LMFDB - Global number field search results

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Results (displaying matches 1-50 of 65) Next

Label	Polynomial	Discriminant	Galois group	Class group
11.1.34522712143931.1	x¹¹ - 11x⁸ + 44x⁵ + 33x⁴ + 44x³ - 11	$ -\,11^{13} $	$F_{11}$ (as 11T4)	Trivial
11.1.53339349076992.1	x¹¹ - 3x¹⁰ + 11x⁹ - 21x⁸ + 36x⁷ - 38x⁶ + 32x⁵ - 2x⁴ - 17x³ + 37x² - 23x + 15	$ -\,2^{10}\cdot 3^{5}\cdot 11^{8} $	$F_{11}$ (as 11T4)	Trivial
11.1.77265229938688.1	x¹¹ - 4x¹⁰ + 6x⁹ + 2x⁸ - 14x⁷ + 10x⁶ + 7x⁵ - 16x⁴ + 2x³ + 8x² - x - 8	$ -\,2^{15}\cdot 11^{9} $	$F_{11}$ (as 11T4)	Trivial
11.1.139234453205859.1	x¹¹ - 3	$ -\,3^{10}\cdot 11^{9} $	$F_{11}$ (as 11T4)	Trivial
11.1.292159150705664.1	x¹¹ - 2	$ -\,2^{10}\cdot 11^{11} $	$F_{11}$ (as 11T4)	Trivial
11.1.891598970659375.1	x¹¹ + 11x⁹ + 44x⁷ + 77x⁵ + 55x³ + 11x - 1	$ -\,5^{5}\cdot 11^{11} $	$F_{11}$ (as 11T4)	Trivial
11.1.2786246783310546875.1	x¹¹ - 5	$ -\,5^{10}\cdot 11^{11} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.11.3483293138903825541.1	x¹¹ - 4x¹⁰ - 17x⁹ + 78x⁸ + 75x⁷ - 494x⁶ - 8x⁵ + 1260x⁴ - 522x³ - 1122x² + 748x - 9	$ 3^{5}\cdot 7^{5}\cdot 31^{8} $	$F_{11}$ (as 11T4)	Trivial
11.11.4910318845910094848.1	x¹¹ - 22x⁹ + 176x⁷ - 616x⁵ + 880x³ - 352x - 88	$ 2^{10}\cdot 7^{5}\cdot 11^{11} $	$F_{11}$ (as 11T4)	Trivial
11.1.17251705690018753536.1	x¹¹ - 6	$ -\,2^{10}\cdot 3^{10}\cdot 11^{11} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.80593485198448207139.1	x¹¹ - 7	$ -\,7^{10}\cdot 11^{11} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.11.552054582080600113152.1	x¹¹ - 33x⁹ + 396x⁷ - 2079x⁵ + 4455x³ - 2673x - 810	$ 2^{15}\cdot 3^{10}\cdot 11^{11} $	$F_{11}$ (as 11T4)	Trivial
11.11.2853116706110000000000.1	x¹¹ - 55x⁹ + 1100x⁷ - 9625x⁵ + 34375x³ - 34375x - 13900	$ 2^{10}\cdot 5^{10}\cdot 11^{11} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.7400249944258160101211.1	x¹¹ - 11	$ -\,11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.11.193763450514676380800000.1	x¹¹ - x¹⁰ - 53x⁹ + 31x⁸ + 996x⁷ - 28x⁶ - 7812x⁵ - 5784x⁴ + 20673x³ + 36219x² + 19909x + 3279	$ 2^{10}\cdot 5^{5}\cdot 7^{10}\cdot 11^{8} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.7577855942920355943640064.1	x¹¹ - 11264	$ -\,2^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.7577855942920355943640064.2	x¹¹ - 176	$ -\,2^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.7577855942920355943640064.3	x¹¹ - 22	$ -\,2^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	$[2]$ (GRH)
11.1.7577855942920355943640064.4	x¹¹ - 242	$ -\,2^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.7577855942920355943640064.5	x¹¹ - 2816	$ -\,2^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.7577855942920355943640064.6	x¹¹ - 352	$ -\,2^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.7577855942920355943640064.7	x¹¹ - 44	$ -\,2^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.7577855942920355943640064.8	x¹¹ - 5632	$ -\,2^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.7577855942920355943640064.9	x¹¹ - 88	$ -\,2^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.7577855942920355943640064.10	x¹¹ - 968	$ -\,2^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.436977358958500095816408339.1	x¹¹ - 11979	$ -\,3^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.436977358958500095816408339.2	x¹¹ - 216513	$ -\,3^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.436977358958500095816408339.3	x¹¹ - 2673	$ -\,3^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.436977358958500095816408339.4	x¹¹ - 297	$ -\,3^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.436977358958500095816408339.5	x¹¹ - 3267	$ -\,3^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.436977358958500095816408339.6	x¹¹ - 33	$ -\,3^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.436977358958500095816408339.7	x¹¹ - 363	$ -\,3^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.436977358958500095816408339.8	x¹¹ - 649539	$ -\,3^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.436977358958500095816408339.9	x¹¹ - 891	$ -\,3^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.436977358958500095816408339.10	x¹¹ - 99	$ -\,3^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.72268065861896094738388671875.1	x¹¹ - 107421875	$ -\,5^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.72268065861896094738388671875.2	x¹¹ - 1375	$ -\,5^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.72268065861896094738388671875.3	x¹¹ - 15125	$ -\,5^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.72268065861896094738388671875.4	x¹¹ - 275	$ -\,5^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.72268065861896094738388671875.5	x¹¹ - 33275	$ -\,5^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.72268065861896094738388671875.6	x¹¹ - 34375	$ -\,5^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.72268065861896094738388671875.7	x¹¹ - 55	$ -\,5^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.72268065861896094738388671875.8	x¹¹ - 605	$ -\,5^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.72268065861896094738388671875.9	x¹¹ - 6655	$ -\,5^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.72268065861896094738388671875.10	x¹¹ - 805255	$ -\,5^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.2090387445666559894871442426539.1	x¹¹ - 1127357	$ -\,7^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.2090387445666559894871442426539.2	x¹¹ - 184877	$ -\,7^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.2090387445666559894871442426539.3	x¹¹ - 3107227739	$ -\,7^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	$[2]$ (GRH)
11.1.2090387445666559894871442426539.4	x¹¹ - 3773	$ -\,7^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.2090387445666559894871442426539.5	x¹¹ - 41503	$ -\,7^{10}\cdot 11^{21} $	$F_{11}$ (as 11T4)	Trivial (GRH)

