LMFDB - $p$-adic family 5.3.5.24a

Defining polynomial over unramified subextension

$x^{5} + 5 a_{4} x^{4} + 25 c_{5} + 5$

Invariants

Residue field characteristic:	$5$
Degree:	$15$
Base field:	$\Q_{5}$
Ramification index $e$:	$5$
Residue field degree $f$:	$3$
Discriminant exponent $c$:	$24$
Artin slopes:	$[2]$
Swan slopes:	$[1]$
Means:	$\langle\frac{4}{5}\rangle$
Rams:	$(1)$
Field count:	$88$ (complete)
Ambiguity:	$15$
Mass:	$124$
Absolute Mass:	$124/3$

Diagrams

Varying

Indices of inseparability:	$[4,0]$
Associated inertia:	$[1]$ (show 55), $[2]$ (show 11), $[4]$ (show 22)
Jump Set:	undefined

Galois groups and Hidden Artin slopes

Select desired size of Galois group.

		Galois groups of order 15
		$C_{15}$ (as 15T1)
hidden slopes	$[\ ]$	5

		Galois groups of order 30
		$C_3\times D_5$ (as 15T3)
hidden slopes	$[\ ]^{2}$	1

		Galois groups of order 60
		$C_3\times F_5$ (as 15T8)
hidden slopes	$[\ ]^{4}$	2

		Galois groups of order 75
		$C_5^2:C_3$ (as 15T9)
hidden slopes	$[2]$	2

		Galois groups of order 150
		$C_5^2:C_6$ (as 15T12)
hidden slopes	$[2]^{2}$	2

		Galois groups of order 300
		$C_5^2:C_{12}$ (as 15T19)
hidden slopes	$[2]^{4}$	4

		Galois groups of order 375
		$C_5\wr C_3$ (as 15T25)
hidden slopes	$[2,2]$	40

$[2]^{5}$	8

Total	48

		Galois groups of order 750
		$C_5^3:C_6$ (as 15T30)
hidden slopes	$[2,2]^{2}$	8

		Galois groups of order 1500
		$C_5^3:C_{12}$ (as 15T38)
hidden slopes	$[2,2]^{4}$	16

