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Results (displaying matches 1-50 of 322) Next

Label	Polynomial	Discriminant	Galois group	Class group
12.4.96717311574016.1	x¹² - x⁸ - 2x⁴ + 1	$ 2^{24}\cdot 7^{8} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.96717311574016.2	x¹² - 4x⁸ + 3x⁴ + 1	$ 2^{24}\cdot 7^{8} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.722204136308736.4	x¹² + 3x⁸ - 6x⁴ + 1	$ 2^{24}\cdot 3^{16} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.722204136308736.5	x¹² - 3x⁴ + 1	$ 2^{24}\cdot 3^{16} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.4739148267126784.3	x¹² - 2x¹⁰ - 3x⁸ + 20x⁶ - 12x⁴ - 18x² + 1	$ 2^{24}\cdot 7^{10} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.4739148267126784.7	x¹² + 4x¹⁰ - 5x⁸ - 6x⁶ + 18x⁴ - 12x² + 1	$ 2^{24}\cdot 7^{10} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.4739148267126784.9	x¹² + 6x¹⁰ + 15x⁸ + 20x⁶ + 8x⁴ - 8x² + 1	$ 2^{24}\cdot 7^{10} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.4739148267126784.10	x¹² - 2x¹⁰ - 10x⁸ + 6x⁶ - 5x⁴ - 4x² + 1	$ 2^{24}\cdot 7^{10} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.4739148267126784.19	x¹² - 4x¹⁰ - 5x⁸ + 6x⁶ + 18x⁴ + 12x² + 1	$ 2^{24}\cdot 7^{10} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.4739148267126784.21	x¹² + 2x¹⁰ - 3x⁸ - 20x⁶ - 12x⁴ + 18x² + 1	$ 2^{24}\cdot 7^{10} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.4739148267126784.26	x¹² - 49x⁴ + 49	$ 2^{24}\cdot 7^{10} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.4739148267126784.27	x¹² - 7x⁸ + 49	$ 2^{24}\cdot 7^{10} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.4739148267126784.28	x¹² - 35x⁸ - 70x⁶ + 98x² + 49	$ 2^{24}\cdot 7^{10} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.4739148267126784.29	x¹² - 21x⁸ - 28x⁶ + 147x⁴ + 196x² + 49	$ 2^{24}\cdot 7^{10} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.6189907940737024.2	x¹² + 6x¹⁰ + 11x⁸ + 4x⁶ - 13x⁴ - 18x² + 1	$ 2^{30}\cdot 7^{8} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.6189907940737024.4	x¹² - 4x¹⁰ - 6x⁸ + 18x⁶ - 17x⁴ + 6x² + 1	$ 2^{30}\cdot 7^{8} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.6499837226778624.13	x¹² + 6x¹⁰ + 12x⁸ + 8x⁶ - 3x⁴ - 6x² + 1	$ 2^{24}\cdot 3^{18} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.6499837226778624.16	x¹² - 9x⁸ - 26x⁶ - 18x⁴ + 1	$ 2^{24}\cdot 3^{18} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.6499837226778624.17	x¹² - 9x⁸ + 26x⁶ - 18x⁴ + 1	$ 2^{24}\cdot 3^{18} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.6499837226778624.25	x¹² - 6x¹⁰ - 3x⁸ + 26x⁶ - 24x⁴ + 6x² + 1	$ 2^{24}\cdot 3^{18} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.6499837226778624.28	x¹² - 6x¹⁰ + 12x⁸ - 8x⁶ - 3x⁴ + 6x² + 1	$ 2^{24}\cdot 3^{18} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.6499837226778624.31	x¹² - 9x⁸ - 10x⁶ + 18x⁴ + 18x² + 1	$ 2^{24}\cdot 3^{18} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.6499837226778624.36	x¹² - 6x¹⁰ + 6x⁶ - 99x⁴ - 108x² + 9	$ 2^{24}\cdot 3^{18} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.6499837226778624.39	x¹² - 9x⁴ + 9	$ 2^{24}\cdot 3^{18} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.6499837226778624.40	x¹² - 9x⁸ + 18x⁴ + 9	$ 2^{24}\cdot 3^{18} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.6499837226778624.42	x¹² - 6x¹⁰ + 6x⁶ + 63x⁴ + 54x² + 9	$ 2^{24}\cdot 