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Degree	Signature	Galois group	Class number	Class group

Regulator	Num. ramified primes	Ramified primes		Unramified primes

CM field	Discriminant		Root discriminant

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Results (displaying matches 1-50 of 65) Next

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

Label	Polynomial	Discriminant	Galois group	Class group
11.1.34522712143931.1	x¹¹ - 11x⁸ + 44x⁵ + 33x⁴ + 44x³ - 11	\( -\,11^{13} \)	$F_{11}$ (as 11T4)	Trivial
11.1.53339349076992.1	x¹¹ - 3x¹⁰ + 11x⁹ - 21x⁸ + 36x⁷ - 38x⁶ + 32x⁵ - 2x⁴ - 17x³ + 37x² - 23x + 15	\( -\,2^{10}\cdot 3^{5}\cdot 11^{8} \)	$F_{11}$ (as 11T4)	Trivial
11.1.77265229938688.1	x¹¹ - 4x¹⁰ + 6x⁹ + 2x⁸ - 14x⁷ + 10x⁶ + 7x⁵ - 16x⁴ + 2x³ + 8x² - x - 8	\( -\,2^{15}\cdot 11^{9} \)	$F_{11}$ (as 11T4)	Trivial
11.1.139234453205859.1	x¹¹ - 3	\( -\,3^{10}\cdot 11^{9} \)	$F_{11}$ (as 11T4)	Trivial
11.1.292159150705664.1	x¹¹ - 2	\( -\,2^{10}\cdot 11^{11} \)	$F_{11}$ (as 11T4)	Trivial
11.1.891598970659375.1	x¹¹ + 11x⁹ + 44x⁷ + 77x⁵ + 55x³ + 11x - 1	\( -\,5^{5}\cdot 11^{11} \)	$F_{11}$ (as 11T4)	Trivial
11.1.2786246783310546875.1	x¹¹ - 5	\( -\,5^{10}\cdot 11^{11} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.11.3483293138903825541.1	x¹¹ - 4x¹⁰ - 17x⁹ + 78x⁸ + 75x⁷ - 494x⁶ - 8x⁵ + 1260x⁴ - 522x³ - 1122x² + 748x - 9	\( 3^{5}\cdot 7^{5}\cdot 31^{8} \)	$F_{11}$ (as 11T4)	Trivial
11.11.4910318845910094848.1	x¹¹ - 22x⁹ + 176x⁷ - 616x⁵ + 880x³ - 352x - 88	\( 2^{10}\cdot 7^{5}\cdot 11^{11} \)	$F_{11}$ (as 11T4)	Trivial
11.1.17251705690018753536.1	x¹¹ - 6	\( -\,2^{10}\cdot 3^{10}\cdot 11^{11} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.80593485198448207139.1	x¹¹ - 7	\( -\,7^{10}\cdot 11^{11} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.11.552054582080600113152.1	x¹¹ - 33x⁹ + 396x⁷ - 2079x⁵ + 4455x³ - 2673x - 810	\( 2^{15}\cdot 3^{10}\cdot 11^{11} \)	$F_{11}$ (as 11T4)	Trivial
11.11.2853116706110000000000.1	x¹¹ - 55x⁹ + 1100x⁷ - 9625x⁵ + 34375x³ - 34375x - 13900	\( 2^{10}\cdot 5^{10}\cdot 11^{11} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.7400249944258160101211.1	x¹¹ - 11	\( -\,11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.11.193763450514676380800000.1	x¹¹ - x¹⁰ - 53x⁹ + 31x⁸ + 996x⁷ - 28x⁶ - 7812x⁵ - 5784x⁴ + 20673x³ + 36219x² + 19909x + 3279	\( 2^{10}\cdot 5^{5}\cdot 7^{10}\cdot 11^{8} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.7577855942920355943640064.1	x¹¹ - 11264	\( -\,2^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.7577855942920355943640064.2	x¹¹ - 176	\( -\,2^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.7577855942920355943640064.3	x¹¹ - 22	\( -\,2^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	$[2]$ (GRH)
