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Label Polynomial Discriminant Galois group Class group
4.0.125.1 x4 - x3 + x2 - x + 1 \( 5^{3} \) $C_4$ (as 4T1) Trivial
4.4.1125.1 x4 - x3 - 4x2 + 4x + 1 \( 3^{2}\cdot 5^{3} \) $C_4$ (as 4T1) Trivial
4.4.2000.1 x4 - 5x2 + 5 \( 2^{4}\cdot 5^{3} \) $C_4$ (as 4T1) Trivial
4.4.2048.1 x4 - 4x2 + 2 \( 2^{11} \) $C_4$ (as 4T1) Trivial
4.0.2048.2 x4 + 4x2 + 2 \( 2^{11} \) $C_4$ (as 4T1) Trivial
4.0.2197.1 x4 - x3 + 2x2 + 4x + 3 \( 13^{3} \) $C_4$ (as 4T1) Trivial
4.4.4913.1 x4 - x3 - 6x2 + x + 1 \( 17^{3} \) $C_4$ (as 4T1) Trivial
4.4.6125.1 x4 - x3 - 9x2 + 9x + 11 \( 5^{3}\cdot 7^{2} \) $C_4$ (as 4T1) Trivial
4.4.8000.1 x4 - 10x2 + 20 \( 2^{6}\cdot 5^{3} \) $C_4$ (as 4T1) Trivial
4.0.8000.2 x4 + 10x2 + 20 \( 2^{6}\cdot 5^{3} \) $C_4$ (as 4T1) $[2]$
4.4.15125.1 x4 - x3 - 14x2 + 14x + 31 \( 5^{3}\cdot 11^{2} \) $C_4$ (as 4T1) Trivial
4.0.18000.1 x4 + 15x2 + 45 \( 2^{4}\cdot 3^{2}\cdot 5^{3} \) $C_4$ (as 4T1) $[2, 2]$
4.4.18432.1 x4 - 12x2 + 18 \( 2^{11}\cdot 3^{2} \) $C_4$ (as 4T1) Trivial
4.0.18432.2 x4 + 12x2 + 18 \( 2^{11}\cdot 3^{2} \) $C_4$ (as 4T1) $[2]$
4.4.19773.1 x4 - x3 - 11x2 - 9x + 3 \( 3^{2}\cdot 13^{3} \) $C_4$ (as 4T1) Trivial
4.0.21125.1 x4 - x3 + 16x2 - 16x + 61 \( 5^{3}\cdot 13^{2} \) $C_4$ (as 4T1) $[2]$
4.0.24389.1 x4 - x3 + 4x2 - 20x + 23 \( 29^{3} \) $C_4$ (as 4T1) Trivial
4.4.35152.1 x4 - 13x2 + 13 \( 2^{4}\cdot 13^{3} \) $C_4$ (as 4T1) Trivial
4.0.36125.1 x4 - x3 + 21x2 - 21x + 101 \( 5^{3}\cdot 17^{2} \) $C_4$ (as 4T1) $[2]$
4.0.44217.1 x4 - x3 + 11x2 + x + 52 \( 3^{2}\cdot 17^{3} \) $C_4$ (as 4T1) $[10]$
4.4.45125.1 x4 - x3 - 24x2 + 24x + 101 \( 5^{3}\cdot 19^{2} \) $C_4$ (as 4T1) Trivial
4.0.50653.1 x4 - x3 + 5x2 - 7x + 49 \( 37^{3} \) $C_4$ (as 4T1) Trivial
4.4.51200.1 x4 - 20x2 + 50 \( 2^{11}\cdot 5^{2} \) $C_4$ (as 4T1) $[2]$
4.0.51200.2 x4 + 20x2 + 50 \( 2^{11}\cdot 5^{2} \) $C_4$ (as 4T1) $[2]$
4.0.54925.1 x4 - x3 + 15x2 + 17x + 29 \( 5^{2}\cdot 13^{3} \) $C_4$ (as 4T1) $[2]$
4.0.55125.1 x4 - x3 + 26x2 - 26x + 151 \( 3^{2}\cdot 5^{3}\cdot 7^{2} \) $C_4$ (as 4T1) $[2, 2]$
