LMFDB - Global number field search results

Further refine search

Results (displaying all 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.8310412719464453125.1	x¹⁶ - x¹⁵ - 2x¹² + 3x¹¹ + 11x¹⁰ - 37x⁹ + 71x⁸ - 109x⁷ + 146x⁶ - 156x⁵ + 134x⁴ - 109x³ + 76x² - 36x + 9	$ 5^{8}\cdot 11^{6}\cdot 229^{3} $	16T1741	Trivial
16.0.8310412719464453125.2	x¹⁶ - 6x¹⁵ + 20x¹⁴ - 45x¹³ + 80x¹² - 129x¹¹ + 216x¹⁰ - 366x⁹ + 575x⁸ - 774x⁷ + 861x⁶ - 741x⁵ + 455x⁴ - 150x³ + 40x² - 9x + 1	$ 5^{8}\cdot 11^{6}\cdot 229^{3} $	16T1741	Trivial
16.4.8310412719464453125.2	x¹⁶ - 2x¹⁵ + x¹⁴ - 4x¹³ + 17x¹² - 24x¹¹ + 4x¹⁰ + 39x⁹ - 24x⁸ - 39x⁷ + 52x⁶ - 15x⁵ - 45x⁴ - 3x³ + 8x² + 4x + 1	$ 5^{8}\cdot 11^{6}\cdot 229^{3} $	16T1741	Trivial
16.8.8310412719464453125.2	x¹⁶ - 5x¹⁵ + 5x¹⁴ + 13x¹³ - 28x¹² + 2x¹¹ + 36x¹⁰ - 27x⁹ - 29x⁸ + 27x⁷ + 36x⁶ - 2x⁵ - 28x⁴ - 13x³ + 5x² + 5x + 1	$ 5^{8}\cdot 11^{6}\cdot 229^{3} $	16T1741	Trivial (GRH)
16.8.1005559939055198828125.1	x¹⁶ - 4x¹⁵ + 3x¹⁴ + 19x¹³ - 35x¹² + 11x¹¹ - 24x¹⁰ - 83x⁹ + 225x⁸ - 83x⁷ - 24x⁶ + 11x⁵ - 35x⁴ + 19x³ + 3x² - 4x + 1	$ 5^{8}\cdot 11^{8}\cdot 229^{3} $	16T1741	Trivial (GRH)
16.0.1005559939055198828125.2	x¹⁶ - 6x¹⁵ + 27x¹⁴ - 75x¹³ + 163x¹² - 267x¹¹ + 345x¹⁰ - 402x⁹ + 414x⁸ - 435x⁷ + 484x⁶ - 423x⁵ + 399x⁴ - 462x³ + 319x² - 90x + 9	$ 5^{8}\cdot 11^{8}\cdot 229^{3} $	16T1741	$[2]$
16.10.1186620610969600000000.1	x¹⁶ - 8x¹⁴ + 29x¹² - 62x¹⁰ + 75x⁸ - 36x⁶ - 9x⁴ + 10x² - 1	$ -\,2^{32}\cdot 5^{8}\cdot 29^{4} $	16T1741	Trivial (GRH)
16.10.1186620610969600000000.2	x¹⁶ - 8x¹⁴ + 28x¹² - 56x¹⁰ + 64x⁸ - 32x⁶ - 3x⁴ + 6x² - 1	$ -\,2^{32}\cdot 5^{8}\cdot 29^{4} $	16T1741	Trivial (GRH)
16.2.1186620610969600000000.3	x¹⁶ + 8x¹⁴ + 29x¹² + 62x¹⁰ + 75x⁸ + 36x⁶ - 9x⁴ - 10x² - 1	$ -\,2^{32}\cdot 5^{8}\cdot 29^{4} $	16T1741	Trivial
16.6.1186620610969600000000.3	x¹⁶ - 4x¹⁴ - 3x¹² + 8x¹⁰ + 19x⁸ + 14x⁶ - 7x⁴ - 8x² - 1	$ -\,2^{32}\cdot 5^{8}\cdot 29^{4} $	16T1741	Trivial (GRH)
16.2.1186620610969600000000.4	x¹⁶ + 8x¹⁴ + 28x¹² + 56x¹⁰ + 64x⁸ + 32x⁶ - 3x⁴ - 6x² - 1	$ -\,2^{32}\cdot 5^{8}\cdot 29^{4} $	16T1741	Trivial
16.6.1186620610969600000000.4	x¹⁶ + 4x¹⁴ - 3x¹² - 8x¹⁰ + 19x⁸ - 14x⁶ - 7x⁴ + 8x² - 1	$ -\,2^{32}\cdot 5^{8}\cdot 29^{4} $	16T1741	Trivial (GRH)
