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The results below are complete, since the LMFDB contains all number fields with absolute discriminant at most 1656109

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Degree Signature Discriminant Root discriminant Galois root discriminant
Ramified prime count Ramified Unramified primes Maximum ramified prime Galois group
Class group structure Class number Regulator Intermediate field Field is
Narrow class group Narrow class number Relative class number CM field $p$-adic completions
Monogenic Index Ines. \(p\) Minimal sibling Unit signature rank
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Results (1-50 of 410 matches)

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Label Polynomial Discriminant Galois group Class group Regulator
2.0.103.1 $x^{2} - x + 26$ $-\,103$ $C_2$ (as 2T1) $[5]$ $1$
2.0.104.1 $x^{2} + 26$ $-\,2^{3}\cdot 13$ $C_2$ (as 2T1) $[6]$ $1$
2.0.107.1 $x^{2} - x + 27$ $-\,107$ $C_2$ (as 2T1) $[3]$ $1$
2.0.111.1 $x^{2} - x + 28$ $-\,3\cdot 37$ $C_2$ (as 2T1) $[8]$ $1$
2.0.115.1 $x^{2} - x + 29$ $-\,5\cdot 23$ $C_2$ (as 2T1) $[2]$ $1$
2.0.116.1 $x^{2} + 29$ $-\,2^{2}\cdot 29$ $C_2$ (as 2T1) $[6]$ $1$
2.0.119.1 $x^{2} - x + 30$ $-\,7\cdot 17$ $C_2$ (as 2T1) $[10]$ $1$
2.0.120.1 $x^{2} + 30$ $-\,2^{3}\cdot 3\cdot 5$ $C_2$ (as 2T1) $[2, 2]$ $1$
2.0.123.1 $x^{2} - x + 31$ $-\,3\cdot 41$ $C_2$ (as 2T1) $[2]$ $1$
2.0.127.1 $x^{2} - x + 32$ $-\,127$ $C_2$ (as 2T1) $[5]$ $1$
2.0.131.1 $x^{2} - x + 33$ $-\,131$ $C_2$ (as 2T1) $[5]$ $1$
2.0.132.1 $x^{2} + 33$ $-\,2^{2}\cdot 3\cdot 11$ $C_2$ (as 2T1) $[2, 2]$ $1$
2.0.136.1 $x^{2} + 34$ $-\,2^{3}\cdot 17$ $C_2$ (as 2T1) $[4]$ $1$
2.0.139.1 $x^{2} - x + 35$ $-\,139$ $C_2$ (as 2T1) $[3]$ $1$
2.0.143.1 $x^{2} - x + 36$ $-\,11\cdot 13$ $C_2$ (as 2T1) $[10]$ $1$
2.0.148.1 $x^{2} + 37$ $-\,2^{2}\cdot 37$ $C_2$ (as 2T1) $[2]$ $1$
2.0.151.1 $x^{2} - x + 38$ $-\,151$ $C_2$ (as 2T1) $[7]$ $1$
2.0.152.1 $x^{2} + 38$ $-\,2^{3}\cdot 19$ $C_2$ (as 2T1) $[6]$ $1$
2.0.155.1 $x^{2} - x + 39$ $-\,5\cdot 31$ $C_2$ (as 2T1) $[4]$ $1$
2.0.159.1 $x^{2} - x + 40$ $-\,3\cdot 53$ $C_2$ (as 2T1) $[10]$ $1$
2.0.163.1 $x^{2} - x + 41$ $-\,163$ $C_2$ (as 2T1) trivial $1$
2.0.164.1 $x^{2} + 41$ $-\,2^{2}\cdot 41$ $C_2$ (as 2T1) $[8]$ $1$
2.0.167.1 $x^{2} - x + 42$ $-\,167$ $C_2$ (as 2T1) $[11]$ $1$
2.0.168.1 $x^{2} + 42$ $-\,2^{3}\cdot 3\cdot 7$ $C_2$ (as 2T1) $[2, 2]$ $1$
2.0.179.1 $x^{2} - x + 45$ $-\,179$ $C_2$ (as 2T1) $[5]$ $1$
2.0.183.1 $x^{2} - x + 46$ $-\,3\cdot 61$ $C_2$ (as 2T1) $[8]$ $1$
2.0.184.1 $x^{2} + 46$ $-\,2^{3}\cdot 23$ $C_2$ (as 2T1) $[4]$ $1$
2.0.187.1 $x^{2} - x + 47$ $-\,11\cdot 17$ $C_2$ (as 2T1) $[2]$ $1$
2.0.191.1 $x^{2} - x + 48$ $-\,191$ $C_2$ (as 2T1) $[13]$ $1$
2.0.195.1 $x^{2} - x + 49$ $-\,3\cdot 5\cdot 13$ $C_2$ (as 2T1) $[2, 2]$ $1$
2.0.199.1 $x^{2} - x + 50$ $-\,199$ $C_2$ (as 2T1) $[9]$ $1$
2.0.203.1 $x^{2} - x + 51$ $-\,7\cdot 29$ $C_2$ (as 2T1) $[4]$ $1$
2.0.211.1 $x^{2} - x + 53$ $-\,211$ $C_2$ (as 2T1) $[3]$ $1$
2.0.212.1 $x^{2} + 53$ $-\,2^{2}\cdot 53$ $C_2$ (as 2T1) $[6]$ $1$
2.0.215.1 $x^{2} - x + 54$ $-\,5\cdot 43$ $C_2$ (as 2T1) $[14]$ $1$
2.0.219.1 $x^{2} - x + 55$ $-\,3\cdot 73$ $C_2$ (as 2T1) $[4]$ $1$
2.0.223.1 $x^{2} - x + 56$ $-\,223$ $C_2$ (as 2T1) $[7]$ $1$
2.0.227.1 $x^{2} - x + 57$ $-\,227$ $C_2$ (as 2T1) $[5]$ $1$
2.0.228.1 $x^{2} + 57$ $-\,2^{2}\cdot 3\cdot 19$ $C_2$ (as 2T1) $[2, 2]$ $1$
2.0.231.1 $x^{2} - x + 58$ $-\,3\cdot 7\cdot 11$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.232.1 $x^{2} + 58$ $-\,2^{3}\cdot 29$ $C_2$ (as 2T1) $[2]$ $1$
2.0.235.1 $x^{2} - x + 59$ $-\,5\cdot 47$ $C_2$ (as 2T1) $[2]$ $1$
2.0.239.1 $x^{2} - x + 60$ $-\,239$ $C_2$ (as 2T1) $[15]$ $1$
2.0.244.1 $x^{2} + 61$ $-\,2^{2}\cdot 61$ $C_2$ (as 2T1) $[6]$ $1$
2.0.247.1 $x^{2} - x + 62$ $-\,13\cdot 19$ $C_2$ (as 2T1) $[6]$ $1$
2.0.248.1 $x^{2} + 62$ $-\,2^{3}\cdot 31$ $C_2$ (as 2T1) $[8]$ $1$
2.0.251.1 $x^{2} - x + 63$ $-\,251$ $C_2$ (as 2T1) $[7]$ $1$
2.0.255.1 $x^{2} - x + 64$ $-\,3\cdot 5\cdot 17$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.259.1 $x^{2} - x + 65$ $-\,7\cdot 37$ $C_2$ (as 2T1) $[4]$ $1$
2.0.260.1 $x^{2} + 65$ $-\,2^{2}\cdot 5\cdot 13$ $C_2$ (as 2T1) $[2, 4]$ $1$
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