}$	$[2,\frac{7}{3}]^{2}$	$[1,\frac{4}{3}]^{2}$	$[14, 6, 0]$	$[2, 1]$	$z^6 + 1,z^2 + 2$	undefined
3.1.9.22a2.7	27	$x^{9} + 18 x^{8} + 3 x^{6} + 9 x^{5} + 3$	$C_3 \wr S_3 $ (as 9T20)	$162$	$3$	$[2, 2, \frac{7}{3}, 3]^{2}$	$[1,1,\frac{4}{3},2]^{2}$	$[2,\frac{7}{3}]^{2}$	$[1,\frac{4}{3}]^{2}$	$[14, 6, 0]$	$[2, 1]$	$z^6 + 1,z^2 + 2$	undefined
3.1.9.22a2.8	27	$x^{9} + 18 x^{8} + 3 x^{6} + 9 x^{5} + 30$	$C_3 \wr S_3 $ (as 9T20)	$162$	$3$	$[2, 2, \frac{7}{3}, 3]^{2}$	$[1,1,\frac{4}{3},2]^{2}$	$[2,\frac{7}{3}]^{2}$	$[1,\frac{4}{3}]^{2}$	$[14, 6, 0]$	$[2, 1]$	$z^6 + 1,z^2 + 2$	undefined
3.1.9.22a2.9	27	$x^{9} + 18 x^{8} + 3 x^{6} + 9 x^{5} + 57$	$C_3 \wr S_3 $ (as 9T20)	$162$	$3$	$[2, 2, \frac{7}{3}, 3]^{2}$	$[1,1,\frac{4}{3},2]^{2}$	$[2,\frac{7}{3}]^{2}$	$[1,\frac{4}{3}]^{2}$	$[14, 6, 0]$	$[2, 1]$	$z^6 + 1,z^2 + 2$	undefined
3.1.9.22a2.10	27	$x^{9} + 9 x^{7} + 3 x^{6} + 9 x^{5} + 3$	$C_3 \wr S_3 $ (as 9T20)	$162$	$3$	$[2, 2, \frac{7}{3}, 3]^{2}$	$[1,1,\frac{4}{3},2]^{2}$	$[2,\frac{7}{3}]^{2}$	$[1,\frac{4}{3}]^{2}$	$[14, 6, 0]$	$[2, 1]$	$z^6 + 1,z^2 + 2$	undefined
3.1.9.22a2.11	27	$x^{9} + 9 x^{7} + 3 x^{6} + 9 x^{5} + 30$	$C_3 \wr S_3 $ (as 9T20)	$162$	$3$	$[2, 2, \frac{7}{3}, 3]^{2}$	$[1,1,\frac{4}{3},2]^{2}$	$[2,\frac{7}{3}]^{2}$	$[1,\frac{4}{3}]^{2}$	$[14, 6, 0]$	$[2, 1]$	$z^6 + 1,z^2 + 2$	undefined
3.1.9.22a2.12	27	$x^{9} + 9 x^{7} + 3 x^{6} + 9 x^{5} + 57$	$C_3 \wr S_3 $ (as 9T20)	$162$	$3$	$[2, 2, \frac{7}{3}, 3]^{2}$	$[1,1,\frac{4}{3},2]^{2}$	$[2,\frac{7}{3}]^{2}$	$[1,\frac{4}{3}]^{2}$	$[14, 6, 0]$	$[2, 1]$	$z^6 + 1,z^2 + 2$	undefined
3.1.9.22a2.13	27	$x^{9} + 9 x^{8} + 9 x^{7} + 3 x^{6} + 9 x^{5} + 3$	$C_3 \wr S_3 $ (as 9T20)	$162$	$3$	$[2, 2, \frac{7}{3}, 3]^{2}$	$[1,1,\frac{4}{3},2]^{2}$	$[2,\frac{7}{3}]^{2}$	$[1,\frac{4}{3}]^{2}$	$[14, 6, 0]$	$[2, 1]$	$z^6 + 1,z^2 + 2$	undefined
3.1.9.22a2.14	27	$x^{9} + 9 x^{8} + 9 x^{7} + 3 x^{6} + 9 x^{5} + 30$	$C_3 \wr S_3 $ (as 9T20)	$162$	$3$	$[2, 2, \frac{7}{3}, 3]^{2}$	$[1,1,\frac{4}{3},2]^{2}$	$[2,\frac{7}{3}]^{2}$	$[1,\frac{4}{3}]^{2}$	$[14, 6, 0]$	$[2, 1]$	$z^6 + 1,z^2 + 2$	undefined