Fields

Galois group	Galois Artin	Indices

Assoc. Inertia	Jump Set	Fields per packet

Sort order	Select

Showing 1-50 of 88

Next Download displayed columns for results to

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
5.3.5.24a1.1	1	$( x^{3} + 3 x + 3 )^{5} + 5 ( x^{3} + 3 x + 3 )^{4} + 5$	$D_5\times C_3$ (as 15T3)	$30$	$3$	$[2]^{6}$	$[1]^{6}$	$[\ ]^{2}$	$[\ ]^{2}$	$[4, 0]$	$[2]$	$z^4 + (4 t^2 + 3 t + 3)$	undefined
5.3.5.24a2.1	1	$( x^{3} + 3 x + 3 )^{5} + 10 ( x^{3} + 3 x + 3 )^{4} + 5$	$F_5\times C_3$ (as 15T8)	$60$	$3$	$[2]^{12}$	$[1]^{12}$	$[\ ]^{4}$	$[\ ]^{4}$	$[4, 0]$	$[4]$	$z^4 + (3 t^2 + t + 1)$	undefined
5.3.5.24a3.1	1	$( x^{3} + 3 x + 3 )^{5} + 15 ( x^{3} + 3 x + 3 )^{4} + 5$	$F_5\times C_3$ (as 15T8)	$60$	$3$	$[2]^{12}$	$[1]^{12}$	$[\ ]^{4}$	$[\ ]^{4}$	$[4, 0]$	$[4]$	$z^4 + (2 t^2 + 4 t + 4)$	undefined
5.3.5.24a4.1	5	$( x^{3} + 3 x + 3 )^{5} + 20 ( x^{3} + 3 x + 3 )^{4} + 5$	$C_{15}$ (as 15T1)	$15$	$15$	$[2]^{3}$	$[1]^{3}$	$[\ ]$	$[\ ]$	$[4, 0]$	$[1]$	$z^4 + (t^2 + 2 t + 2)$	undefined
5.3.5.24a4.2	5	$( x^{3} + 3 x + 3 )^{5} + 20 ( x^{3} + 3 x + 3 )^{4} + 30$	$C_{15}$ (as 15T1)	$15$	$15$	$[2]^{3}$	$[1]^{3}$	$[\ ]$	$[\ ]$	$[4, 0]$	$[1]$	$z^4 + (t^2 + 2 t + 2)$	undefined
5.3.5.24a4.3	5	$( x^{3} + 3 x + 3 )^{5} + 20 ( x^{3} + 3 x + 3 )^{4} + 55$	$C_{15}$ (as 15T1)	$15$	$15$	$[2]^{3}$	$[1]^{3}$	$[\ ]$	$[\ ]$	$[4, 0]$	$[1]$	$z^4 + (t^2 + 2 t + 2)$	undefined
5.3.5.24a4.4	5	$( x^{3} + 3 x + 3 )^{5} + 20 ( x^{3} + 3 x + 3 )^{4} + 80$	$C_{15}$ (as 15T1)	$15$	$15$	$[2]^{3}$	$[1]^{3}$	$[\ ]$	$[\ ]$	$[4, 0]$	$[1]$	$z^4 + (t^2 + 2 t + 2)$	undefined
5.3.5.24a4.5	5	$( x^{3} + 3 x + 3 )^{5} + 20 ( x^{3} + 3 x + 3 )^{4} + 105$	$C_{15}$ (as 15T1)	$15$	$15$	$[2]^{3}$	$[1]^{3}$	$[\ ]$	$[\ ]$	$[4, 0]$	$[1]$	$z^4 + (t^2 + 2 t + 2)$	undefined
5.3.5.24a5.1	1	$( x^{3} + 3 x + 3 )^{5} + 5 x ( x^{3} + 3 x + 3 )^{4} + 5$	$(C_5^2 : C_4):C_3$ (as 15T19)	$300$	$1$	$[2, 2]^{12}$	$[1,1]^{12}$	$[2]^{4}$	$[1]^{4}$	$[4, 0]$	$[4]$	$z^4 + (3 t^2 + t + 3)$	undefined
5.3.5.24a6.1	1	$( x^{3} + 3 x + 3 )^{5} + 10 x ( x^{3} + 3 x + 3 )^{4} + 5$	$(C_5^2 : C_3):C_2$ (as 15T12)	$150$	$1$	$[2, 2]^{6}$	$[1,1]^{6}$	$[2]^{2}$	$[1]^{2}$	$[4, 0]$	$[2]$	$z^4 + (t^2 + 2 t + 1)$	undefined
5.3.5.24a7.1	1	$( x^{3} + 3 x + 3 )^{5} + \left(10 x + 10\right) ( x^{3} + 3 x + 3 )^{4} + 5$	$C_5^3:C_{12}$ (as 15T38)	$1500$	$1$	$[2, 2, 2]^{12}$	$[1,1,1]^{12}$	$[2,2]^{4}$	$[1,1]^{4}$	$[4, 0]$	$[4]$	$z^4 + (4 t^2 + 3 t + 2)$	undefined
