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Label Polynomial Discriminant Galois group Class group
4.4.4205.1 x4 - x3 - 5x2 - x + 1 \( 5\cdot 29^{2} \) $D_{4}$ (as 4T3) trivial
4.2.5887.1 x4 - x3 - 3x2 - 2x + 4 \( -\,7\cdot 29^{2} \) $D_{4}$ (as 4T3) trivial
4.0.7569.1 x4 - x3 + 8x2 + 7x + 49 \( 3^{2}\cdot 29^{2} \) $C_2^2$ (as 4T2) $[3]$
4.0.10933.1 x4 - x3 - x2 - 3x + 9 \( 13\cdot 29^{2} \) $D_{4}$ (as 4T3) trivial
4.2.19343.1 x4 - x3 + 11x + 5 \( -\,23\cdot 29^{2} \) $D_{4}$ (as 4T3) trivial
4.0.41209.1 x4 - x3 + 5x2 - 6x + 7 \( 7^{2}\cdot 29^{2} \) $A_4$ (as 4T4) $[2]$
4.2.49619.1 x4 - x3 - 2x2 + 12x - 1 \( -\,29^{2}\cdot 59 \) $D_{4}$ (as 4T3) trivial
4.0.53824.1 x4 - 2x3 - 9x2 + 10x + 83 \( 2^{6}\cdot 29^{2} \) $C_2^2$ (as 4T2) trivial
4.4.53824.1 x4 - 2x3 - 17x2 + 18x + 23 \( 2^{6}\cdot 29^{2} \) $C_2^2$ (as 4T2) trivial
4.0.67280.1 x4 + 7x2 + 5 \( 2^{4}\cdot 5\cdot 29^{2} \) $D_{4}$ (as 4T3) $[2]$
4.2.69803.1 x4 - x3 + 5x2 + 23x + 7 \( -\,29^{2}\cdot 83 \) $D_{4}$ (as 4T3) trivial
4.2.86623.1 x4 - 2x3 + 11x2 - 10x - 4 \( -\,29^{2}\cdot 103 \) $D_{4}$ (as 4T3) trivial
4.2.89987.1 x4 - 2x3 + x - 7 \( -\,29^{2}\cdot 107 \) $D_{4}$ (as 4T3) trivial
4.4.91669.1 x4 - 2x3 - 6x2 + 7x + 5 \( 29^{2}\cdot 109 \) $D_{4}$ (as 4T3) trivial
4.2.94192.1 x4 - x2 - 7 \( -\,2^{4}\cdot 7\cdot 29^{2} \) $D_{4}$ (as 4T3) trivial
4.0.98397.1 x4 - 2x3 + 10x2 - 9x + 42 \( 3^{2}\cdot 13\cdot 29^{2} \) $D_{4}$ (as 4T3) $[6]$
4.0.98397.3 x4 - x3 - 50x2 + 36x + 687 \( 3^{2}\cdot 13\cdot 29^{2} \) $D_{4}$ (as 4T3) $[2]$
4.0.101761.1 x4 - 9x2 + 100 \( 11^{2}\cdot 29^{2} \) $C_2^2$ (as 4T2) $[5]$
4.2.116899.1 x4 - x3 - 18x + 5 \( -\,29^{2}\cdot 139 \) $D_{4}$ (as 4T3) trivial
4.0.121104.1 x4 + 13x2 + 64 \( 2^{4}\cdot 3^{2}\cdot 29^{2} \) $C_2^2$ (as 4T2) $[3, 6]$
4.4.121104.1 x4 - 2x3 - 19x2 + 20x + 13 \( 2^{4}\cdot 3^{2}\cdot 29^{2} \) $C_2^2$ (as 4T2) trivial
4.0.121104.3 x4 - 29x2 + 841 \( 2^{4}\cdot 3^{2}\cdot 29^{2} \) $C_2^2$ (as 4T2) $[6]$
4.0.125309.1 x4 - x3 + 3x2 - 5x + 25 \( 29^{2}\cdot 149 \) $D_{4}$ (as 4T3) $[5]$
4.0.145493.1 x4 - 2x3 + 10x2 - 9x + 13 \( 29^{2}\cdot 173 \) $D_{4}$ (as 4T3) $[3]$
4.2.147175.1 x4 - x3 - 2x2 - 17x - 1 \( -\,5^{2}\cdot 7\cdot 29^{2} \) $D_{4}$ (as 4T3) $[2, 2]$
