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Degree Signature Class number Class group structure CM field
Ramified prime count Ramified Unramified primes Galois group Galois
Discriminant Root discriminant Galois root discriminant Regulator Intermediate field
$p$-adic completions Minimal sibling Monogenic Index Ines. \(p\)
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Results (1-50 of 1678348 matches)

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Label Polynomial Discriminant Galois group Class group Regulator
4.0.117.1 $x^{4} - x^{3} - x^{2} + x + 1$ $3^{2}\cdot 13$ $D_{4}$ (as 4T3) trivial $0.543535072498$
4.0.125.1 $x^{4} - x^{3} + x^{2} - x + 1$ $5^{3}$ $C_4$ (as 4T1) trivial $0.962423650119$
4.0.144.1 $x^{4} - x^{2} + 1$ $2^{4}\cdot 3^{2}$ $C_2^2$ (as 4T2) trivial $1.31695789692$
4.0.189.1 $x^{4} - x^{3} + 2 x + 1$ $3^{3}\cdot 7$ $D_{4}$ (as 4T3) trivial $0.862554627662$
4.0.225.1 $x^{4} - x^{3} + 2 x^{2} + x + 1$ $3^{2}\cdot 5^{2}$ $C_2^2$ (as 4T2) trivial $0.962423650119$
4.0.229.1 $x^{4} - x + 1$ $229$ $S_4$ (as 4T5) trivial $0.337377803572$
4.0.256.1 $x^{4} + 1$ $2^{8}$ $C_2^2$ (as 4T2) trivial $1.76274717404$
4.0.257.1 $x^{4} + x^{2} - x + 1$ $257$ $S_4$ (as 4T5) trivial $0.442137828732$
4.0.272.1 $x^{4} + x^{2} - 2 x + 1$ $2^{4}\cdot 17$ $D_{4}$ (as 4T3) trivial $0.732857675974$
4.0.320.1 $x^{4} - 2 x^{3} + 2$ $2^{6}\cdot 5$ $D_{4}$ (as 4T3) trivial $1.06127506191$
4.0.333.1 $x^{4} - x^{3} - 2 x^{2} + 3$ $3^{2}\cdot 37$ $D_{4}$ (as 4T3) trivial $1.46078161311$
4.0.392.1 $x^{4} - x^{3} + x + 1$ $2^{3}\cdot 7^{2}$ $D_{4}$ (as 4T3) trivial $0.632974319201$
4.0.400.1 $x^{4} + 3 x^{2} + 1$ $2^{4}\cdot 5^{2}$ $C_2^2$ (as 4T2) trivial $0.962423650119$
4.0.432.1 $x^{4} - 3 x^{2} + 3$ $2^{4}\cdot 3^{3}$ $D_{4}$ (as 4T3) trivial $1.66288589106$
4.0.441.1 $x^{4} - x^{3} - x^{2} - 2 x + 4$ $3^{2}\cdot 7^{2}$ $C_2^2$ (as 4T2) trivial $1.56679923697$
4.0.512.1 $x^{4} - 2 x^{2} + 2$ $2^{9}$ $D_{4}$ (as 4T3) trivial $1.52857091948$
4.0.513.1 $x^{4} - x^{3} - 3 x^{2} + 2 x + 4$ $3^{3}\cdot 19$ $D_{4}$ (as 4T3) trivial $1.96497837511$
4.0.549.1 $x^{4} - 2 x^{3} - 2 x^{2} + 3 x + 3$ $3^{2}\cdot 61$ $D_{4}$ (as 4T3) trivial $2.11437619251$
4.0.576.1 $x^{4} - 2 x^{2} + 4$ $2^{6}\cdot 3^{2}$ $C_2^2$ (as 4T2) trivial $2.29243166956$
4.0.576.2 $x^{4} + 2 x^{2} + 4$ $2^{6}\cdot 3^{2}$ $C_2^2$ (as 4T2) trivial $1.76274717404$
4.0.592.1 $x^{4} + 2 x^{2} - 2 x + 1$ $2^{4}\cdot 37$ $S_4$ (as 4T5) trivial $0.917818607957$
4.0.605.1 $x^{4} - x^{3} + x^{2} + x + 1$ $5\cdot 11^{2}$ $D_{4}$ (as 4T3) trivial $0.767197218251$
4.0.656.1 $x^{4} - 2 x^{3} - x^{2} + 2 x + 2$ $2^{4}\cdot 41$ $D_{4}$ (as 4T3) trivial $2.42610665212$
