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Degree Signature Ramified prime count Ramified Unramified primes
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Regulator $p$-adic completions Monogenic Index Ines. \(p\)
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Results (1-50 of at least 1000)

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Label Polynomial Discriminant Galois group Class group Regulator
4.0.320.1 $x^{4} - 2 x^{3} + 2$ $2^{6}\cdot 5$ $D_{4}$ (as 4T3) trivial $1.06127506191$
4.0.832.1 $x^{4} - 2 x^{3} - 2 x + 5$ $2^{6}\cdot 13$ $D_{4}$ (as 4T3) trivial $2.13862208632$
4.0.1856.1 $x^{4} - 2 x^{3} - 4 x + 10$ $2^{6}\cdot 29$ $D_{4}$ (as 4T3) trivial $3.94944515305$
4.0.2368.1 $x^{4} - 2 x^{3} - 4 x^{2} + 4 x + 10$ $2^{6}\cdot 37$ $D_{4}$ (as 4T3) trivial $4.08424332908$
4.0.2880.1 $x^{4} - 2 x^{3} - 4 x^{2} + 2 x + 13$ $2^{6}\cdot 3^{2}\cdot 5$ $D_{4}$ (as 4T3) $[2]$ $2.4529137425$
4.0.3392.1 $x^{4} - 2 x^{3} - 6 x + 17$ $2^{6}\cdot 53$ $D_{4}$ (as 4T3) trivial $4.87147534378$
4.0.3904.1 $x^{4} - 2 x^{3} - 4 x^{2} + 18$ $2^{6}\cdot 61$ $D_{4}$ (as 4T3) trivial $4.38251094778$
4.0.5440.1 $x^{4} - 2 x^{3} - 4 x^{2} - 2 x + 25$ $2^{6}\cdot 5\cdot 17$ $D_{4}$ (as 4T3) $[2]$ $3.64839740439$
4.0.5440.2 $x^{4} - 2 x^{3} - 8 x + 26$ $2^{6}\cdot 5\cdot 17$ $D_{4}$ (as 4T3) $[2]$ $2.89946869917$
4.0.6464.1 $x^{4} - 2 x^{3} - 8 x^{2} + 8 x + 26$ $2^{6}\cdot 101$ $D_{4}$ (as 4T3) trivial $8.58077191183$
4.2.6848.1 $x^{4} - 2 x^{3} - 4 x^{2} + 2$ $-\,2^{6}\cdot 107$ $S_4$ (as 4T5) trivial $5.50019201536$
4.0.6976.1 $x^{4} - 2 x^{3} - 8 x^{2} + 6 x + 29$ $2^{6}\cdot 109$ $D_{4}$ (as 4T3) trivial $5.60844679333$
4.0.7488.4 $x^{4} - 2 x^{3} - 4 x^{2} - 4 x + 34$ $2^{6}\cdot 3^{2}\cdot 13$ $D_{4}$ (as 4T3) $[2]$ $3.72832308832$
4.2.9408.1 $x^{4} - 2 x^{3} - 4 x^{2} - 2 x + 1$ $-\,2^{6}\cdot 3\cdot 7^{2}$ $D_{4}$ (as 4T3) trivial $6.68939472295$
4.2.9408.2 $x^{4} - 2 x^{3} - 6 x + 9$ $-\,2^{6}\cdot 3\cdot 7^{2}$ $D_{4}$ (as 4T3) trivial $9.40204384113$
4.0.9536.1 $x^{4} - 2 x^{3} - 8 x^{2} + 2 x + 41$ $2^{6}\cdot 149$ $D_{4}$ (as 4T3) trivial $5.75473555283$
4.0.10048.1 $x^{4} - 2 x^{3} - 4 x^{2} - 6 x + 45$ $2^{6}\cdot 157$ $D_{4}$ (as 4T3) trivial $8.9414982303$
4.0.11072.1 $x^{4} - 2 x^{3} - 12 x + 50$ $2^{6}\cdot 173$ $D_{4}$ (as 4T3) trivial $9.05341839444$
4.0.11584.1 $x^{4} - 2 x^{3} - 8 x^{2} + 50$ $2^{6}\cdot 181$ $D_{4}$ (as 4T3) trivial $12.3313465879$
4.0.12608.1 $x^{4} - 2 x^{3} - 12 x^{2} + 12 x + 50$ $2^{6}\cdot 197$ $D_{4}$ (as 4T3) trivial $9.2348397007$
4.0.13120.1 $x^{4} - 2 x^{3} - 12 x^{2} + 10 x + 53$ $2^{6}\cdot 5\cdot 41$ $D_{4}$ (as 4T3) $[2]$ $5.9165496554$
4.0.13120.2 $x^{4} - 2 x^{3} - 4 x^{2} - 8 x + 58$ $2^{6}\cdot 5\cdot 41$ $D_{4}$ (as 4T3) $[2]$ $6.19113660664$
4.0.14144.1 $x^{4} - 2 x^{3} - 12 x^{2} + 8 x + 58$ $2^{6}\cdot 13\cdot 17$ $D_{4}$ (as 4T3) $[2]$ $3.32611947946$
4.0.14144.2 $x^{4} - 2 x^{3} - 8 x^{2} - 2 x + 61$ $2^{6}\cdot 13\cdot 17$ $D_{4}$ (as 4T3) $[2]$ $6.61291481396$