4.2.167359.2 x4 - x3 + 3x2 + 24x - 4 \( -\,29^{2}\cdot 199 \) $D_{4}$ (as 4T3) trivial
4.4.174928.1 x4 - 9x2 + 13 \( 2^{4}\cdot 13\cdot 29^{2} \) $D_{4}$ (as 4T3) trivial
4.2.181656.1 x4 - 2x3 - 6x2 - 22x + 5 \( -\,2^{3}\cdot 3^{3}\cdot 29^{2} \) $S_4$ (as 4T5) $[2]$
4.0.181656.2 x4 - x3 + 9x2 - 37x + 64 \( 2^{3}\cdot 3^{3}\cdot 29^{2} \) $D_{4}$ (as 4T3) $[6]$
4.2.187543.1 x4 - x3 - 9x2 + 30x - 28 \( -\,29^{2}\cdot 223 \) $D_{4}$ (as 4T3) trivial
4.0.189225.1 x4 - 7x2 + 121 \( 3^{2}\cdot 5^{2}\cdot 29^{2} \) $C_2^2$ (as 4T2) $[2, 2]$
4.0.189225.3 x4 - x3 - 5x2 + 57x + 204 \( 3^{2}\cdot 5^{2}\cdot 29^{2} \) $C_2^2$ (as 4T2) $[24]$
4.0.189225.4 x4 - x3 + 37x2 + 36x + 1296 \( 3^{2}\cdot 5^{2}\cdot 29^{2} \) $C_2^2$ (as 4T2) $[8]$
4.2.190907.1 x4 - x3 - 16x2 + 48x - 45 \( -\,29^{2}\cdot 227 \) $D_{4}$ (as 4T3) trivial
4.2.200999.1 x4 - 2x3 + 9x2 - 8x - 13 \( -\,29^{2}\cdot 239 \) $D_{4}$ (as 4T3) trivial
4.4.202681.1 x4 - x3 - 12x2 + 17x - 1 \( 29^{2}\cdot 241 \) $D_{4}$ (as 4T3) trivial
4.0.206045.1 x4 - x3 + 9x2 + 21x + 35 \( 5\cdot 7^{2}\cdot 29^{2} \) $D_{4}$ (as 4T3) $[2, 2]$
4.0.211932.1 x4 - 5x2 + 28 \( 2^{2}\cdot 3^{2}\cdot 7\cdot 29^{2} \) $D_{4}$ (as 4T3) $[6]$
4.0.211932.2 x4 + 5x2 + 28 \( 2^{2}\cdot 3^{2}\cdot 7\cdot 29^{2} \) $D_{4}$ (as 4T3) $[6]$
4.0.215296.1 x4 + 28x2 + 225 \( 2^{8}\cdot 29^{2} \) $C_2^2$ (as 4T2) $[6]$
4.0.215296.2 x4 - 28x2 + 225 \( 2^{8}\cdot 29^{2} \) $C_2^2$ (as 4T2) $[6]$
4.0.222865.1 x4 - 2x3 + 15x2 - 14x + 20 \( 5\cdot 29^{2}\cdot 53 \) $D_{4}$ (as 4T3) $[8]$
4.0.222865.2 x4 - x3 + 5x2 - 6x + 36 \( 5\cdot 29^{2}\cdot 53 \) $D_{4}$ (as 4T3) $[6]$
4.4.243049.1 x4 - 23x2 + 9 \( 17^{2}\cdot 29^{2} \) $C_2^2$ (as 4T2) trivial
4.0.249777.2 x4 - 2x3 + 9x2 - 8x + 103 \( 3^{3}\cdot 11\cdot 29^{2} \) $D_{4}$ (as 4T3) $[6]$
4.2.264915.1 x4 - 2x3 - 12x2 + 13x - 23 \( -\,3^{2}\cdot 5\cdot 7\cdot 29^{2} \) $D_{4}$ (as 4T3) $[2]$
4.2.264915.2 x4 - x3 + 5x2 - 35x + 7 \( -\,3^{2}\cdot 5\cdot 7\cdot 29^{2} \) $D_{4}$ (as 4T3) $[2]$
4.2.269120.1 x4 - 6x2 - 20 \( -\,2^{6}\cdot 5\cdot 29^{2} \) $D_{4}$ (as 4T3) $[2]$
4.2.269120.2 x4 + 6x2 - 20 \( -\,2^{6}\cdot 5\cdot 29^{2} \) $D_{4}$ (as 4T3) $[2]$
4.0.269120.2 x4 - 2x3 + 20x2 + 10x + 25 \( 2^{6}\cdot 5\cdot 29^{2} \) $D_{4}$ (as 4T3) $[12]$
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