11.1.7577855942920355943640064.4	x¹¹ - 242	\( -\,2^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.7577855942920355943640064.5	x¹¹ - 2816	\( -\,2^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.7577855942920355943640064.6	x¹¹ - 352	\( -\,2^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.7577855942920355943640064.7	x¹¹ - 44	\( -\,2^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.7577855942920355943640064.8	x¹¹ - 5632	\( -\,2^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.7577855942920355943640064.9	x¹¹ - 88	\( -\,2^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.7577855942920355943640064.10	x¹¹ - 968	\( -\,2^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.436977358958500095816408339.1	x¹¹ - 11979	\( -\,3^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.436977358958500095816408339.2	x¹¹ - 216513	\( -\,3^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.436977358958500095816408339.3	x¹¹ - 2673	\( -\,3^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.436977358958500095816408339.4	x¹¹ - 297	\( -\,3^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.436977358958500095816408339.5	x¹¹ - 3267	\( -\,3^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.436977358958500095816408339.6	x¹¹ - 33	\( -\,3^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.436977358958500095816408339.7	x¹¹ - 363	\( -\,3^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.436977358958500095816408339.8	x¹¹ - 649539	\( -\,3^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.436977358958500095816408339.9	x¹¹ - 891	\( -\,3^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.436977358958500095816408339.10	x¹¹ - 99	\( -\,3^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.72268065861896094738388671875.1	x¹¹ - 107421875	\( -\,5^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.72268065861896094738388671875.2	x¹¹ - 1375	\( -\,5^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.72268065861896094738388671875.3	x¹¹ - 15125	\( -\,5^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.72268065861896094738388671875.4	x¹¹ - 275	\( -\,5^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.72268065861896094738388671875.5	x¹¹ - 33275	\( -\,5^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.72268065861896094738388671875.6	x¹¹ - 34375	\( -\,5^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.72268065861896094738388671875.7	x¹¹ - 55	\( -\,5^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.72268065861896094738388671875.8	x¹¹ - 605	\( -\,5^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.72268065861896094738388671875.9	x¹¹ - 6655	\( -\,5^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.72268065861896094738388671875.10	x¹¹ - 805255	\( -\,5^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.2090387445666559894871442426539.1	x¹¹ - 1127357	\( -\,7^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.2090387445666559894871442426539.2	x¹¹ - 184877	\( -\,7^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.2090387445666559894871442426539.3	x¹¹ - 3107227739	\( -\,7^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	$[2]$ (GRH)
11.1.2090387445666559894871442426539.4	x¹¹ - 3773	\( -\,7^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)
11.1.2090387445666559894871442426539.5	x¹¹ - 41503	\( -\,7^{10}\cdot 11^{21} \)	$F_{11}$ (as 11T4)	Trivial (GRH)