Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying matches 1-50 of )

Label	Polynomial	Discriminant	Galois group	Class group
4.0.1921600.2	x^4 - 2x^3 + 47x^2 + 104x + 144	\( 2^{6}\cdot 5^{2}\cdot 1201 \)	$D_{4}$ (as 4T3)	$[2, 58]$
4.0.2228265.3	x^4 - x^3 - 8x^2 - 108x + 432	\( 3^{2}\cdot 5\cdot 13^{2}\cdot 293 \)	$D_{4}$ (as 4T3)	$[104]$
4.0.2471625.1	x^4 - x^3 + 41x^2 - 191x + 406	\( 3^{2}\cdot 5^{3}\cdot 13^{3} \)	$C_4$ (as 4T1)	$[2, 52]$
4.0.2712225.1	x^4 - 2x^3 + 31x^2 - 30x + 80	\( 3\cdot 5^{2}\cdot 29^{2}\cdot 43 \)	$D_{4}$ (as 4T3)	$[104]$
4.0.2752576.4	x^4 - 2x^3 + 111x^2 - 56x + 2744	\( 2^{6}\cdot 41\cdot 1049 \)	$D_{4}$ (as 4T3)	$[104]$
4.0.2764864.1	x^4 - 2x^3 + 127x^2 - 24x + 2744	\( 2^{6}\cdot 43201 \)	$D_{4}$ (as 4T3)	$[105]$
4.0.2832200.2	x^4 - x^3 - x^2 + 75x + 270	\( 2^{3}\cdot 5^{2}\cdot 7^{2}\cdot 17^{2} \)	$D_{4}$ (as 4T3)	$[2, 60]$
4.0.2859400.2	x^4 - x^3 - 18x + 324	\( 2^{3}\cdot 5^{2}\cdot 17\cdot 29^{2} \)	$D_{4}$ (as 4T3)	$[104]$
4.0.2892601.1	x^4 - 2x^3 + 91x^2 - 90x + 648	\( 17^{2}\cdot 10009 \)	$D_{4}$ (as 4T3)	$[113]$
4.0.2921536.1	x^4 - 2x^3 + 131x^2 - 24x + 2898	\( 2^{6}\cdot 191\cdot 239 \)	$D_{4}$ (as 4T3)	$[102]$
4.0.2943944.1	x^4 - x^3 + 31x^2 + 29x + 60	\( 2^{3}\cdot 71^{2}\cdot 73 \)	$D_{4}$ (as 4T3)	$[126]$
4.0.2958400.4	x^4 + 38x^2 + 576	\( 2^{6}\cdot 5^{2}\cdot 43^{2} \)	$C_2^2$ (as 4T2)	$[140]$
4.0.3066001.1	x^4 + 43x^2 + 900	\( 17^{2}\cdot 103^{2} \)	$C_2^2$ (as 4T2)	$[120]$
4.0.3079873.1	x^4 - 2x^3 + 73x^2 - 72x + 684	\( 17^{2}\cdot 10657 \)	$D_{4}$ (as 4T3)	$[109]$
4.0.3100116.2	x^4 - x^3 + 9x^2 + 93x + 216	\( 2^{2}\cdot 3\cdot 19\cdot 13597 \)	$S_4$ (as 4T5)	$[102]$
4.0.3114553.1	x^4 - 2x^3 + 59x^2 - 58x + 688	\( 13\cdot 17^{2}\cdot 829 \)	$D_{4}$ (as 4T3)	$[102]$
4.0.3169296.2	x^4 + 73x^2 - 12x + 1432	\( 2^{4}\cdot 3^{2}\cdot 13\cdot 1693 \)	$D_{4}$ (as 4T3)	$[104]$
4.0.3182656.4	x^4 - 2x^3 + 109x^2 - 108x + 3362	\( 2^{6}\cdot 223^{2} \)	$C_2^2$ (as 4T2)	$[112]$
4.0.3186225.2	x^4 - x^3 + 34x^2 - 240x + 480	\( 3^{2}\cdot 5^{2}\cdot 7^{2}\cdot 17^{2} \)	$C_2^2$ (as 4T2)	$[2, 60]$
4.0.3194944.1	x^4 - 2x^3 + 121x^2 - 120x + 3150	\( 2^{6}\cdot 49921 \)	$D_{4}$ (as 4T3)	$[109]$
4.0.3246337.1	x^4 - 2x^3 + 57x^2 - 56x + 716	\( 17^{2}\cdot 47\cdot 239 \)	$D_{4}$ (as 4T3)	$[108]$
4.0.3247168.10	x^4 - 2x^3 + 139x^2 - 24x + 3218	\( 2^{6}\cdot 113\cdot 449 \)	$D_{4}$ (as 4T3)	$[110]$
4.0.3265600.7	x^4 + 44x^2 - 60x + 639	\( 2^{6}\cdot 5^{2}\cdot 13\cdot 157 \)	$D_{4}$ (as 4T3)	$[116]$
4.0.3285641.1	x^4 - x^3 + 105x^2 - 63x + 2966	\( 17^{2}\cdot 11369 \)	$D_{4}$ (as 4T3)	$[103]$
4.0.3286800.1	x^4 - 2x^3 + 79x^2 - 78x + 1446	\( 2^{4}\cdot 3^{2}\cdot 5^{2}\cdot 11\cdot 83 \)	$D_{4}$ (as 4T3)	$[2, 54]$