16.6.1186620610969600000000.5	x¹⁶ - 4x¹⁴ - 4x¹² + 6x¹⁰ + 30x⁸ + 42x⁶ + 19x⁴ - 1	$ -\,2^{32}\cdot 5^{8}\cdot 29^{4} $	16T1741	Trivial (GRH)
16.6.1186620610969600000000.6	x¹⁶ + 4x¹⁴ - 4x¹² - 6x¹⁰ + 30x⁸ - 42x⁶ + 19x⁴ - 1	$ -\,2^{32}\cdot 5^{8}\cdot 29^{4} $	16T1741	Trivial (GRH)
16.4.4501084363494400000000.1	x¹⁶ + 2x¹⁴ - 21x¹² - 37x¹⁰ + 30x⁸ + 264x⁶ + 171x⁴ + 410x² + 229	$ 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 229^{3} $	16T1741	Trivial (GRH)
16.0.4501084363494400000000.2	x¹⁶ + 4x¹⁴ + 3x¹² + 13x¹⁰ + 65x⁸ - 68x⁶ - 183x⁴ + 85x² + 229	$ 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 229^{3} $	16T1741	Trivial (GRH)
16.4.4501084363494400000000.2	x¹⁶ + 6x¹⁴ + 11x¹² - 29x¹⁰ - 125x⁸ - 223x⁶ - 506x⁴ - 415x² + 229	$ 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 229^{3} $	16T1741	Trivial (GRH)
16.4.4501084363494400000000.3	x¹⁶ + x¹⁴ - 22x¹² - 62x¹⁰ + 56x⁸ + 499x⁶ + 907x⁴ + 732x² + 229	$ 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 229^{3} $	16T1741	Trivial (GRH)
16.4.59895026602726400000000.3	x¹⁶ - 28x¹² + 31x¹⁰ + 102x⁸ - 549x⁶ + 805x⁴ - 632x² + 149	$ 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 149^{3} $	16T1741	Trivial (GRH)
16.4.59895026602726400000000.4	x¹⁶ + 12x¹⁴ + 11x¹² - 101x¹⁰ - 270x⁸ - 304x⁶ - 6x⁴ + 147x² + 149	$ 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 149^{3} $	16T1741	Trivial (GRH)
16.0.24695998799082214400000000.2	x¹⁶ + 35x¹⁴ + 391x¹² + 2107x¹⁰ + 6265x⁸ + 10736x⁶ + 10474x⁴ + 5361x² + 1109	$ 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 1109^{3} $	16T1741	$[186]$ (GRH)
16.16.24695998799082214400000000.2	x¹⁶ - 35x¹⁴ + 391x¹² - 2107x¹⁰ + 6265x⁸ - 10736x⁶ + 10474x⁴ - 5361x² + 1109	$ 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 1109^{3} $	16T1741	Trivial (GRH)
16.0.6322175692565046886400000000.1	x¹⁶ - 8x¹⁵ + 46x¹⁴ - 96x¹³ + 204x¹² + 156x¹¹ + 858x¹⁰ - 378x⁹ + 3484x⁸ - 16316x⁷ + 66552x⁶ - 37640x⁵ + 4243x⁴ + 41710x³ + 22326x² + 66586x + 35321	$ 2^{24}\cdot 5^{8}\cdot 29^{4}\cdot 1109^{3} $	16T1741	$[186]$ (GRH)
16.16.6322175692565046886400000000.1	x¹⁶ - 8x¹⁵ - 26x¹⁴ + 236x¹³ + 326x¹² - 2316x¹¹ - 2404x¹⁰ + 9078x⁹ + 9644x⁸ - 13868x⁷ - 17678x⁶ + 5316x⁵ + 11153x⁴ + 838x³ - 2182x² - 342x + 101	$ 2^{24}\cdot 5^{8}\cdot 29^{4}\cdot 1109^{3} $	16T1741	Trivial (GRH)

