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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 Ramified prime count Ramified Unramified primes
Galois group Field is Intermediate field Class group structure Class number
Discriminant Root discriminant Galois root discriminant Narrow class group Narrow class number
CM field Relative class number Regulator $p$-adic completions Monogenic
Index Ines. \(p\) Minimal sibling Unit signature rank
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Results (38 matches)

  displayed columns for results
Label Polynomial Discriminant Galois group Class group Regulator
2.0.3.1 $x^{2} - x + 1$ $-\,3$ $C_2$ (as 2T1) trivial $1$
2.0.4.1 $x^{2} + 1$ $-\,2^{2}$ $C_2$ (as 2T1) trivial $1$
2.0.7.1 $x^{2} - x + 2$ $-\,7$ $C_2$ (as 2T1) trivial $1$
2.0.8.1 $x^{2} + 2$ $-\,2^{3}$ $C_2$ (as 2T1) trivial $1$
2.0.11.1 $x^{2} - x + 3$ $-\,11$ $C_2$ (as 2T1) trivial $1$
2.0.15.1 $x^{2} - x + 4$ $-\,3\cdot 5$ $C_2$ (as 2T1) $[2]$ $1$
2.0.19.1 $x^{2} - x + 5$ $-\,19$ $C_2$ (as 2T1) trivial $1$
2.0.20.1 $x^{2} + 5$ $-\,2^{2}\cdot 5$ $C_2$ (as 2T1) $[2]$ $1$
2.0.23.1 $x^{2} - x + 6$ $-\,23$ $C_2$ (as 2T1) $[3]$ $1$
2.0.24.1 $x^{2} + 6$ $-\,2^{3}\cdot 3$ $C_2$ (as 2T1) $[2]$ $1$
2.0.31.1 $x^{2} - x + 8$ $-\,31$ $C_2$ (as 2T1) $[3]$ $1$
2.0.35.1 $x^{2} - x + 9$ $-\,5\cdot 7$ $C_2$ (as 2T1) $[2]$ $1$
2.0.39.1 $x^{2} - x + 10$ $-\,3\cdot 13$ $C_2$ (as 2T1) $[4]$ $1$
2.0.40.1 $x^{2} + 10$ $-\,2^{3}\cdot 5$ $C_2$ (as 2T1) $[2]$ $1$
2.0.43.1 $x^{2} - x + 11$ $-\,43$ $C_2$ (as 2T1) trivial $1$
2.0.47.1 $x^{2} - x + 12$ $-\,47$ $C_2$ (as 2T1) $[5]$ $1$
2.0.51.1 $x^{2} - x + 13$ $-\,3\cdot 17$ $C_2$ (as 2T1) $[2]$ $1$
2.0.52.1 $x^{2} + 13$ $-\,2^{2}\cdot 13$ $C_2$ (as 2T1) $[2]$ $1$
2.0.55.1 $x^{2} - x + 14$ $-\,5\cdot 11$ $C_2$ (as 2T1) $[4]$ $1$
2.0.56.1 $x^{2} + 14$ $-\,2^{3}\cdot 7$ $C_2$ (as 2T1) $[4]$ $1$
2.0.59.1 $x^{2} - x + 15$ $-\,59$ $C_2$ (as 2T1) $[3]$ $1$
2.0.67.1 $x^{2} - x + 17$ $-\,67$ $C_2$ (as 2T1) trivial $1$
2.0.68.1 $x^{2} + 17$ $-\,2^{2}\cdot 17$ $C_2$ (as 2T1) $[4]$ $1$
2.0.71.1 $x^{2} - x + 18$ $-\,71$ $C_2$ (as 2T1) $[7]$ $1$
2.0.79.1 $x^{2} - x + 20$ $-\,79$ $C_2$ (as 2T1) $[5]$ $1$
2.0.83.1 $x^{2} - x + 21$ $-\,83$ $C_2$ (as 2T1) $[3]$ $1$
2.0.84.1 $x^{2} + 21$ $-\,2^{2}\cdot 3\cdot 7$ $C_2$ (as 2T1) $[2, 2]$ $1$
2.0.87.1 $x^{2} - x + 22$ $-\,3\cdot 29$ $C_2$ (as 2T1) $[6]$ $1$
2.0.88.1 $x^{2} + 22$ $-\,2^{3}\cdot 11$ $C_2$ (as 2T1) $[2]$ $1$
2.0.91.1 $x^{2} - x + 23$ $-\,7\cdot 13$ $C_2$ (as 2T1) $[2]$ $1$
2.0.95.1 $x^{2} - x + 24$ $-\,5\cdot 19$ $C_2$ (as 2T1) $[8]$ $1$
3.1.23.1 $x^{3} - x^{2} + 1$ $-\,23$ $S_3$ (as 3T2) trivial $0.281199574323$
3.1.31.1 $x^{3} + x - 1$ $-\,31$ $S_3$ (as 3T2) trivial $0.38224508584$
3.1.44.1 $x^{3} - x^{2} + x + 1$ $-\,2^{2}\cdot 11$ $S_3$ (as 3T2) trivial $0.609377863436$
3.1.59.1 $x^{3} + 2 x - 1$ $-\,59$ $S_3$ (as 3T2) trivial $0.790985720639$
3.1.76.1 $x^{3} - 2 x - 2$ $-\,2^{2}\cdot 19$ $S_3$ (as 3T2) trivial $1.01859181978$
3.1.83.1 $x^{3} - x^{2} + x - 2$ $-\,83$ $S_3$ (as 3T2) trivial $1.04069259944$
3.1.87.1 $x^{3} - x^{2} + 2 x + 1$ $-\,3\cdot 29$ $S_3$ (as 3T2) trivial $0.934844845546$
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