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Degree	Residue characteristic	Galois group	Galois unramified degree	Assoc. Inertia

Ramification index	Discriminant exponent	Inertia subgroup	Galois tame degree	Indices

Residue field degree	Top slope	Wild	Visible	Wild inertia subgroup

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Results (1-50 of 108 matches)

Next Download displayed columns to Pari/GP SageMath Magma Oscar

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Ind. of Insep.	Assoc. Inertia
3.20.15.1	$20$	x²⁰ + 23x¹⁶ + 4x¹⁵ - 606x¹² - 756x¹¹ + 6x¹⁰ + 1862x⁸ + 7788x⁷ + 1044x⁶ + 4x⁵ + 11581x⁴ - 5788x³ + 894x² - 52x + 4	$3$	$4$	$5$	$15$	$C_5\times D_4$ (as 20T12)	$10$	$4$	$[\ ]$	$[\ ]_{4}^{10}$	$[0]$	$[2]$
3.20.15.2	$20$	x²⁰ + 162x⁴ - 243	$3$	$4$	$5$	$15$	$C_5\times D_4$ (as 20T12)	$10$	$4$	$[\ ]$	$[\ ]_{4}^{10}$	$[0]$	$[2]$
7.20.15.1	$20$	x²⁰ + 39x¹⁶ + 16x¹⁵ - 344x¹² - 7232x¹¹ + 96x¹⁰ + 4344x⁸ + 131648x⁷ + 38272x⁶ + 256x⁵ + 59536x⁴ - 212224x³ + 84096x² - 8704x + 9328	$7$	$4$	$5$	$15$	$C_5\times D_4$ (as 20T12)	$10$	$4$	$[\ ]$	$[\ ]_{4}^{10}$	$[0]$	$[2]$
7.20.15.2	$20$	x²⁰ + 2401x⁴ - 67228	$7$	$4$	$5$	$15$	$C_5\times D_4$ (as 20T12)	$10$	$4$	$[\ ]$	$[\ ]_{4}^{10}$	$[0]$	$[2]$
11.20.15.1	$20$	x²⁰ + 40x¹⁷ + 55x¹⁶ + 36x¹⁵ + 600x¹⁴ - 4400x¹³ + 2290x¹² - 21740x¹¹ + 46686x¹⁰ - 86000x⁹ + 43110x⁸ + 772900x⁷ + 1137540x⁶ - 870924x⁵ - 3796395x⁴ - 658460x³ + 3912270x² + 1160940x + 1076652	$11$	$4$	$5$	$15$	$C_5\times D_4$ (as 20T12)	$10$	$4$	$[\ ]$	$[\ ]_{4}^{10}$	$[0]$	$[2]$
11.20.15.2	$20$	x²⁰ - 13310x⁸ - 1449459	$11$	$4$	$5$	$15$	$C_5\times D_4$ (as 20T12)	$10$	$4$	$[\ ]$	$[\ ]_{4}^{10}$	$[0]$	$[2]$
11.20.19.1	$20$	x²⁰ + 33	$11$	$20$	$1$	$19$	$C_5\times D_4$ (as 20T12)	$2$	$20$	$[\ ]$	$[\ ]_{20}^{2}$	$[0]$	$[2]$
11.20.19.10	$20$	x²⁰ + 66	$11$	$20$	$1$	$19$	$C_5\times D_4$ (as 20T12)	$2$	$20$	$[\ ]$	$[\ ]_{20}^{2}$	$[0]$	$[2]$
11.20.19.2	$20$	x²⁰ + 55	$11$	$20$	$1$	$19$	$C_5\times D_4$ (as 20T12)	$2$	$20$	$[\ ]$	$[\ ]_{20}^{2}$	$[0]$	$[2]$
11.20.19.3	$20$	x²⁰ + 11	$11$	$20$	$1$	$19$	$C_5\times D_4$ (as 20T12)	$2$	$20$	$[\ ]$	$[\ ]_{20}^{2}$	$[0]$	$[2]$