Introduction	Features
Universe	News

Degree	Signature	Galois group	Class number	Class group

Regulator	Num. ramified primes	Ramified primes		Unramified primes

CM field	Discriminant		Root discriminant

Introduction and more

L-functions

Modular Forms

Varieties

Fields

Representations

Groups

Knowledge

Learn more about

Further refine search

Results (displaying all 24 matches)

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
16.0.8310412719464453125.1	x¹⁶ - x¹⁵ - 2x¹² + 3x¹¹ + 11x¹⁰ - 37x⁹ + 71x⁸ - 109x⁷ + 146x⁶ - 156x⁵ + 134x⁴ - 109x³ + 76x² - 36x + 9	\( 5^{8}\cdot 11^{6}\cdot 229^{3} \)	16T1741	Trivial
16.0.8310412719464453125.2	x¹⁶ - 6x¹⁵ + 20x¹⁴ - 45x¹³ + 80x¹² - 129x¹¹ + 216x¹⁰ - 366x⁹ + 575x⁸ - 774x⁷ + 861x⁶ - 741x⁵ + 455x⁴ - 150x³ + 40x² - 9x + 1	\( 5^{8}\cdot 11^{6}\cdot 229^{3} \)	16T1741	Trivial
16.4.8310412719464453125.2	x¹⁶ - 2x¹⁵ + x¹⁴ - 4x¹³ + 17x¹² - 24x¹¹ + 4x¹⁰ + 39x⁹ - 24x⁸ - 39x⁷ + 52x⁶ - 15x⁵ - 45x⁴ - 3x³ + 8x² + 4x + 1	\( 5^{8}\cdot 11^{6}\cdot 229^{3} \)	16T1741	Trivial
16.8.8310412719464453125.2	x¹⁶ - 5x¹⁵ + 5x¹⁴ + 13x¹³ - 28x¹² + 2x¹¹ + 36x¹⁰ - 27x⁹ - 29x⁸ + 27x⁷ + 36x⁶ - 2x⁵ - 28x⁴ - 13x³ + 5x² + 5x + 1	\( 5^{8}\cdot 11^{6}\cdot 229^{3} \)	16T1741	Trivial (GRH)
16.8.1005559939055198828125.1	x¹⁶ - 4x¹⁵ + 3x¹⁴ + 19x¹³ - 35x¹² + 11x¹¹ - 24x¹⁰ - 83x⁹ + 225x⁸ - 83x⁷ - 24x⁶ + 11x⁵ - 35x⁴ + 19x³ + 3x² - 4x + 1	\( 5^{8}\cdot 11^{8}\cdot 229^{3} \)	16T1741	Trivial (GRH)
16.0.1005559939055198828125.2	x¹⁶ - 6x¹⁵ + 27x¹⁴ - 75x¹³ + 163x¹² - 267x¹¹ + 345x¹⁰ - 402x⁹ + 414x⁸ - 435x⁷ + 484x⁶ - 423x⁵ + 399x⁴ - 462x³ + 319x² - 90x + 9	\( 5^{8}\cdot 11^{8}\cdot 229^{3} \)	16T1741	$[2]$
16.10.1186620610969600000000.1	x¹⁶ - 8x¹⁴ + 29x¹² - 62x¹⁰ + 75x⁸ - 36x⁶ - 9x⁴ + 10x² - 1	\( -\,2^{32}\cdot 5^{8}\cdot 29^{4} \)	16T1741	Trivial (GRH)
16.10.1186620610969600000000.2	x¹⁶ - 8x¹⁴ + 28x¹² - 56x¹⁰ + 64x⁸ - 32x⁶ - 3x⁴ + 6x² - 1	\( -\,2^{32}\cdot 5^{8}\cdot 29^{4} \)	16T1741	Trivial (GRH)
16.2.1186620610969600000000.3	x¹⁶ + 8x¹⁴ + 29x¹² + 62x¹⁰ + 75x⁸ + 36x⁶ - 9x⁴ - 10x² - 1	\( -\,2^{32}\cdot 5^{8}\cdot 29^{4} \)	16T1741	Trivial
16.6.1186620610969600000000.3	x¹⁶ - 4x¹⁴ - 3x¹² + 8x¹⁰ + 19x⁸ + 14x⁶ - 7x⁴ - 8x² - 1	\( -\,2^{32}\cdot 5^{8}\cdot 29^{4} \)	16T1741	Trivial (GRH)
16.2.1186620610969600000000.4	x¹⁶ + 8x¹⁴ + 28x¹² + 56x¹⁰ + 64x⁸ + 32x⁶ - 3x⁴ - 6x² - 1	\( -\,2^{32}\cdot 5^{8}\cdot 29^{4} \)	16T1741	Trivial