5.3.5.24a8.1	4	$( x^{3} + 3 x + 3 )^{5} + 15 x ( x^{3} + 3 x + 3 )^{4} + 5$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2]^{15}$	$[1,1]^{15}$	$[2]^{5}$	$[1]^{5}$	$[4, 0]$	$[1]$	$z^4 + (4 t^2 + 3 t + 4)$	undefined
5.3.5.24a8.2	4	$( x^{3} + 3 x + 3 )^{5} + 15 x ( x^{3} + 3 x + 3 )^{4} + 25 x^{2} + 5$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2]^{15}$	$[1,1]^{15}$	$[2]^{5}$	$[1]^{5}$	$[4, 0]$	$[1]$	$z^4 + (4 t^2 + 3 t + 4)$	undefined
5.3.5.24a8.3	4	$( x^{3} + 3 x + 3 )^{5} + 15 x ( x^{3} + 3 x + 3 )^{4} + 50 x^{2} + 5$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2]^{15}$	$[1,1]^{15}$	$[2]^{5}$	$[1]^{5}$	$[4, 0]$	$[1]$	$z^4 + (4 t^2 + 3 t + 4)$	undefined
5.3.5.24a8.4	4	$( x^{3} + 3 x + 3 )^{5} + 15 x ( x^{3} + 3 x + 3 )^{4} + 75 x^{2} + 5$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2]^{15}$	$[1,1]^{15}$	$[2]^{5}$	$[1]^{5}$	$[4, 0]$	$[1]$	$z^4 + (4 t^2 + 3 t + 4)$	undefined
5.3.5.24a8.5	1	$( x^{3} + 3 x + 3 )^{5} + 15 x ( x^{3} + 3 x + 3 )^{4} + 100 x^{2} + 5$	$C_5^2 : C_3$ (as 15T9)	$75$	$5$	$[2, 2]^{3}$	$[1,1]^{3}$	$[2]$	$[1]$	$[4, 0]$	$[1]$	$z^4 + (4 t^2 + 3 t + 4)$	undefined
5.3.5.24a9.1	1	$( x^{3} + 3 x + 3 )^{5} + 20 x ( x^{3} + 3 x + 3 )^{4} + 5$	$(C_5^2 : C_4):C_3$ (as 15T19)	$300$	$1$	$[2, 2]^{12}$	$[1,1]^{12}$	$[2]^{4}$	$[1]^{4}$	$[4, 0]$	$[4]$	$z^4 + (2 t^2 + 4 t + 2)$	undefined
5.3.5.24a10.1	5	$( x^{3} + 3 x + 3 )^{5} + \left(20 x + 15\right) ( x^{3} + 3 x + 3 )^{4} + 5$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2, 2]^{3}$	$[1,1,1]^{3}$	$[2,2]$	$[1,1]$	$[4, 0]$	$[1]$	$z^4 + (4 t^2 + 3 t + 1)$	undefined
5.3.5.24a10.2	5	$( x^{3} + 3 x + 3 )^{5} + \left(20 x + 15\right) ( x^{3} + 3 x + 3 )^{4} + 30$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2, 2]^{3}$	$[1,1,1]^{3}$	$[2,2]$	$[1,1]$	$[4, 0]$	$[1]$	$z^4 + (4 t^2 + 3 t + 1)$	undefined
5.3.5.24a10.3	5	$( x^{3} + 3 x + 3 )^{5} + \left(20 x + 15\right) ( x^{3} + 3 x + 3 )^{4} + 55$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2, 2]^{3}$	$[1,1,1]^{3}$	$[2,2]$	$[1,1]$	$[4, 0]$	$[1]$	$z^4 + (4 t^2 + 3 t + 1)$	undefined
5.3.5.24a10.4	5	$( x^{3} + 3 x + 3 )^{5} + \left(20 x + 15\right) ( x^{3} + 3 x + 3 )^{4} + 80$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2, 2]^{3}$	$[1,1,1]^{3}$	$[2,2]$	$[1,1]$	$[4, 0]$	$[1]$	$z^4 + (4 t^2 + 3 t + 1)$	undefined