11.20.19.4	$20$	x²⁰ + 99	$11$	$20$	$1$	$19$	$C_5\times D_4$ (as 20T12)	$2$	$20$	$[\ ]$	$[\ ]_{20}^{2}$	$[0]$	$[2]$
11.20.19.5	$20$	x²⁰ + 44	$11$	$20$	$1$	$19$	$C_5\times D_4$ (as 20T12)	$2$	$20$	$[\ ]$	$[\ ]_{20}^{2}$	$[0]$	$[2]$
11.20.19.6	$20$	x²⁰ + 110	$11$	$20$	$1$	$19$	$C_5\times D_4$ (as 20T12)	$2$	$20$	$[\ ]$	$[\ ]_{20}^{2}$	$[0]$	$[2]$
11.20.19.7	$20$	x²⁰ + 22	$11$	$20$	$1$	$19$	$C_5\times D_4$ (as 20T12)	$2$	$20$	$[\ ]$	$[\ ]_{20}^{2}$	$[0]$	$[2]$
11.20.19.8	$20$	x²⁰ + 77	$11$	$20$	$1$	$19$	$C_5\times D_4$ (as 20T12)	$2$	$20$	$[\ ]$	$[\ ]_{20}^{2}$	$[0]$	$[2]$
11.20.19.9	$20$	x²⁰ + 88	$11$	$20$	$1$	$19$	$C_5\times D_4$ (as 20T12)	$2$	$20$	$[\ ]$	$[\ ]_{20}^{2}$	$[0]$	$[2]$
19.20.15.1	$20$	x²⁰ + 115x¹⁶ + 68x¹⁵ - 7640x¹² - 82960x¹¹ + 1734x¹⁰ + 130840x⁸ + 4391440x⁷ + 1884280x⁶ + 19652x⁵ + 5940880x⁴ - 19545920x³ + 10970440x² - 1768680x + 813425	$19$	$4$	$5$	$15$	$C_5\times D_4$ (as 20T12)	$10$	$4$	$[\ ]$	$[\ ]_{4}^{10}$	$[0]$	$[2]$
19.20.15.2	$20$	x²⁰ + 651605x⁴ - 42093683	$19$	$4$	$5$	$15$	$C_5\times D_4$ (as 20T12)	$10$	$4$	$[\ ]$	$[\ ]_{4}^{10}$	$[0]$	$[2]$
23.20.15.1	$20$	x²⁰ + 127x¹⁶ + 72x¹⁵ - 2936x¹² - 106992x¹¹ + 1944x¹⁰ + 148688x⁸ + 6352704x⁷ + 2545344x⁶ + 23328x⁵ + 6398336x⁴ - 33590016x³ + 18423936x² - 2612736x + 3784976	$23$	$4$	$5$	$15$	$C_5\times D_4$ (as 20T12)	$10$	$4$	$[\ ]$	$[\ ]_{4}^{10}$	$[0]$	$[2]$
23.20.15.2	$20$	x²⁰ + 839523x⁴ - 115854174	$23$	$4$	$5$	$15$	$C_5\times D_4$ (as 20T12)	$10$	$4$	$[\ ]$	$[\ ]_{4}^{10}$	$[0]$	$[2]$
31.20.15.1	$20$	x²⁰ + 183x¹⁶ + 112x¹⁵ - 16136x¹² - 223328x¹¹ + 4704x¹⁰ + 496752x⁸ + 18886784x⁷ + 8329216x⁶ + 87808x⁵ + 35766016x⁴ - 136428544x³ + 79704576x² - 12995584x + 10899712	$31$	$4$	$5$	$15$	$C_5\times D_4$ (as 20T12)	$10$	$4$	$[\ ]$	$[\ ]_{4}^{10}$	$[0]$	$[2]$
31.20.15.2	$20$	x²⁰ + 6464647x⁴ - 801616228	$31$	$4$	$5$	$15$	$C_5\times D_4$ (as 20T12)	$10$	$4$	$[\ ]$	$[\ ]_{4}^{10}$	$[0]$	$[2]$
31.20.19.1	$20$	x²⁰ + 124	$31$	$20$	$1$	$19$	$C_5\times D_4$ (as 20T12)	$2$	$20$	$[\ ]$	$[\ ]_{20}^{2}$	$[0]$	$[2]$
31.20.19.10	$20$	x²⁰ + 372	$31$	$20$	$1$	$19$	$C_5\times D_4$ (as 20T12)	$2$	$20$	$[\ ]$	$[\ ]_{20}^{2}$	$[0]$	$[2]$