3^{18} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.13685690504052736.5	x¹² + 3x⁸ - 10x⁴ + 1	$ 2^{24}\cdot 13^{8} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.13685690504052736.6	x¹² + x⁸ - 4x⁴ + 1	$ 2^{24}\cdot 13^{8} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.13973766757433344.6	x¹² - 9x¹⁰ - 12x⁸ + 21x⁶ + x⁴ - 2x² + 4	$ 2^{14}\cdot 31^{8} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.13973766757433344.7	x¹² - 13x¹⁰ + 38x⁸ + 27x⁶ - 29x⁴ + 4x² + 4	$ 2^{14}\cdot 31^{8} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.13973766757433344.11	x¹² + 11x⁸ - 32x⁴ + 16	$ 2^{14}\cdot 31^{8} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.13973766757433344.12	x¹² - 13x¹⁰ + 57x⁸ - 86x⁶ - 8x⁴ + 56x² + 16	$ 2^{14}\cdot 31^{8} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.46221064723759104.23	x¹² - 6x¹⁰ + 3x⁸ + 28x⁶ - 45x⁴ + 18x² + 9	$ 2^{30}\cdot 3^{16} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.46221064723759104.24	x¹² - 12x⁸ - 26x⁶ - 9x⁴ + 18x² + 9	$ 2^{30}\cdot 3^{16} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.55895067029733376.2	x¹² + 15x⁸ - 49x⁴ + 1	$ 2^{16}\cdot 31^{8} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.55895067029733376.9	x¹² - 4x⁸ - 5x⁴ + 16	$ 2^{16}\cdot 31^{8} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.284936905588473856.8	x¹² + 3x⁸ - 16x⁴ + 1	$ 2^{24}\cdot 19^{8} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.284936905588473856.9	x¹² + 2x⁸ - 5x⁴ + 1	$ 2^{24}\cdot 19^{8} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial (GRH)
12.0.303175916851972129.1	x¹² - 3x¹¹ + 8x¹⁰ + 7x⁹ + 13x⁸ - 11x⁷ - 15x⁶ + 101x⁵ - 85x⁴ - 168x³ + 197x² - 17x + 1	$ 7^{10}\cdot 181^{4} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	$[4]$
12.0.303175916851972129.2	x¹² - 3x¹¹ + 18x¹⁰ - 32x⁹ + 104x⁸ - 103x⁷ + 265x⁶ - 123x⁵ + 374x⁴ - 66x³ + 274x² - 9x + 1	$ 7^{10}\cdot 181^{4} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	$[4]$
12.4.303305489096114176.3	x¹² + 2x¹⁰ - 3x⁸ - 6x⁶ - 68x⁴ - 24x² + 1	$ 2^{30}\cdot 7^{10} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.303305489096114176.4	x¹² + 10x¹⁰ + 23x⁸ + 6x⁶ + 18x⁴ - 16x² + 1	$ 2^{30}\cdot 7^{10} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.303305489096114176.7	x¹² - 10x¹⁰ + 23x⁸ - 6x⁶ + 18x⁴ + 16x² + 1	$ 2^{30}\cdot 7^{10} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.303305489096114176.8	x¹² - 2x¹⁰ - 3x⁸ + 6x⁶ - 68x⁴ + 24x² + 1	$ 2^{30}\cdot 7^{10} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.303305489096114176.12	x¹² - 14x⁸ + 126x⁶ + 147x⁴ - 686x² + 49	$ 2^{30}\cdot 7^{10} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.303305489096114176.13	x¹² - 28x⁸ + 70x⁶ - 49x⁴ - 294x² + 49	$ 2^{30}\cdot 7^{10} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.303305489096114176.16	x¹² - 28x⁸ - 70x⁶ - 49x⁴ + 294x² + 49	$ 2^{30}\cdot 7^{10} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.303305489096114176.17	x¹² - 14x⁸ - 126x⁶ + 147x⁴ + 686x² + 49	$ 2^{30}\cdot 7^{10} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.303305489096114176.20	x¹² - 2x¹⁰ - 17x⁸ + 62x⁶ - 26x⁴ - 144x² + 169	$ 2^{30}\cdot 7^{10} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.303305489096114176.22	x¹² + 6x¹⁰ + x⁸ - 78x⁶ - 48x⁴ + 188x² + 169	$ 2^{30}\cdot 7^{10} $	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial

