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Label Polynomial Discriminant Galois group Class group
4.2.41743.1 x4 - 2x3 - 5x2 - 7x - 4 \( -\,13^{3}\cdot 19 \) $S_4$ (as 4T5) $[2]$
4.4.274625.1 x4 - x3 - 24x2 + 4x + 16 \( 5^{3}\cdot 13^{3} \) $C_4$ (as 4T1) $[2]$
4.2.384475.1 x4 - 2x3 + 8x2 - 7x - 4 \( -\,5^{2}\cdot 7\cdot 13^{3} \) $D_{4}$ (as 4T3) $[2]$
4.2.413036.1 x4 - x3 + 2x2 + 56x + 68 \( -\,2^{2}\cdot 13^{3}\cdot 47 \) $S_4$ (as 4T5) $[2]$
4.2.439400.1 x4 - x3 - 11x2 + 30x - 10 \( -\,2^{3}\cdot 5^{2}\cdot 13^{3} \) $D_{4}$ (as 4T3) $[2]$
4.0.439400.1 x4 + 13x2 + 26 \( 2^{3}\cdot 5^{2}\cdot 13^{3} \) $D_{4}$ (as 4T3) $[20]$
4.0.538265.1 x4 - x3 + 15x2 + 4x + 16 \( 5\cdot 7^{2}\cdot 13^{3} \) $D_{4}$ (as 4T3) $[4]$
4.2.595387.1 x4 - x3 + 2x2 + 4x - 49 \( -\,13^{3}\cdot 271 \) $S_4$ (as 4T5) $[2]$
4.2.639327.1 x4 - 13x2 - 13x + 26 \( -\,3\cdot 13^{3}\cdot 97 \) $S_4$ (as 4T5) $[2]$
4.0.703040.1 x4 - 2x3 - 5x2 + 6x + 35 \( 2^{6}\cdot 5\cdot 13^{3} \) $D_{4}$ (as 4T3) $[12]$
4.0.703040.2 x4 - 2x3 - 5x2 - 20x + 100 \( 2^{6}\cdot 5\cdot 13^{3} \) $D_{4}$ (as 4T3) $[20]$
4.2.755768.1 x4 - x3 - 11x2 - 22x - 10 \( -\,2^{3}\cdot 13^{3}\cdot 43 \) $S_4$ (as 4T5) $[2]$
4.0.782132.1 x4 - x3 + 2x2 + 4x + 120 \( 2^{2}\cdot 13^{3}\cdot 89 \) $S_4$ (as 4T5) $[4]$
4.2.841451.1 x4 - 2x3 - 18x2 - 33x - 17 \( -\,13^{3}\cdot 383 \) $S_4$ (as 4T5) $[4]$
4.2.841451.2 x4 - 2x3 - 18x2 - 7x - 82 \( -\,13^{3}\cdot 383 \) $S_4$ (as 4T5) $[4]$
4.2.982059.1 x4 - x3 - 11x2 - 9x + 29 \( -\,3\cdot 13^{3}\cdot 149 \) $S_4$ (as 4T5) $[2]$
4.0.1080924.1 x4 - x3 + 28x2 - 9x + 185 \( 2^{2}\cdot 3\cdot 13^{3}\cdot 41 \) $S_4$ (as 4T5) $[20]$
4.2.1096303.1 x4 - x3 - 11x2 + 56x + 16 \( -\,13^{3}\cdot 499 \) $S_4$ (as 4T5) $[2]$
4.2.1098500.2 x4 - x3 - 24x2 - 61x - 49 \( -\,2^{2}\cdot 5^{3}\cdot 13^{3} \) $D_{4}$ (as 4T3) $[2, 4]$
4.2.1124864.1 x4 - 52x - 143 \( -\,2^{9}\cdot 13^{3} \) $S_4$ (as 4T5) $[4]$
4.0.1127061.2 x4 - x3 + 15x2 - 35x + 68 \( 3^{3}\cdot 13^{3}\cdot 19 \) $S_4$ (as 4T5) $[4]$
4.2.1157819.1 x4 - x3 + 15x2 - 48x + 16 \( -\,13^{3}\cdot 17\cdot 31 \) $S_4$ (as 4T5) $[2]$
4.2.1184183.1 x4 - 2x3 - 5x2 - 7x + 9 \( -\,7^{2}\cdot 11\cdot 13^{3} \) $S_4$ (as 4T5) $[2]$
4.2.1186380.1 x4 - x3 - 24x2 + 56x + 16 \( -\,2^{2}\cdot 3^{3}\cdot 5\cdot 13^{3} \) $S_4$ (as 4T5) $[4]$
4.0.1302821.2 x4 - x3 + 28x2 + 4x + 224 \( 13^{3}\cdot 593 \) $S_4$ (as 4T5) $[12]$