31.20.19.2	$20$	x²⁰ + 62	$31$	$20$	$1$	$19$	$C_5\times D_4$ (as 20T12)	$2$	$20$	$[\ ]$	$[\ ]_{20}^{2}$	$[0]$	$[2]$
31.20.19.3	$20$	x²⁰ + 31	$31$	$20$	$1$	$19$	$C_5\times D_4$ (as 20T12)	$2$	$20$	$[\ ]$	$[\ ]_{20}^{2}$	$[0]$	$[2]$
31.20.19.4	$20$	x²⁰ + 496	$31$	$20$	$1$	$19$	$C_5\times D_4$ (as 20T12)	$2$	$20$	$[\ ]$	$[\ ]_{20}^{2}$	$[0]$	$[2]$
31.20.19.5	$20$	x²⁰ + 248	$31$	$20$	$1$	$19$	$C_5\times D_4$ (as 20T12)	$2$	$20$	$[\ ]$	$[\ ]_{20}^{2}$	$[0]$	$[2]$
31.20.19.6	$20$	x²⁰ + 186	$31$	$20$	$1$	$19$	$C_5\times D_4$ (as 20T12)	$2$	$20$	$[\ ]$	$[\ ]_{20}^{2}$	$[0]$	$[2]$
31.20.19.7	$20$	x²⁰ + 93	$31$	$20$	$1$	$19$	$C_5\times D_4$ (as 20T12)	$2$	$20$	$[\ ]$	$[\ ]_{20}^{2}$	$[0]$	$[2]$
31.20.19.8	$20$	x²⁰ + 527	$31$	$20$	$1$	$19$	$C_5\times D_4$ (as 20T12)	$2$	$20$	$[\ ]$	$[\ ]_{20}^{2}$	$[0]$	$[2]$
31.20.19.9	$20$	x²⁰ + 341	$31$	$20$	$1$	$19$	$C_5\times D_4$ (as 20T12)	$2$	$20$	$[\ ]$	$[\ ]_{20}^{2}$	$[0]$	$[2]$
43.20.15.1	$20$	x²⁰ + 247x¹⁶ + 160x¹⁵ - 22406x¹² - 443360x¹¹ + 9600x¹⁰ + 1154878x⁸ + 50839520x⁷ + 23545600x⁶ + 256000x⁵ + 108808501x⁴ - 506526880x³ + 315030400x² - 52992000x + 67086875	$43$	$4$	$5$	$15$	$C_5\times D_4$ (as 20T12)	$10$	$4$	$[\ ]$	$[\ ]_{4}^{10}$	$[0]$	$[2]$
43.20.15.2	$20$	x²⁰ + 27350408x⁴ - 5880337720	$43$	$4$	$5$	$15$	$C_5\times D_4$ (as 20T12)	$10$	$4$	$[\ ]$	$[\ ]_{4}^{10}$	$[0]$	$[2]$
47.20.15.1	$20$	x²⁰ + 239x¹⁶ + 168x¹⁵ + 16456x¹² - 512736x¹¹ + 10584x¹⁰ + 1044344x⁸ + 58233504x⁷ + 28209888x⁶ + 296352x⁵ + 37144336x⁴ - 619796352x³ + 426986784x² - 69346368x + 213552128	$47$	$4$	$5$	$15$	$C_5\times D_4$ (as 20T12)	$10$	$4$	$[\ ]$	$[\ ]_{4}^{10}$	$[0]$	$[2]$
47.20.15.2	$20$	x²⁰ + 4879681x⁴ - 9632490294	$47$	$4$	$5$	$15$	$C_5\times D_4$ (as 20T12)	$10$	$4$	$[\ ]$	$[\ ]_{4}^{10}$	$[0]$	$[2]$
59.20.15.1	$20$	x²⁰ + 327x¹⁶ + 228x¹⁵ - 21446x¹² - 868908x¹¹ + 19494x¹⁰ + 2546718x⁸ + 132747756x⁷ + 65486844x⁶ + 740772x⁵ + 286716661x⁴ - 1801845924x³ + 1214651646x² - 212601564x + 409702860	$59$	$4$	$5$	$15$	$C_5\times D_4$ (as 20T12)	$10$	$4$	$[\ ]$	$[\ ]_{4}^{10}$	$[0]$	$[2]$
59.20.15.2	$20$	x²⁰ + 96938888x⁴ - 40750685043	$59$	$4$	$5$	$15$	$C_5\times D_4$ (as 20T12)	$10$	$4$	$[\ ]$	$[\ ]_{4}^{10}$	$[0]$	$[2]$