3.1.9.22a2.15	27	$x^{9} + 9 x^{8} + 9 x^{7} + 3 x^{6} + 9 x^{5} + 57$	$C_3 \wr S_3 $ (as 9T20)	$162$	$3$	$[2, 2, \frac{7}{3}, 3]^{2}$	$[1,1,\frac{4}{3},2]^{2}$	$[2,\frac{7}{3}]^{2}$	$[1,\frac{4}{3}]^{2}$	$[14, 6, 0]$	$[2, 1]$	$z^6 + 1,z^2 + 2$	undefined
3.1.9.22a2.16	27	$x^{9} + 18 x^{8} + 9 x^{7} + 3 x^{6} + 9 x^{5} + 3$	$C_3 \wr S_3 $ (as 9T20)	$162$	$3$	$[2, 2, \frac{7}{3}, 3]^{2}$	$[1,1,\frac{4}{3},2]^{2}$	$[2,\frac{7}{3}]^{2}$	$[1,\frac{4}{3}]^{2}$	$[14, 6, 0]$	$[2, 1]$	$z^6 + 1,z^2 + 2$	undefined
3.1.9.22a2.17	27	$x^{9} + 18 x^{8} + 9 x^{7} + 3 x^{6} + 9 x^{5} + 30$	$C_3 \wr S_3 $ (as 9T20)	$162$	$3$	$[2, 2, \frac{7}{3}, 3]^{2}$	$[1,1,\frac{4}{3},2]^{2}$	$[2,\frac{7}{3}]^{2}$	$[1,\frac{4}{3}]^{2}$	$[14, 6, 0]$	$[2, 1]$	$z^6 + 1,z^2 + 2$	undefined
3.1.9.22a2.18	27	$x^{9} + 18 x^{8} + 9 x^{7} + 3 x^{6} + 9 x^{5} + 57$	$C_3 \wr S_3 $ (as 9T20)	$162$	$3$	$[2, 2, \frac{7}{3}, 3]^{2}$	$[1,1,\frac{4}{3},2]^{2}$	$[2,\frac{7}{3}]^{2}$	$[1,\frac{4}{3}]^{2}$	$[14, 6, 0]$	$[2, 1]$	$z^6 + 1,z^2 + 2$	undefined
3.1.9.22a2.19	27	$x^{9} + 18 x^{7} + 3 x^{6} + 9 x^{5} + 3$	$C_3 \wr S_3 $ (as 9T20)	$162$	$3$	$[2, 2, \frac{7}{3}, 3]^{2}$	$[1,1,\frac{4}{3},2]^{2}$	$[2,\frac{7}{3}]^{2}$	$[1,\frac{4}{3}]^{2}$	$[14, 6, 0]$	$[2, 1]$	$z^6 + 1,z^2 + 2$	undefined
3.1.9.22a2.20	27	$x^{9} + 18 x^{7} + 3 x^{6} + 9 x^{5} + 30$	$C_3 \wr S_3 $ (as 9T20)	$162$	$3$	$[2, 2, \frac{7}{3}, 3]^{2}$	$[1,1,\frac{4}{3},2]^{2}$	$[2,\frac{7}{3}]^{2}$	$[1,\frac{4}{3}]^{2}$	$[14, 6, 0]$	$[2, 1]$	$z^6 + 1,z^2 + 2$	undefined
3.1.9.22a2.21	27	$x^{9} + 18 x^{7} + 3 x^{6} + 9 x^{5} + 57$	$C_3 \wr S_3 $ (as 9T20)	$162$	$3$	$[2, 2, \frac{7}{3}, 3]^{2}$	$[1,1,\frac{4}{3},2]^{2}$	$[2,\frac{7}{3}]^{2}$	$[1,\frac{4}{3}]^{2}$	$[14, 6, 0]$	$[2, 1]$	$z^6 + 1,z^2 + 2$	undefined
3.1.9.22a2.22	27	$x^{9} + 9 x^{8} + 18 x^{7} + 3 x^{6} + 9 x^{5} + 3$	$C_3 \wr S_3 $ (as 9T20)	$162$	$3$	$[2, 2, \frac{7}{3}, 3]^{2}$	$[1,1,\frac{4}{3},2]^{2}$	$[2,\frac{7}{3}]^{2}$	$[1,\frac{4}{3}]^{2}$	$[14, 6, 0]$	$[2, 1]$	$z^6 + 1,z^2 + 2$	undefined