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Results (displaying matches 1-50 of 322) 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
12.4.96717311574016.1	x¹² - x⁸ - 2x⁴ + 1	\( 2^{24}\cdot 7^{8} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.96717311574016.2	x¹² - 4x⁸ + 3x⁴ + 1	\( 2^{24}\cdot 7^{8} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.722204136308736.4	x¹² + 3x⁸ - 6x⁴ + 1	\( 2^{24}\cdot 3^{16} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.722204136308736.5	x¹² - 3x⁴ + 1	\( 2^{24}\cdot 3^{16} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.4739148267126784.3	x¹² - 2x¹⁰ - 3x⁸ + 20x⁶ - 12x⁴ - 18x² + 1	\( 2^{24}\cdot 7^{10} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.4739148267126784.7	x¹² + 4x¹⁰ - 5x⁸ - 6x⁶ + 18x⁴ - 12x² + 1	\( 2^{24}\cdot 7^{10} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.4739148267126784.9	x¹² + 6x¹⁰ + 15x⁸ + 20x⁶ + 8x⁴ - 8x² + 1	\( 2^{24}\cdot 7^{10} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.4739148267126784.10	x¹² - 2x¹⁰ - 10x⁸ + 6x⁶ - 5x⁴ - 4x² + 1	\( 2^{24}\cdot 7^{10} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.4739148267126784.19	x¹² - 4x¹⁰ - 5x⁸ + 6x⁶ + 18x⁴ + 12x² + 1	\( 2^{24}\cdot 7^{10} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.4739148267126784.21	x¹² + 2x¹⁰ - 3x⁸ - 20x⁶ - 12x⁴ + 18x² + 1	\( 2^{24}\cdot 7^{10} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.4739148267126784.26	x¹² - 49x⁴ + 49	\( 2^{24}\cdot 7^{10} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.4739148267126784.27	x¹² - 7x⁸ + 49	\( 2^{24}\cdot 7^{10} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.4739148267126784.28	x¹² - 35x⁸ - 70x⁶ + 98x² + 49	\( 2^{24}\cdot 7^{10} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.4739148267126784.29	x¹² - 21x⁸ - 28x⁶ + 147x⁴ + 196x² + 49	\( 2^{24}\cdot 7^{10} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.6189907940737024.2	x¹² + 6x¹⁰ + 11x⁸ + 4x⁶ - 13x⁴ - 18x² + 1	\( 2^{30}\cdot 7^{8} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.6189907940737024.4	x¹² - 4x¹⁰ - 6x⁸ + 18x⁶ - 17x⁴ + 6x² + 1	\( 2^{30}\cdot 7^{8} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.6499837226778624.13	x¹² + 6x¹⁰ + 12x⁸ + 8x⁶ - 3x⁴ - 6x² + 1	\( 2^{24}\cdot 3^{18} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.6499837226778624.16	x¹² - 9x⁸ - 26x⁶ - 18x⁴ + 1	\( 2^{24}\cdot 3^{18} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.6499837226778624.17	x¹² - 9x⁸ + 26x⁶ - 18x⁴ + 1	\( 2^{24}\cdot 3^{18} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.6499837226778624.25	x¹² - 6x¹⁰ - 3x⁸ + 26x⁶ - 24x⁴ + 6x² + 1	\( 2^{24}\cdot 3^{18} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.6499837226778624.28	x¹² - 6x¹⁰ + 12x⁸ - 8x⁶ - 3x⁴ + 6x² + 1	\( 2^{24}\cdot 3^{18} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.6499837226778624.31	x¹² - 9x⁸ - 10x⁶ + 18x⁴ + 18x² + 1	\( 2^{24}\cdot 3^{18} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.6499837226778624.36	x¹² - 6x¹⁰ + 6x⁶ - 99x⁴ - 108x² + 9	\( 2^{24}\cdot 3^{18} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.6499837226778624.39	x¹² - 9x⁴ + 9	\( 2^{24}\cdot 3^{18} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.6499837226778624.40	x¹² - 9x⁸ + 18x⁴ + 9	\( 2^{24}\cdot 3^{18} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.6499837226778624.42	x¹² - 6x¹⁰ + 6x⁶ + 63x⁴ + 54x² + 9	\( 2^{24}\cdot 