4.4.66125.1 x4 - x3 - 29x2 + 29x + 151 \( 5^{3}\cdot 23^{2} \) $C_4$ (as 4T1) Trivial
4.4.68921.1 x4 - x3 - 15x2 - 18x - 4 \( 41^{3} \) $C_4$ (as 4T1) Trivial
4.4.72000.1 x4 - 30x2 + 180 \( 2^{6}\cdot 3^{2}\cdot 5^{3} \) $C_4$ (as 4T1) $[2]$
4.0.72000.2 x4 + 30x2 + 180 \( 2^{6}\cdot 3^{2}\cdot 5^{3} \) $C_4$ (as 4T1) $[2, 2]$
4.0.78608.1 x4 + 17x2 + 68 \( 2^{4}\cdot 17^{3} \) $C_4$ (as 4T1) $[2, 2]$
4.0.98000.1 x4 + 35x2 + 245 \( 2^{4}\cdot 5^{3}\cdot 7^{2} \) $C_4$ (as 4T1) $[2, 2]$
4.4.100352.1 x4 - 28x2 + 98 \( 2^{11}\cdot 7^{2} \) $C_4$ (as 4T1) Trivial
4.0.100352.5 x4 + 28x2 + 98 \( 2^{11}\cdot 7^{2} \) $C_4$ (as 4T1) $[2, 2]$
4.0.105125.2 x4 - x3 + 36x2 - 36x + 281 \( 5^{3}\cdot 29^{2} \) $C_4$ (as 4T1) $[2, 2]$
4.4.107653.1 x4 - x3 - 24x2 - 22x + 29 \( 7^{2}\cdot 13^{3} \) $C_4$ (as 4T1) Trivial
4.4.120125.1 x4 - x3 - 39x2 + 39x + 281 \( 5^{3}\cdot 31^{2} \) $C_4$ (as 4T1) Trivial
4.4.122825.1 x4 - x3 - 23x2 + x + 86 \( 5^{2}\cdot 17^{3} \) $C_4$ (as 4T1) $[2]$
4.0.136125.2 x4 - x3 + 41x2 - 41x + 361 \( 3^{2}\cdot 5^{3}\cdot 11^{2} \) $C_4$ (as 4T1) $[2, 2, 2]$
4.4.140608.1 x4 - 26x2 + 52 \( 2^{6}\cdot 13^{3} \) $C_4$ (as 4T1) Trivial
4.0.140608.2 x4 + 26x2 + 52 \( 2^{6}\cdot 13^{3} \) $C_4$ (as 4T1) $[2]$
4.0.148877.1 x4 - x3 + 7x2 + 43x + 47 \( 53^{3} \) $C_4$ (as 4T1) Trivial
4.0.171125.1 x4 - x3 + 46x2 - 46x + 451 \( 5^{3}\cdot 37^{2} \) $C_4$ (as 4T1) $[10]$
4.4.190125.1 x4 - x3 - 49x2 + 49x + 451 \( 3^{2}\cdot 5^{3}\cdot 13^{2} \) $C_4$ (as 4T1) $[2]$
4.0.210125.1 x4 - x3 + 51x2 - 51x + 551 \( 5^{3}\cdot 41^{2} \) $C_4$ (as 4T1) $[2, 4]$
4.4.219501.1 x4 - x3 - 25x2 + 67x - 35 \( 3^{2}\cdot 29^{3} \) $C_4$ (as 4T1) Trivial
4.0.226981.1 x4 - x3 + 8x2 - 42x + 117 \( 61^{3} \) $C_4$ (as 4T1) Trivial
4.4.231125.1 x4 - x3 - 54x2 + 54x + 551 \( 5^{3}\cdot 43^{2} \) $C_4$ (as 4T1) Trivial
4.0.240737.1 x4 - x3 + 28x2 + x + 239 \( 7^{2}\cdot 17^{3} \) $C_4$ (as 4T1) $[2]$
4.0.242000.2 x4 + 55x2 + 605 \( 2^{4}\cdot 5^{3}\cdot 11^{2} \) $C_4$ (as 4T1) $[2, 2, 2]$

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