4.4.14656.1 $x^{4} - 2 x^{3} - 4 x^{2} + 4 x + 2$ $2^{6}\cdot 229$ $S_4$ (as 4T5) trivial $11.1614390382$
4.0.14656.4 $x^{4} - 2 x^{3} - 14 x + 65$ $2^{6}\cdot 229$ $D_{4}$ (as 4T3) trivial $14.3506756726$
4.2.15552.1 $x^{4} - 2 x^{3} - 4 x + 2$ $-\,2^{6}\cdot 3^{5}$ $S_4$ (as 4T5) trivial $10.7650556319$
4.0.15680.1 $x^{4} - 2 x^{3} - 12 x^{2} + 6 x + 65$ $2^{6}\cdot 5\cdot 7^{2}$ $D_{4}$ (as 4T3) $[2]$ $6.01244231173$
4.0.16704.1 $x^{4} - 2 x^{3} - 4 x^{2} - 10 x + 73$ $2^{6}\cdot 3^{2}\cdot 29$ $D_{4}$ (as 4T3) $[2]$ $3.50029752264$
4.0.17216.1 $x^{4} - 2 x^{3} - 8 x^{2} - 4 x + 74$ $2^{6}\cdot 269$ $D_{4}$ (as 4T3) trivial $6.32044257896$
4.0.17728.1 $x^{4} - 2 x^{3} - 12 x^{2} + 4 x + 74$ $2^{6}\cdot 277$ $D_{4}$ (as 4T3) trivial $13.0566022495$
4.2.18112.1 $x^{4} - 2 x^{3} - 2 x - 3$ $-\,2^{6}\cdot 283$ $S_4$ (as 4T5) trivial $12.1786682802$
4.0.18752.1 $x^{4} - 2 x^{3} - 16 x + 82$ $2^{6}\cdot 293$ $D_{4}$ (as 4T3) trivial $11.5142938791$
4.0.20288.1 $x^{4} - 2 x^{3} - 12 x^{2} + 2 x + 85$ $2^{6}\cdot 317$ $D_{4}$ (as 4T3) trivial $11.5712790683$
4.0.20800.1 $x^{4} - 2 x^{3} - 8 x^{2} - 6 x + 89$ $2^{6}\cdot 5^{2}\cdot 13$ $D_{4}$ (as 4T3) $[2, 2]$ $3.55532475501$
4.2.21184.1 $x^{4} - 2 x^{3} - 4 x^{2} + 2 x + 5$ $-\,2^{6}\cdot 331$ $S_4$ (as 4T5) trivial $9.13454484792$
4.0.21312.2 $x^{4} - 2 x^{3} - 16 x^{2} + 14 x + 85$ $2^{6}\cdot 3^{2}\cdot 37$ $D_{4}$ (as 4T3) $[2]$ $6.36642041754$
4.0.22336.1 $x^{4} - 2 x^{3} - 16 x^{2} + 12 x + 90$ $2^{6}\cdot 349$ $D_{4}$ (as 4T3) trivial $18.9976349941$
4.0.23360.1 $x^{4} - 2 x^{3} - 12 x^{2} + 98$ $2^{6}\cdot 5\cdot 73$ $D_{4}$ (as 4T3) $[2]$ $7.10771889774$
4.0.23360.2 $x^{4} - 2 x^{3} - 18 x + 101$ $2^{6}\cdot 5\cdot 73$ $D_{4}$ (as 4T3) $[2]$ $5.26019833863$
4.0.23872.1 $x^{4} - 2 x^{3} - 16 x^{2} + 10 x + 97$ $2^{6}\cdot 373$ $D_{4}$ (as 4T3) trivial $13.0569618621$
4.0.24896.1 $x^{4} - 2 x^{3} - 8 x^{2} - 8 x + 106$ $2^{6}\cdot 389$ $D_{4}$ (as 4T3) trivial $6.51069116685$
4.0.25408.1 $x^{4} - 2 x^{3} - 4 x^{2} - 14 x + 109$ $2^{6}\cdot 397$ $D_{4}$ (as 4T3) trivial $15.0273117082$
4.2.26304.1 $x^{4} - 2 x^{3} - 4 x^{2} - 6 x - 3$ $-\,2^{6}\cdot 3\cdot 137$ $S_4$ (as 4T5) trivial $13.1699967625$
4.0.26944.1 $x^{4} - 2 x^{3} - 12 x^{2} - 2 x + 113$ $2^{6}\cdot 421$ $D_{4}$ (as 4T3) trivial $9.93898662004$
4.0.28480.1 $x^{4} - 2 x^{3} - 16 x^{2} + 6 x + 117$ $2^{6}\cdot 5\cdot 89$ $D_{4}$ (as 4T3) $[2]$ $7.20714850606$
4.0.28480.2 $x^{4} - 2 x^{3} - 20 x + 122$ $2^{6}\cdot 5\cdot 89$ $D_{4}$ (as 4T3) $[2]$ $6.04724892497$
4.2.28864.2 $x^{4} - 2 x^{3} + 4 x^{2} + 6 x + 1$ $-\,2^{6}\cdot 11\cdot 41$ $S_4$ (as 4T5) trivial $10.2598930823$
4.0.29504.1 $x^{4} - 2 x^{3} - 8 x^{2} - 10 x + 125$ $2^{6}\cdot 461$ $D_{4}$ (as 4T3) trivial $20.0531368298$
4.0.30016.1 $x^{4} - 2 x^{3} + 4 x^{2} + 4 x + 2$ $2^{6}\cdot 7\cdot 67$ $S_4$ (as 4T5) $[2]$ $5.77732721057$
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