16.6.1186620610969600000000.4	x¹⁶ + 4x¹⁴ - 3x¹² - 8x¹⁰ + 19x⁸ - 14x⁶ - 7x⁴ + 8x² - 1	\( -\,2^{32}\cdot 5^{8}\cdot 29^{4} \)	16T1741	Trivial (GRH)
16.6.1186620610969600000000.5	x¹⁶ - 4x¹⁴ - 4x¹² + 6x¹⁰ + 30x⁸ + 42x⁶ + 19x⁴ - 1	\( -\,2^{32}\cdot 5^{8}\cdot 29^{4} \)	16T1741	Trivial (GRH)
16.6.1186620610969600000000.6	x¹⁶ + 4x¹⁴ - 4x¹² - 6x¹⁰ + 30x⁸ - 42x⁶ + 19x⁴ - 1	\( -\,2^{32}\cdot 5^{8}\cdot 29^{4} \)	16T1741	Trivial (GRH)
16.4.4501084363494400000000.1	x¹⁶ + 2x¹⁴ - 21x¹² - 37x¹⁰ + 30x⁸ + 264x⁶ + 171x⁴ + 410x² + 229	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 229^{3} \)	16T1741	Trivial (GRH)
16.0.4501084363494400000000.2	x¹⁶ + 4x¹⁴ + 3x¹² + 13x¹⁰ + 65x⁸ - 68x⁶ - 183x⁴ + 85x² + 229	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 229^{3} \)	16T1741	Trivial (GRH)
16.4.4501084363494400000000.2	x¹⁶ + 6x¹⁴ + 11x¹² - 29x¹⁰ - 125x⁸ - 223x⁶ - 506x⁴ - 415x² + 229	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 229^{3} \)	16T1741	Trivial (GRH)
16.4.4501084363494400000000.3	x¹⁶ + x¹⁴ - 22x¹² - 62x¹⁰ + 56x⁸ + 499x⁶ + 907x⁴ + 732x² + 229	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 229^{3} \)	16T1741	Trivial (GRH)
16.4.59895026602726400000000.3	x¹⁶ - 28x¹² + 31x¹⁰ + 102x⁸ - 549x⁶ + 805x⁴ - 632x² + 149	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 149^{3} \)	16T1741	Trivial (GRH)
16.4.59895026602726400000000.4	x¹⁶ + 12x¹⁴ + 11x¹² - 101x¹⁰ - 270x⁸ - 304x⁶ - 6x⁴ + 147x² + 149	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 149^{3} \)	16T1741	Trivial (GRH)
16.0.24695998799082214400000000.2	x¹⁶ + 35x¹⁴ + 391x¹² + 2107x¹⁰ + 6265x⁸ + 10736x⁶ + 10474x⁴ + 5361x² + 1109	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 1109^{3} \)	16T1741	$[186]$ (GRH)
16.16.24695998799082214400000000.2	x¹⁶ - 35x¹⁴ + 391x¹² - 2107x¹⁰ + 6265x⁸ - 10736x⁶ + 10474x⁴ - 5361x² + 1109	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 1109^{3} \)	16T1741	Trivial (GRH)
16.0.6322175692565046886400000000.1	x¹⁶ - 8x¹⁵ + 46x¹⁴ - 96x¹³ + 204x¹² + 156x¹¹ + 858x¹⁰ - 378x⁹ + 3484x⁸ - 16316x⁷ + 66552x⁶ - 37640x⁵ + 4243x⁴ + 41710x³ + 22326x² + 66586x + 35321	\( 2^{24}\cdot 5^{8}\cdot 29^{4}\cdot 1109^{3} \)	16T1741	$[186]$ (GRH)
16.16.6322175692565046886400000000.1	x¹⁶ - 8x¹⁵ - 26x¹⁴ + 236x¹³ + 326x¹² - 2316x¹¹ - 2404x¹⁰ + 9078x⁹ + 9644x⁸ - 13868x⁷ - 17678x⁶ + 5316x⁵ + 11153x⁴ + 838x³ - 2182x² - 342x + 101	\( 2^{24}\cdot 5^{8}\cdot 29^{4}\cdot 1109^{3} \)	16T1741	Trivial (GRH)