3.1.9.22a2.23	27	$x^{9} + 9 x^{8} + 18 x^{7} + 3 x^{6} + 9 x^{5} + 30$	$C_3 \wr S_3 $ (as 9T20)	$162$	$3$	$[2, 2, \frac{7}{3}, 3]^{2}$	$[1,1,\frac{4}{3},2]^{2}$	$[2,\frac{7}{3}]^{2}$	$[1,\frac{4}{3}]^{2}$	$[14, 6, 0]$	$[2, 1]$	$z^6 + 1,z^2 + 2$	undefined
3.1.9.22a2.24	27	$x^{9} + 9 x^{8} + 18 x^{7} + 3 x^{6} + 9 x^{5} + 57$	$C_3 \wr S_3 $ (as 9T20)	$162$	$3$	$[2, 2, \frac{7}{3}, 3]^{2}$	$[1,1,\frac{4}{3},2]^{2}$	$[2,\frac{7}{3}]^{2}$	$[1,\frac{4}{3}]^{2}$	$[14, 6, 0]$	$[2, 1]$	$z^6 + 1,z^2 + 2$	undefined
3.1.9.22a2.25	27	$x^{9} + 18 x^{8} + 18 x^{7} + 3 x^{6} + 9 x^{5} + 3$	$C_3 \wr S_3 $ (as 9T20)	$162$	$3$	$[2, 2, \frac{7}{3}, 3]^{2}$	$[1,1,\frac{4}{3},2]^{2}$	$[2,\frac{7}{3}]^{2}$	$[1,\frac{4}{3}]^{2}$	$[14, 6, 0]$	$[2, 1]$	$z^6 + 1,z^2 + 2$	undefined
3.1.9.22a2.26	27	$x^{9} + 18 x^{8} + 18 x^{7} + 3 x^{6} + 9 x^{5} + 30$	$C_3 \wr S_3 $ (as 9T20)	$162$	$3$	$[2, 2, \frac{7}{3}, 3]^{2}$	$[1,1,\frac{4}{3},2]^{2}$	$[2,\frac{7}{3}]^{2}$	$[1,\frac{4}{3}]^{2}$	$[14, 6, 0]$	$[2, 1]$	$z^6 + 1,z^2 + 2$	undefined
3.1.9.22a2.27	27	$x^{9} + 18 x^{8} + 18 x^{7} + 3 x^{6} + 9 x^{5} + 57$	$C_3 \wr S_3 $ (as 9T20)	$162$	$3$	$[2, 2, \frac{7}{3}, 3]^{2}$	$[1,1,\frac{4}{3},2]^{2}$	$[2,\frac{7}{3}]^{2}$	$[1,\frac{4}{3}]^{2}$	$[14, 6, 0]$	$[2, 1]$	$z^6 + 1,z^2 + 2$	undefined
3.1.9.22a3.1	18	$x^{9} + 6 x^{6} + 18 x^{5} + 3$	$C_3 \wr C_3 $ (as 9T17)	$81$	$3$	$[2, 2, 3]^{3}$	$[1,1,2]^{3}$	$[2]^{3}$	$[1]^{3}$	$[14, 6, 0]$	$[1, 1]$	$z^6 + 2,2 z^2 + 1$	undefined
3.1.9.22a3.2	18	$x^{9} + 6 x^{6} + 18 x^{5} + 30$	$C_3 \wr C_3 $ (as 9T17)	$81$	$3$	$[2, 2, 3]^{3}$	$[1,1,2]^{3}$	$[2]^{3}$	$[1]^{3}$	$[14, 6, 0]$	$[1, 1]$	$z^6 + 2,2 z^2 + 1$	undefined
3.1.9.22a3.3	18	$x^{9} + 9 x^{8} + 6 x^{6} + 18 x^{5} + 3$	$C_3 \wr C_3 $ (as 9T17)	$81$	$3$	$[2, 2, 3]^{3}$	$[1,1,2]^{3}$	$[2]^{3}$	$[1]^{3}$	$[14, 6, 0]$	$[1, 1]$	$z^6 + 2,2 z^2 + 1$	undefined
3.1.9.22a3.4	6	$x^{9} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 3$	$C_9:C_3$ (as 9T6)	$27$	$3$	$[2, 3]^{3}$	$[1,2]^{3}$	$[\ ]^{3}$	$[\ ]^{3}$	$[14, 6, 0]$	$[1, 1]$	$z^6 + 2,2 z^2 + 1$	undefined
3.1.9.22a3.5	6	$x^{9} + 9 x^{8} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 3$	$C_9:C_3$ (as 9T6)	$27$	$3$	$[2, 3]^{3}$	$[1,2]^{3}$	$[\ ]^{3}$	$[\ ]^{3}$	$[14, 6, 0]$	$[1, 1]$	$z^6 + 2,2 z^2 + 1$	undefined