4.0.657.1 $x^{4} - x^{3} + 5 x^{2} - 2 x + 4$ $3^{2}\cdot 73$ $D_{4}$ (as 4T3) trivial $2.0335456547$
4.0.697.1 $x^{4} - x^{3} + 2 x^{2} - x + 2$ $17\cdot 41$ $S_4$ (as 4T5) trivial $1.03324185123$
4.0.761.1 $x^{4} - x^{3} + x^{2} + 2 x + 1$ $761$ $S_4$ (as 4T5) trivial $0.990699508768$
4.0.784.1 $x^{4} - 3 x^{2} + 4$ $2^{4}\cdot 7^{2}$ $C_2^2$ (as 4T2) trivial $2.76865938331$
4.0.788.1 $x^{4} - x^{3} + 2 x^{2} - 2 x + 2$ $2^{2}\cdot 197$ $S_4$ (as 4T5) trivial $1.39411358598$
4.0.832.1 $x^{4} - 2 x^{3} - 2 x + 5$ $2^{6}\cdot 13$ $D_{4}$ (as 4T3) trivial $2.13862208632$
4.0.837.1 $x^{4} - x^{3} - 3 x^{2} - x + 7$ $3^{3}\cdot 31$ $D_{4}$ (as 4T3) trivial $2.41883810412$
4.0.873.1 $x^{4} - x^{3} - 4 x^{2} + x + 7$ $3^{2}\cdot 97$ $D_{4}$ (as 4T3) trivial $2.42800256046$
4.0.892.1 $x^{4} - x^{3} - x^{2} + 2$ $2^{2}\cdot 223$ $S_4$ (as 4T5) trivial $1.29274426912$
4.0.981.1 $x^{4} - x^{3} - 4 x^{2} + 4 x + 7$ $3^{2}\cdot 109$ $D_{4}$ (as 4T3) trivial $2.15221875719$
4.0.985.1 $x^{4} - x^{3} + 2 x^{2} - 3 x + 2$ $5\cdot 197$ $S_4$ (as 4T5) trivial $1.34361173004$
4.0.1008.1 $x^{4} - 5 x^{2} + 7$ $2^{4}\cdot 3^{2}\cdot 7$ $D_{4}$ (as 4T3) trivial $3.39588318368$
4.0.1008.2 $x^{4} + 5 x^{2} + 7$ $2^{4}\cdot 3^{2}\cdot 7$ $D_{4}$ (as 4T3) trivial $2.41611328691$
4.0.1016.1 $x^{4} - x^{3} + x^{2} - 2 x + 2$ $2^{3}\cdot 127$ $S_4$ (as 4T5) trivial $1.27428442991$
4.0.1025.1 $x^{4} - x^{3} + 3 x^{2} - 2 x + 4$ $5^{2}\cdot 41$ $D_{4}$ (as 4T3) trivial $0.962423650119$
4.0.1040.1 $x^{4} - 3 x^{2} - 2 x + 5$ $2^{4}\cdot 5\cdot 13$ $D_{4}$ (as 4T3) trivial $1.8522660627$
4.0.1040.2 $x^{4} + x^{2} - 4 x + 4$ $2^{4}\cdot 5\cdot 13$ $D_{4}$ (as 4T3) trivial $3.46864904298$
4.0.1076.1 $x^{4} - x^{3} + 3 x^{2} - 3 x + 2$ $2^{2}\cdot 269$ $S_4$ (as 4T5) trivial $1.77702641037$
4.0.1088.1 $x^{4} - 2 x^{3} + x^{2} - 2 x + 3$ $2^{6}\cdot 17$ $D_{4}$ (as 4T3) trivial $1.17996602392$
4.0.1088.2 $x^{4} - 2 x^{3} + 5 x^{2} - 4 x + 2$ $2^{6}\cdot 17$ $D_{4}$ (as 4T3) trivial $1.76274717404$
4.0.1089.1 $x^{4} - x^{3} - 2 x^{2} - 3 x + 9$ $3^{2}\cdot 11^{2}$ $C_2^2$ (as 4T2) trivial $3.82816847133$
4.0.1129.1 $x^{4} - x^{3} - x + 2$ $1129$ $S_4$ (as 4T5) trivial $1.26901928105$
4.0.1161.1 $x^{4} - x^{3} + 6 x^{2} - x + 7$ $3^{3}\cdot 43$ $D_{4}$ (as 4T3) trivial $3.48142350173$
4.0.1168.1 $x^{4} - x^{2} - 4 x + 5$ $2^{4}\cdot 73$ $D_{4}$ (as 4T3) trivial $1.8902413596$
4.0.1197.1 $x^{4} - 2 x^{3} - 4 x^{2} + 5 x + 7$ $3^{2}\cdot 7\cdot 19$ $D_{4}$ (as 4T3) trivial $2.3192389338$
4.0.1197.2 $x^{4} - x^{3} - 5 x^{2} + 3 x + 9$ $3^{2}\cdot 7\cdot 19$ $D_{4}$ (as 4T3) trivial $3.57713438377$
4.0.1225.1 $x^{4} - x^{3} + 5 x^{2} + 2 x + 4$ $5^{2}\cdot 7^{2}$ $C_2^2$ (as 4T2) trivial $0.962423650119$
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