$p$-adic family 5.1.15.27a

• Label: 5.1.15.27a
• Base: 5.1.1.0a1.1
• Degree: \(15\)
• e: \(15\)
• f: \(1\)
• c: \(27\)

Defining polynomial

$x^{15} + 5 b_{14} x^{14} + 5 a_{13} x^{13} + 25 b_{16} x + 5$

Invariants

Residue field characteristic:	$5$
Degree:	$15$
Base field:	$\Q_{5}$
Ramification index $e$:	$15$
Residue field degree $f$:	$1$
Discriminant exponent $c$:	$27$
Artin slopes:	$[\frac{25}{12}]$
Swan slopes:	$[\frac{13}{12}]$
Means:	$\langle\frac{13}{15}\rangle$
Rams:	$(\frac{13}{4})$
Field count:	$100$ (complete)
Ambiguity:	$1$
Mass:	$100$
Absolute Mass:	$100$

Diagrams

Varying

Indices of inseparability:	$[13,0]$
Associated inertia:	$[2,1]$
Jump Set:	undefined

Galois groups and Hidden Artin slopes

Select desired size of Galois group.

		Galois groups of order 600
		$C_5^2:(C_4\times S_3)$ (as 15T27)
hidden slopes	$[\frac{25}{12}]^{2}_{4}$	20

		Galois groups of order 3000
		$C_5^3:(C_4\times S_3)$ (as 15T49)
hidden slopes	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	80

Fields

Showing 1-50 of 100

  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
5.1.15.27a1.1	20	$x^{15} + 5 x^{13} + 5$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$600$	$1$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.2	20	$x^{15} + 5 x^{13} + 25 x + 5$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$600$	$1$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.3	20	$x^{15} + 5 x^{13} + 50 x + 5$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$600$	$1$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.4	20	$x^{15} + 5 x^{13} + 75 x + 5$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$600$	$1$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.5	20	$x^{15} + 5 x^{13} + 100 x + 5$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$600$	$1$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.6	80	$x^{15} + 5 x^{14} + 5 x^{13} + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.7	80	$x^{15} + 5 x^{14} + 5 x^{13} + 25 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.8	80	$x^{15} + 5 x^{14} + 5 x^{13} + 50 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.9	80	$x^{15} + 5 x^{14} + 5 x^{13} + 75 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.10	80	$x^{15} + 5 x^{14} + 5 x^{13} + 100 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.11	80	$x^{15} + 10 x^{14} + 5 x^{13} + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.12	80	$x^{15} + 10 x^{14} + 5 x^{13} + 25 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.13	80	$x^{15} + 10 x^{14} + 5 x^{13} + 50 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.14	80	$x^{15} + 10 x^{14} + 5 x^{13} + 75 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.15	80	$x^{15} + 10 x^{14} + 5 x^{13} + 100 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.16	80	$x^{15} + 15 x^{14} + 5 x^{13} + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.17	80	$x^{15} + 15 x^{14} + 5 x^{13} + 25 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.18	80	$x^{15} + 15 x^{14} + 5 x^{13} + 50 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.19	80	$x^{15} + 15 x^{14} + 5 x^{13} + 75 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.20	80	$x^{15} + 15 x^{14} + 5 x^{13} + 100 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.21	80	$x^{15} + 20 x^{14} + 5 x^{13} + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.22	80	$x^{15} + 20 x^{14} + 5 x^{13} + 25 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.23	80	$x^{15} + 20 x^{14} + 5 x^{13} + 50 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.24	80	$x^{15} + 20 x^{14} + 5 x^{13} + 75 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.25	80	$x^{15} + 20 x^{14} + 5 x^{13} + 100 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 2$	undefined
5.1.15.27a1.26	20	$x^{15} + 10 x^{13} + 5$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$600$	$1$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.27	20	$x^{15} + 10 x^{13} + 25 x + 5$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$600$	$1$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.28	20	$x^{15} + 10 x^{13} + 50 x + 5$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$600$	$1$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.29	20	$x^{15} + 10 x^{13} + 75 x + 5$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$600$	$1$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.30	20	$x^{15} + 10 x^{13} + 100 x + 5$	$C_5^2:(C_4\times S_3)$ (as 15T27)	$600$	$1$	$[\frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{25}{12}]^{2}_{4}$	$[\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.31	80	$x^{15} + 5 x^{14} + 10 x^{13} + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.32	80	$x^{15} + 5 x^{14} + 10 x^{13} + 25 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.33	80	$x^{15} + 5 x^{14} + 10 x^{13} + 50 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.34	80	$x^{15} + 5 x^{14} + 10 x^{13} + 75 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.35	80	$x^{15} + 5 x^{14} + 10 x^{13} + 100 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.36	80	$x^{15} + 10 x^{14} + 10 x^{13} + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.37	80	$x^{15} + 10 x^{14} + 10 x^{13} + 25 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.38	80	$x^{15} + 10 x^{14} + 10 x^{13} + 50 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.39	80	$x^{15} + 10 x^{14} + 10 x^{13} + 75 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.40	80	$x^{15} + 10 x^{14} + 10 x^{13} + 100 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.41	80	$x^{15} + 15 x^{14} + 10 x^{13} + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.42	80	$x^{15} + 15 x^{14} + 10 x^{13} + 25 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.43	80	$x^{15} + 15 x^{14} + 10 x^{13} + 50 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.44	80	$x^{15} + 15 x^{14} + 10 x^{13} + 75 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.45	80	$x^{15} + 15 x^{14} + 10 x^{13} + 100 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.46	80	$x^{15} + 20 x^{14} + 10 x^{13} + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.47	80	$x^{15} + 20 x^{14} + 10 x^{13} + 25 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.48	80	$x^{15} + 20 x^{14} + 10 x^{13} + 50 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.49	80	$x^{15} + 20 x^{14} + 10 x^{13} + 75 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined
5.1.15.27a1.50	80	$x^{15} + 20 x^{14} + 10 x^{13} + 100 x + 5$	$C_5^3:(C_4\times S_3)$ (as 15T49)	$3000$	$1$	$[\frac{7}{4}, \frac{25}{12}, \frac{25}{12}]_{12}^{2}$	$[\frac{3}{4},\frac{13}{12},\frac{13}{12}]_{12}^{2}$	$[\frac{7}{4},\frac{25}{12}]^{2}_{4}$	$[\frac{3}{4},\frac{13}{12}]^{2}_{4}$	$[13, 0]$	$[2, 1]$	$z^{10} + 3 z^5 + 3,3 z + 4$	undefined

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