67.20.15.1	$20$	x²⁰ + 343x¹⁶ + 260x¹⁵ + 28834x¹² - 1130740x¹¹ + 25350x¹⁰ + 3042502x⁸ + 184045420x⁷ + 96346900x⁶ + 1098500x⁵ + 175273021x⁴ - 2795646620x³ + 2075041150x² - 365800500x + 1213842500	$67$	$4$	$5$	$15$	$C_5\times D_4$ (as 20T12)	$10$	$4$	$[\ ]$	$[\ ]_{4}^{10}$	$[0]$	$[2]$
67.20.15.2	$20$	x²⁰ + 40302242x⁴ - 87758131955	$67$	$4$	$5$	$15$	$C_5\times D_4$ (as 20T12)	$10$	$4$	$[\ ]$	$[\ ]_{4}^{10}$	$[0]$	$[2]$
71.20.15.1	$20$	x²⁰ + 427x¹⁶ + 256x¹⁵ - 101006x¹² - 1167616x¹¹ + 24576x¹⁰ + 6592958x⁸ + 229720832x⁷ + 99762176x⁶ + 1048576x⁵ + 1112578061x⁴ - 3815557888x³ + 2174541824x² - 353370112x + 577001367	$71$	$4$	$5$	$15$	$C_5\times D_4$ (as 20T12)	$10$	$4$	$[\ ]$	$[\ ]_{4}^{10}$	$[0]$	$[2]$
71.20.15.2	$20$	x²⁰ + 457410258x⁴ - 115470678464	$71$	$4$	$5$	$15$	$C_5\times D_4$ (as 20T12)	$10$	$4$	$[\ ]$	$[\ ]_{4}^{10}$	$[0]$	$[2]$
71.20.19.1	$20$	x²⁰ + 142	$71$	$20$	$1$	$19$	$C_5\times D_4$ (as 20T12)	$2$	$20$	$[\ ]$	$[\ ]_{20}^{2}$	$[0]$	$[2]$
71.20.19.10	$20$	x²⁰ + 1988	$71$	$20$	$1$	$19$	$C_5\times D_4$ (as 20T12)	$2$	$20$	$[\ ]$	$[\ ]_{20}^{2}$	$[0]$	$[2]$
71.20.19.2	$20$	x²⁰ + 355	$71$	$20$	$1$	$19$	$C_5\times D_4$ (as 20T12)	$2$	$20$	$[\ ]$	$[\ ]_{20}^{2}$	$[0]$	$[2]$
71.20.19.3	$20$	x²⁰ + 71	$71$	$20$	$1$	$19$	$C_5\times D_4$ (as 20T12)	$2$	$20$	$[\ ]$	$[\ ]_{20}^{2}$	$[0]$	$[2]$
71.20.19.4	$20$	x²⁰ + 284	$71$	$20$	$1$	$19$	$C_5\times D_4$ (as 20T12)	$2$	$20$	$[\ ]$	$[\ ]_{20}^{2}$	$[0]$	$[2]$
71.20.19.5	$20$	x²⁰ + 710	$71$	$20$	$1$	$19$	$C_5\times D_4$ (as 20T12)	$2$	$20$	$[\ ]$	$[\ ]_{20}^{2}$	$[0]$	$[2]$
71.20.19.6	$20$	x²⁰ + 1633	$71$	$20$	$1$	$19$	$C_5\times D_4$ (as 20T12)	$2$	$20$	$[\ ]$	$[\ ]_{20}^{2}$	$[0]$	$[2]$
71.20.19.7	$20$	x²⁰ + 994	$71$	$20$	$1$	$19$	$C_5\times D_4$ (as 20T12)	$2$	$20$	$[\ ]$	$[\ ]_{20}^{2}$	$[0]$	$[2]$

Next Download displayed columns to Pari/GP SageMath Magma Oscar

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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 $\F_{q}$

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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.