3^{18} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.13685690504052736.5	x¹² + 3x⁸ - 10x⁴ + 1	\( 2^{24}\cdot 13^{8} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.13685690504052736.6	x¹² + x⁸ - 4x⁴ + 1	\( 2^{24}\cdot 13^{8} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.13973766757433344.6	x¹² - 9x¹⁰ - 12x⁸ + 21x⁶ + x⁴ - 2x² + 4	\( 2^{14}\cdot 31^{8} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.13973766757433344.7	x¹² - 13x¹⁰ + 38x⁸ + 27x⁶ - 29x⁴ + 4x² + 4	\( 2^{14}\cdot 31^{8} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.13973766757433344.11	x¹² + 11x⁸ - 32x⁴ + 16	\( 2^{14}\cdot 31^{8} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.13973766757433344.12	x¹² - 13x¹⁰ + 57x⁸ - 86x⁶ - 8x⁴ + 56x² + 16	\( 2^{14}\cdot 31^{8} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.46221064723759104.23	x¹² - 6x¹⁰ + 3x⁸ + 28x⁶ - 45x⁴ + 18x² + 9	\( 2^{30}\cdot 3^{16} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.46221064723759104.24	x¹² - 12x⁸ - 26x⁶ - 9x⁴ + 18x² + 9	\( 2^{30}\cdot 3^{16} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.55895067029733376.2	x¹² + 15x⁸ - 49x⁴ + 1	\( 2^{16}\cdot 31^{8} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.55895067029733376.9	x¹² - 4x⁸ - 5x⁴ + 16	\( 2^{16}\cdot 31^{8} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.284936905588473856.8	x¹² + 3x⁸ - 16x⁴ + 1	\( 2^{24}\cdot 19^{8} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.284936905588473856.9	x¹² + 2x⁸ - 5x⁴ + 1	\( 2^{24}\cdot 19^{8} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial (GRH)
12.0.303175916851972129.1	x¹² - 3x¹¹ + 8x¹⁰ + 7x⁹ + 13x⁸ - 11x⁷ - 15x⁶ + 101x⁵ - 85x⁴ - 168x³ + 197x² - 17x + 1	\( 7^{10}\cdot 181^{4} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	$[4]$
12.0.303175916851972129.2	x¹² - 3x¹¹ + 18x¹⁰ - 32x⁹ + 104x⁸ - 103x⁷ + 265x⁶ - 123x⁵ + 374x⁴ - 66x³ + 274x² - 9x + 1	\( 7^{10}\cdot 181^{4} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	$[4]$
12.4.303305489096114176.3	x¹² + 2x¹⁰ - 3x⁸ - 6x⁶ - 68x⁴ - 24x² + 1	\( 2^{30}\cdot 7^{10} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.303305489096114176.4	x¹² + 10x¹⁰ + 23x⁸ + 6x⁶ + 18x⁴ - 16x² + 1	\( 2^{30}\cdot 7^{10} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.303305489096114176.7	x¹² - 10x¹⁰ + 23x⁸ - 6x⁶ + 18x⁴ + 16x² + 1	\( 2^{30}\cdot 7^{10} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.303305489096114176.8	x¹² - 2x¹⁰ - 3x⁸ + 6x⁶ - 68x⁴ + 24x² + 1	\( 2^{30}\cdot 7^{10} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.303305489096114176.12	x¹² - 14x⁸ + 126x⁶ + 147x⁴ - 686x² + 49	\( 2^{30}\cdot 7^{10} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.303305489096114176.13	x¹² - 28x⁸ + 70x⁶ - 49x⁴ - 294x² + 49	\( 2^{30}\cdot 7^{10} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.303305489096114176.16	x¹² - 28x⁸ - 70x⁶ - 49x⁴ + 294x² + 49	\( 2^{30}\cdot 7^{10} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.303305489096114176.17	x¹² - 14x⁸ - 126x⁶ + 147x⁴ + 686x² + 49	\( 2^{30}\cdot 7^{10} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.303305489096114176.20	x¹² - 2x¹⁰ - 17x⁸ + 62x⁶ - 26x⁴ - 144x² + 169	\( 2^{30}\cdot 7^{10} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial
12.4.303305489096114176.22	x¹² + 6x¹⁰ + x⁸ - 78x⁶ - 48x⁴ + 188x² + 169	\( 2^{30}\cdot 7^{10} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	Trivial