4.0.3342400.4	x^4 - 2x^3 + 77x^2 - 76x + 1194	\( 2^{6}\cdot 5^{2}\cdot 2089 \)	$D_{4}$ (as 4T3)	$[144]$
4.0.3349008.2	x^4 + 97x^2 - 108x + 1528	\( 2^{4}\cdot 3^{2}\cdot 13\cdot 1789 \)	$D_{4}$ (as 4T3)	$[104]$
4.0.3369024.2	x^4 - 2x^3 + 119x^2 - 76x + 3358	\( 2^{6}\cdot 3^{2}\cdot 5849 \)	$D_{4}$ (as 4T3)	$[102]$
4.0.3376192.4	x^4 - 2x^3 + 141x^2 - 140x + 3332	\( 2^{6}\cdot 71\cdot 743 \)	$D_{4}$ (as 4T3)	$[110]$
4.0.3385057.2	x^4 - x^3 + 113x^2 - 135x + 3078	\( 13\cdot 17^{3}\cdot 53 \)	$D_{4}$ (as 4T3)	$[2, 58]$
4.0.3403553.2	x^4 - 2x^3 + 65x^2 - 64x + 752	\( 17^{2}\cdot 11777 \)	$D_{4}$ (as 4T3)	$[105]$
4.0.3438864.1	x^4 - 2x^3 + 103x^2 - 102x + 1518	\( 2^{4}\cdot 3^{2}\cdot 11\cdot 13\cdot 167 \)	$D_{4}$ (as 4T3)	$[2, 52]$
4.0.3441025.4	x^4 + 183x^2 + 8836	\( 5^{2}\cdot 7^{2}\cdot 53^{2} \)	$C_2^2$ (as 4T2)	$[112]$
4.0.3441232.1	x^4 + 11x^2 - 18x + 90	\( 2^{4}\cdot 215077 \)	$S_4$ (as 4T5)	$[106]$
4.0.3445776.1	x^4 - 2x^3 + 91x^2 - 90x + 1518	\( 2^{4}\cdot 3^{2}\cdot 23929 \)	$D_{4}$ (as 4T3)	$[118]$
4.0.3462208.1	x^4 - 2x^3 + 147x^2 - 20x + 3428	\( 2^{6}\cdot 47\cdot 1151 \)	$D_{4}$ (as 4T3)	$[104]$
4.0.3486025.1	x^4 - x^3 + 188x^2 - 67x + 8779	\( 5^{2}\cdot 19\cdot 41\cdot 179 \)	$D_{4}$ (as 4T3)	$[2, 52]$
4.0.3508288.2	x^4 - 2x^3 + 119x^2 - 92x + 3502	\( 2^{6}\cdot 7\cdot 41\cdot 191 \)	$D_{4}$ (as 4T3)	$[2, 54]$
4.0.3559824.1	x^4 + 79x^2 - 30x + 1606	\( 2^{4}\cdot 3^{2}\cdot 59\cdot 419 \)	$D_{4}$ (as 4T3)	$[106]$
4.0.3572076.2	x^4 - 2x^3 + x^2 - 12x + 324	\( 2^{2}\cdot 3\cdot 19\cdot 15667 \)	$S_4$ (as 4T5)	$[112]$
4.0.3582016.2	x^4 - 2x^3 + 121x^2 - 120x + 3528	\( 2^{6}\cdot 97\cdot 577 \)	$D_{4}$ (as 4T3)	$[106]$
4.0.3585025.1	x^4 - x^3 + 199x^2 - 30x + 9020	\( 5^{2}\cdot 143401 \)	$D_{4}$ (as 4T3)	$[103]$
4.0.3609664.2	x^4 - 2x^3 + 125x^2 - 124x + 3556	\( 2^{6}\cdot 56401 \)	$D_{4}$ (as 4T3)	$[111]$
4.0.3624000.2	x^4 + 60x^2 - 140x + 735	\( 2^{6}\cdot 3\cdot 5^{3}\cdot 151 \)	$D_{4}$ (as 4T3)	$[4, 28]$
4.0.3624025.1	x^4 - x^3 + 198x^2 - 37x + 9119	\( 5^{2}\cdot 144961 \)	$D_{4}$ (as 4T3)	$[103]$
4.0.3645504.2	x^4 - 2x^3 + 153x^2 - 152x + 3598	\( 2^{6}\cdot 3^{2}\cdot 6329 \)	$D_{4}$ (as 4T3)	$[110]$
4.0.3664809.1	x^4 - 2x^3 + 63x^2 - 62x + 808	\( 3^{2}\cdot 17^{2}\cdot 1409 \)	$D_{4}$ (as 4T3)	$[106]$
4.0.3687025.1	x^4 - x^3 + 193x^2 - 72x + 9284	\( 5^{2}\cdot 147481 \)	$D_{4}$ (as 4T3)	$[101]$
4.0.3698184.1	x^4 - 2x^3 + 42x^2 + 42x + 45	\( 2^{3}\cdot 3\cdot 7\cdot 22013 \)	$S_4$ (as 4T5)	$[103]$
4.0.3722225.1	x^4 - 2x^3 + 37x^2 - 36x + 64	\( 5^{2}\cdot 13^{2}\cdot 881 \)	$D_{4}$ (as 4T3)	$[2, 54]$

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