5.3.5.24a10.5	5	$( x^{3} + 3 x + 3 )^{5} + \left(20 x + 15\right) ( x^{3} + 3 x + 3 )^{4} + 105$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2, 2]^{3}$	$[1,1,1]^{3}$	$[2,2]$	$[1,1]$	$[4, 0]$	$[1]$	$z^4 + (4 t^2 + 3 t + 1)$	undefined
5.3.5.24a11.1	5	$( x^{3} + 3 x + 3 )^{5} + \left(20 x + 20\right) ( x^{3} + 3 x + 3 )^{4} + 5$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2, 2]^{3}$	$[1,1,1]^{3}$	$[2,2]$	$[1,1]$	$[4, 0]$	$[1]$	$z^4 + (3 t^2 + t + 4)$	undefined
5.3.5.24a11.2	5	$( x^{3} + 3 x + 3 )^{5} + \left(20 x + 20\right) ( x^{3} + 3 x + 3 )^{4} + 30$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2, 2]^{3}$	$[1,1,1]^{3}$	$[2,2]$	$[1,1]$	$[4, 0]$	$[1]$	$z^4 + (3 t^2 + t + 4)$	undefined
5.3.5.24a11.3	5	$( x^{3} + 3 x + 3 )^{5} + \left(20 x + 20\right) ( x^{3} + 3 x + 3 )^{4} + 55$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2, 2]^{3}$	$[1,1,1]^{3}$	$[2,2]$	$[1,1]$	$[4, 0]$	$[1]$	$z^4 + (3 t^2 + t + 4)$	undefined
5.3.5.24a11.4	5	$( x^{3} + 3 x + 3 )^{5} + \left(20 x + 20\right) ( x^{3} + 3 x + 3 )^{4} + 80$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2, 2]^{3}$	$[1,1,1]^{3}$	$[2,2]$	$[1,1]$	$[4, 0]$	$[1]$	$z^4 + (3 t^2 + t + 4)$	undefined
5.3.5.24a11.5	5	$( x^{3} + 3 x + 3 )^{5} + \left(20 x + 20\right) ( x^{3} + 3 x + 3 )^{4} + 105$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2, 2]^{3}$	$[1,1,1]^{3}$	$[2,2]$	$[1,1]$	$[4, 0]$	$[1]$	$z^4 + (3 t^2 + t + 4)$	undefined
5.3.5.24a12.1	5	$( x^{3} + 3 x + 3 )^{5} + 5 x^{2} ( x^{3} + 3 x + 3 )^{4} + 5$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2, 2]^{3}$	$[1,1,1]^{3}$	$[2,2]$	$[1,1]$	$[4, 0]$	$[1]$	$z^4 + (t^2 + 4 t + 1)$	undefined
5.3.5.24a12.2	5	$( x^{3} + 3 x + 3 )^{5} + 5 x^{2} ( x^{3} + 3 x + 3 )^{4} + 30$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2, 2]^{3}$	$[1,1,1]^{3}$	$[2,2]$	$[1,1]$	$[4, 0]$	$[1]$	$z^4 + (t^2 + 4 t + 1)$	undefined
5.3.5.24a12.3	5	$( x^{3} + 3 x + 3 )^{5} + 5 x^{2} ( x^{3} + 3 x + 3 )^{4} + 55$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2, 2]^{3}$	$[1,1,1]^{3}$	$[2,2]$	$[1,1]$	$[4, 0]$	$[1]$	$z^4 + (t^2 + 4 t + 1)$	undefined
5.3.5.24a12.4	5	$( x^{3} + 3 x + 3 )^{5} + 5 x^{2} ( x^{3} + 3 x + 3 )^{4} + 80$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2, 2]^{3}$	$[1,1,1]^{3}$	$[2,2]$	$[1,1]$	$[4, 0]$	$[1]$	$z^4 + (t^2 + 4 t + 1)$	undefined
5.3.5.24a12.5	5	$( x^{3} + 3 x + 3 )^{5} + 5 x^{2} ( x^{3} + 3 x + 3 )^{4} + 105$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2, 2]^{3}$	$[1,1,1]^{3}$	$[2,2]$	$[1,1]$	$[4, 0]$	$[1]$	$z^4 + (t^2 + 4 t + 1)$	undefined