3.1.9.22a3.6	9	$x^{9} + 18 x^{8} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 3$	$C_9$ (as 9T1)	$9$	$9$	$[2, 3]$	$[1,2]$	$[\ ]$	$[\ ]$	$[14, 6, 0]$	$[1, 1]$	$z^6 + 2,2 z^2 + 1$	undefined
3.1.9.22a3.7	9	$x^{9} + 18 x^{8} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 30$	$C_9$ (as 9T1)	$9$	$9$	$[2, 3]$	$[1,2]$	$[\ ]$	$[\ ]$	$[14, 6, 0]$	$[1, 1]$	$z^6 + 2,2 z^2 + 1$	undefined
3.1.9.22a3.8	9	$x^{9} + 18 x^{8} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 57$	$C_9$ (as 9T1)	$9$	$9$	$[2, 3]$	$[1,2]$	$[\ ]$	$[\ ]$	$[14, 6, 0]$	$[1, 1]$	$z^6 + 2,2 z^2 + 1$	undefined
3.1.9.22a3.9	18	$x^{9} + 18 x^{7} + 6 x^{6} + 18 x^{5} + 3$	$C_3 \wr C_3 $ (as 9T17)	$81$	$3$	$[2, 2, 3]^{3}$	$[1,1,2]^{3}$	$[2]^{3}$	$[1]^{3}$	$[14, 6, 0]$	$[1, 1]$	$z^6 + 2,2 z^2 + 1$	undefined
3.1.9.22a3.10	18	$x^{9} + 18 x^{7} + 6 x^{6} + 18 x^{5} + 30$	$C_3 \wr C_3 $ (as 9T17)	$81$	$3$	$[2, 2, 3]^{3}$	$[1,1,2]^{3}$	$[2]^{3}$	$[1]^{3}$	$[14, 6, 0]$	$[1, 1]$	$z^6 + 2,2 z^2 + 1$	undefined
3.1.9.22a3.11	18	$x^{9} + 9 x^{8} + 18 x^{7} + 6 x^{6} + 18 x^{5} + 3$	$C_3 \wr C_3 $ (as 9T17)	$81$	$3$	$[2, 2, 3]^{3}$	$[1,1,2]^{3}$	$[2]^{3}$	$[1]^{3}$	$[14, 6, 0]$	$[1, 1]$	$z^6 + 2,2 z^2 + 1$	undefined
3.1.9.22a3.12	18	$x^{9} + 6 x^{6} + 18 x^{5} + 12$	$C_3 \wr C_3 $ (as 9T17)	$81$	$3$	$[2, 2, 3]^{3}$	$[1,1,2]^{3}$	$[2]^{3}$	$[1]^{3}$	$[14, 6, 0]$	$[1, 1]$	$z^6 + 2,2 z^2 + 1$	undefined
3.1.9.22a3.13	18	$x^{9} + 18 x^{8} + 6 x^{6} + 18 x^{5} + 12$	$C_3 \wr C_3 $ (as 9T17)	$81$	$3$	$[2, 2, 3]^{3}$	$[1,1,2]^{3}$	$[2]^{3}$	$[1]^{3}$	$[14, 6, 0]$	$[1, 1]$	$z^6 + 2,2 z^2 + 1$	undefined
3.1.9.22a3.14	18	$x^{9} + 18 x^{8} + 6 x^{6} + 18 x^{5} + 39$	$C_3 \wr C_3 $ (as 9T17)	$81$	$3$	$[2, 2, 3]^{3}$	$[1,1,2]^{3}$	$[2]^{3}$	$[1]^{3}$	$[14, 6, 0]$	$[1, 1]$	$z^6 + 2,2 z^2 + 1$	undefined

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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	3.1.9.22a
Base	3.1.1.0a1.1
Degree	\(9\)
e	\(9\)
f	\(1\)
c	\(22\)

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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.