4.0.1537900.1 x4 - x3 + 2x2 - 9x + 81 \( 2^{2}\cdot 5^{2}\cdot 7\cdot 13^{3} \) $D_{4}$ (as 4T3) $[2, 4]$
4.4.1537900.2 x4 - 39x2 + 364 \( 2^{2}\cdot 5^{2}\cdot 7\cdot 13^{3} \) $D_{4}$ (as 4T3) $[2]$
4.2.1546688.2 x4 - 2x3 + 21x2 - 20x - 4 \( -\,2^{6}\cdot 11\cdot 13^{3} \) $D_{4}$ (as 4T3) $[2]$
4.4.1555476.1 x4 - x3 - 37x2 + 69x + 120 \( 2^{2}\cdot 3\cdot 13^{3}\cdot 59 \) $S_4$ (as 4T5) $[2]$
4.0.1557673.1 x4 - 13x2 - 13x + 78 \( 13^{3}\cdot 709 \) $S_4$ (as 4T5) $[4]$
4.2.1729039.1 x4 - x3 - 11x2 + 17x - 62 \( -\,13^{3}\cdot 787 \) $S_4$ (as 4T5) $[2]$
4.2.1757600.1 x4 + 13x2 - 104 \( -\,2^{5}\cdot 5^{2}\cdot 13^{3} \) $D_{4}$ (as 4T3) $[4]$
4.4.1757600.1 x4 - 13x2 + 26 \( 2^{5}\cdot 5^{2}\cdot 13^{3} \) $D_{4}$ (as 4T3) $[2]$
4.2.1766388.1 x4 - x3 - 24x2 - 74x - 88 \( -\,2^{2}\cdot 3\cdot 13^{3}\cdot 67 \) $S_4$ (as 4T5) $[2]$
4.2.1775176.1 x4 - 2x3 - 5x2 - 20x + 48 \( -\,2^{3}\cdot 13^{3}\cdot 101 \) $S_4$ (as 4T5) $[2]$
4.2.1896011.1 x4 - 2x3 + 8x2 + 19x - 17 \( -\,13^{3}\cdot 863 \) $S_4$ (as 4T5) $[2]$
4.0.1898208.1 x4 - 2x3 - 18x2 + 6x + 165 \( 2^{5}\cdot 3^{3}\cdot 13^{3} \) $S_4$ (as 4T5) $[4]$
4.2.1959724.1 x4 - x3 - 24x2 + 56x - 36 \( -\,2^{2}\cdot 13^{3}\cdot 223 \) $S_4$ (as 4T5) $[2, 2]$
4.2.1959724.2 x4 - x3 + 15x2 - 35x + 16 \( -\,2^{2}\cdot 13^{3}\cdot 223 \) $S_4$ (as 4T5) $[2, 2]$
4.2.1986088.1 x4 - 2x3 - 18x2 - 20x + 48 \( -\,2^{3}\cdot 13^{3}\cdot 113 \) $S_4$ (as 4T5) $[2]$
4.2.2003664.1 x4 - 2x3 - 5x2 - 72x + 243 \( -\,2^{4}\cdot 3\cdot 13^{3}\cdot 19 \) $S_4$ (as 4T5) $[2]$
4.0.2032225.2 x4 - x3 + 15x2 + 17x + 224 \( 5^{2}\cdot 13^{3}\cdot 37 \) $D_{4}$ (as 4T3) $[68]$
4.0.2102529.1 x4 - x3 + 28x2 - 9x + 198 \( 3\cdot 11\cdot 13^{3}\cdot 29 \) $S_4$ (as 4T5) $[12]$
4.2.2126696.1 x4 - x3 + 2x2 + 17x + 3 \( -\,2^{3}\cdot 11^{2}\cdot 13^{3} \) $S_4$ (as 4T5) $[4]$
4.0.2126696.1 x4 - x3 + 28x2 + 4x + 16 \( 2^{3}\cdot 11^{2}\cdot 13^{3} \) $D_{4}$ (as 4T3) $[20]$
4.2.2203591.1 x4 - x3 - 11x2 + 56x - 153 \( -\,13^{3}\cdot 17\cdot 59 \) $S_4$ (as 4T5) $[2]$
4.2.2214576.1 x4 - 2x3 + 8x2 + 32x - 56 \( -\,2^{4}\cdot 3^{2}\cdot 7\cdot 13^{3} \) $S_4$ (as 4T5) $[4]$
4.2.2240940.1 x4 - x3 - 11x2 - 9x - 10 \( -\,2^{2}\cdot 3\cdot 5\cdot 13^{3}\cdot 17 \) $S_4$ (as 4T5) $[2]$
4.0.2243137.1 x4 - x3 + 15x2 + 4x + 3 \( 13^{3}\cdot 1021 \) $S_4$ (as 4T5) $[4]$
4.2.2328820.1 x4 - 13x2 - 130x + 26 \( -\,2^{2}\cdot 5\cdot 13^{3}\cdot 53 \) $S_4$ (as 4T5) $[2]$
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