5.3.5.24a13.1	1	$( x^{3} + 3 x + 3 )^{5} + \left(5 x^{2} + 5 x + 5\right) ( x^{3} + 3 x + 3 )^{4} + 5$	$C_5^3:C_{12}$ (as 15T38)	$1500$	$1$	$[2, 2, 2]^{12}$	$[1,1,1]^{12}$	$[2,2]^{4}$	$[1,1]^{4}$	$[4, 0]$	$[4]$	$z^4 + (3 t^2 + 3 t + 2)$	undefined
5.3.5.24a14.1	1	$( x^{3} + 3 x + 3 )^{5} + \left(5 x^{2} + 10 x + 5\right) ( x^{3} + 3 x + 3 )^{4} + 5$	$C_5^3:C_6$ (as 15T30)	$750$	$1$	$[2, 2, 2]^{6}$	$[1,1,1]^{6}$	$[2,2]^{2}$	$[1,1]^{2}$	$[4, 0]$	$[2]$	$z^4 + (t^2 + 4 t)$	undefined
5.3.5.24a15.1	1	$( x^{3} + 3 x + 3 )^{5} + \left(5 x^{2} + 15 x + 10\right) ( x^{3} + 3 x + 3 )^{4} + 5$	$C_5^3:C_6$ (as 15T30)	$750$	$1$	$[2, 2, 2]^{6}$	$[1,1,1]^{6}$	$[2,2]^{2}$	$[1,1]^{2}$	$[4, 0]$	$[2]$	$z^4 + (3 t^2 + 3 t + 1)$	undefined
5.3.5.24a16.1	1	$( x^{3} + 3 x + 3 )^{5} + \left(5 x^{2} + 15 x + 15\right) ( x^{3} + 3 x + 3 )^{4} + 5$	$C_5^3:C_{12}$ (as 15T38)	$1500$	$1$	$[2, 2, 2]^{12}$	$[1,1,1]^{12}$	$[2,2]^{4}$	$[1,1]^{4}$	$[4, 0]$	$[4]$	$z^4 + (2 t^2 + t + 4)$	undefined
5.3.5.24a17.1	5	$( x^{3} + 3 x + 3 )^{5} + \left(5 x^{2} + 20 x + 5\right) ( x^{3} + 3 x + 3 )^{4} + 5$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2, 2]^{3}$	$[1,1,1]^{3}$	$[2,2]$	$[1,1]$	$[4, 0]$	$[1]$	$z^4 + (2 t^2 + t + 1)$	undefined
5.3.5.24a17.2	5	$( x^{3} + 3 x + 3 )^{5} + \left(5 x^{2} + 20 x + 5\right) ( x^{3} + 3 x + 3 )^{4} + 30$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2, 2]^{3}$	$[1,1,1]^{3}$	$[2,2]$	$[1,1]$	$[4, 0]$	$[1]$	$z^4 + (2 t^2 + t + 1)$	undefined
5.3.5.24a17.3	5	$( x^{3} + 3 x + 3 )^{5} + \left(5 x^{2} + 20 x + 5\right) ( x^{3} + 3 x + 3 )^{4} + 55$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2, 2]^{3}$	$[1,1,1]^{3}$	$[2,2]$	$[1,1]$	$[4, 0]$	$[1]$	$z^4 + (2 t^2 + t + 1)$	undefined
5.3.5.24a17.4	5	$( x^{3} + 3 x + 3 )^{5} + \left(5 x^{2} + 20 x + 5\right) ( x^{3} + 3 x + 3 )^{4} + 80$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2, 2]^{3}$	$[1,1,1]^{3}$	$[2,2]$	$[1,1]$	$[4, 0]$	$[1]$	$z^4 + (2 t^2 + t + 1)$	undefined
5.3.5.24a17.5	5	$( x^{3} + 3 x + 3 )^{5} + \left(5 x^{2} + 20 x + 5\right) ( x^{3} + 3 x + 3 )^{4} + 105$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2, 2]^{3}$	$[1,1,1]^{3}$	$[2,2]$	$[1,1]$	$[4, 0]$	$[1]$	$z^4 + (2 t^2 + t + 1)$	undefined
5.3.5.24a18.1	1	$( x^{3} + 3 x + 3 )^{5} + 10 x^{2} ( x^{3} + 3 x + 3 )^{4} + 5$	$C_5^3:C_{12}$ (as 15T38)	$1500$	$1$	$[2, 2, 2]^{12}$	$[1,1,1]^{12}$	$[2,2]^{4}$	$[1,1]^{4}$	$[4, 0]$	$[4]$	$z^4 + (2 t^2 + 3 t + 2)$	undefined
5.3.5.24a19.1	5	$( x^{3} + 3 x + 3 )^{5} + \left(10 x^{2} + 5 x + 5\right) ( x^{3} + 3 x + 3 )^{4} + 5$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2, 2]^{3}$	$[1,1,1]^{3}$	$[2,2]$	$[1,1]$	$[4, 0]$	$[1]$	$z^4 + (4 t^2 + 2 t + 3)$	undefined
5.3.5.24a19.2	5	$( x^{3} + 3 x + 3 )^{5} + \left(10 x^{2} + 5 x + 5\right) ( x^{3} + 3 x + 3 )^{4} + 30$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2, 2]^{3}$	$[1,1,1]^{3}$	$[2,2]$	$[1,1]$	$[4, 0]$	$[1]$	$z^4 + (4 t^2 + 2 t + 3)$	undefined
5.3.5.24a19.3	5	$( x^{3} + 3 x + 3 )^{5} + \left(10 x^{2} + 5 x + 5\right) ( x^{3} + 3 x + 3 )^{4} + 55$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2, 2]^{3}$	$[1,1,1]^{3}$	$[2,2]$	$[1,1]$	$[4, 0]$	$[1]$	$z^4 + (4 t^2 + 2 t + 3)$	undefined
5.3.5.24a19.4	5	$( x^{3} + 3 x + 3 )^{5} + \left(10 x^{2} + 5 x + 5\right) ( x^{3} + 3 x + 3 )^{4} + 80$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2, 2]^{3}$	$[1,1,1]^{3}$	$[2,2]$	$[1,1]$	$[4, 0]$	$[1]$	$z^4 + (4 t^2 + 2 t + 3)$	undefined
5.3.5.24a19.5	5	$( x^{3} + 3 x + 3 )^{5} + \left(10 x^{2} + 5 x + 5\right) ( x^{3} + 3 x + 3 )^{4} + 105$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2, 2]^{3}$	$[1,1,1]^{3}$	$[2,2]$	$[1,1]$	$[4, 0]$	$[1]$	$z^4 + (4 t^2 + 2 t + 3)$	undefined
5.3.5.24a20.1	1	$( x^{3} + 3 x + 3 )^{5} + \left(10 x^{2} + 10 x\right) ( x^{3} + 3 x + 3 )^{4} + 5$	$C_5^3:C_6$ (as 15T30)	$750$	$1$	$[2, 2, 2]^{6}$	$[1,1,1]^{6}$	$[2,2]^{2}$	$[1,1]^{2}$	$[4, 0]$	$[2]$	$z^4 + (3 t^2 + 3)$	undefined
5.3.5.24a21.1	1	$( x^{3} + 3 x + 3 )^{5} + \left(10 x^{2} + 10 x + 15\right) ( x^{3} + 3 x + 3 )^{4} + 5$	$C_5^3:C_{12}$ (as 15T38)	$1500$	$1$	$[2, 2, 2]^{12}$	$[1,1,1]^{12}$	$[2,2]^{4}$	$[1,1]^{4}$	$[4, 0]$	$[4]$	$z^4 + (4 t + 2)$	undefined
5.3.5.24a22.1	5	$( x^{3} + 3 x + 3 )^{5} + \left(10 x^{2} + 10 x + 20\right) ( x^{3} + 3 x + 3 )^{4} + 5$	$C_5\wr C_3$ (as 15T25)	$375$	$5$	$[2, 2, 2]^{3}$	$[1,1,1]^{3}$	$[2,2]$	$[1,1]$	$[4, 0]$	$[1]$	$z^4 + (4 t^2 + 2 t)$	undefined

Next Download displayed columns for results to

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	5.3.5.24a
Base	5.1.1.0a1.1
Degree	\(15\)
e	\(5\)
f	\(3\)
c	\(24\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Defining polynomial over unramified subextension

Invariants

Diagrams

Varying

Galois groups and Hidden Artin slopes

Fields

Showing 1-50 of 88

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