↑

Learn more

Refine search

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. \(p\)
Sort order Select

Results (1-50 of 410445 matches)

Next   displayed columns for results
Label Polynomial Discriminant Galois group Class group Regulator
4.2.507.1 $x^{4} - x^{3} - x^{2} - x + 1$ $-\,3\cdot 13^{2}$ $D_{4}$ (as 4T3) trivial $0.649395711926$
4.2.2704.1 $x^{4} - 3 x^{2} - 1$ $-\,2^{4}\cdot 13^{2}$ $D_{4}$ (as 4T3) trivial $2.55514700441$
4.0.2873.1 $x^{4} - x^{3} + x^{2} - 2 x + 4$ $13^{2}\cdot 17$ $D_{4}$ (as 4T3) trivial $2.38952643457$
4.4.4225.1 $x^{4} - 9 x^{2} + 4$ $5^{2}\cdot 13^{2}$ $C_2^2$ (as 4T2) trivial $3.19257767414$
4.2.8112.1 $x^{4} - x^{2} - 3$ $-\,2^{4}\cdot 3\cdot 13^{2}$ $D_{4}$ (as 4T3) trivial $6.15369517281$
4.0.8281.1 $x^{4} - x^{3} + 5 x^{2} - 4 x + 3$ $7^{2}\cdot 13^{2}$ $A_4$ (as 4T4) $[2]$ $2.66193075$
4.0.8281.2 $x^{4} - 3 x^{2} + 25$ $7^{2}\cdot 13^{2}$ $C_2^2$ (as 4T2) trivial $2.38952643457$
4.4.10816.1 $x^{4} - 2 x^{3} - 9 x^{2} + 10 x - 1$ $2^{6}\cdot 13^{2}$ $C_2^2$ (as 4T2) trivial $4.87014657656$
4.0.10816.2 $x^{4} - 2 x^{3} - x^{2} + 2 x + 27$ $2^{6}\cdot 13^{2}$ $C_2^2$ (as 4T2) $[3]$ $2.38952643457$
4.0.11661.1 $x^{4} - x^{3} + 3 x^{2} - 3 x + 9$ $3\cdot 13^{2}\cdot 23$ $D_{4}$ (as 4T3) $[2]$ $2.38952643457$
4.4.11661.1 $x^{4} - 2 x^{3} - 4 x^{2} + 5 x + 3$ $3\cdot 13^{2}\cdot 23$ $D_{4}$ (as 4T3) trivial $8.58274234488$
4.2.13351.1 $x^{4} - x^{3} - 2 x^{2} - 7 x - 3$ $-\,13^{2}\cdot 79$ $D_{4}$ (as 4T3) trivial $7.72158948671$
4.2.14703.2 $x^{4} - 2 x^{3} + 7 x^{2} - 6 x - 4$ $-\,3\cdot 13^{2}\cdot 29$ $D_{4}$ (as 4T3) trivial $6.32993857103$
4.2.14703.3 $x^{4} - x^{3} + 3 x^{2} + 10 x - 4$ $-\,3\cdot 13^{2}\cdot 29$ $D_{4}$ (as 4T3) trivial $10.026984968$
4.2.16900.2 $x^{4} - x^{2} - 16$ $-\,2^{2}\cdot 5^{2}\cdot 13^{2}$ $D_{4}$ (as 4T3) $[2]$ $9.63060791938$
4.4.17069.1 $x^{4} - x^{3} - 8 x^{2} - 4 x + 3$ $13^{2}\cdot 101$ $D_{4}$ (as 4T3) trivial $8.83283066561$
4.2.18083.1 $x^{4} - x^{3} + 5 x^{2} - 17 x + 3$ $-\,13^{2}\cdot 107$ $D_{4}$ (as 4T3) trivial $10.996558893$
4.0.18252.1 $x^{4} - x^{3} + 6 x^{2} + 2 x + 4$ $2^{2}\cdot 3^{3}\cdot 13^{2}$ $D_{4}$ (as 4T3) $[4]$ $5.39746890278$
4.0.18252.2 $x^{4} - 3 x^{2} + 12$ $2^{2}\cdot 3^{3}\cdot 13^{2}$ $D_{4}$ (as 4T3) $[4]$ $2.47180204665$
4.0.20449.1 $x^{4} - x^{2} + 36$ $11^{2}\cdot 13^{2}$ $C_2^2$ (as 4T2) $[5]$ $2.38952643457$
4.0.21801.1 $x^{4} - x^{3} + 6 x^{2} - 11 x + 17$ $3\cdot 13^{2}\cdot 43$ $D_{4}$ (as 4T3) $[4]$ $2.38952643457$
4.4.21801.1 $x^{4} - x^{3} - 7 x^{2} + 2 x + 4$ $3\cdot 13^{2}\cdot 43$ $D_{4}$ (as 4T3) trivial $10.6046729554$
4.2.22139.1 $x^{4} - x^{3} - 7 x^{2} - 11 x - 9$ $-\,13^{2}\cdot 131$ $D_{4}$ (as 4T3) trivial $12.3706674547$
4.2.23491.1 $x^{4} - x^{3} + x^{2} + 11 x - 9$ $-\,13^{2}\cdot 139$ $D_{4}$ (as 4T3) trivial $7.41171737731$
4.2.24336.2 $x^{4} - 9 x^{2} - 9$ $-\,2^{4}\cdot 3^{2}\cdot 13^{2}$ $D_{4}$ (as 4T3) $[2]$ $4.45446328808$
4.4.25857.1 $x^{4} - x^{3} - 8 x^{2} + 9 x + 3$ $3^{2}\cdot 13^{2}\cdot 17$ $D_{4}$ (as 4T3) trivial $14.4793070433$
4.2.26871.1 $x^{4} - 2 x^{3} + 5 x^{2} - 4 x - 9$ $-\,3\cdot 13^{2}\cdot 53$ $D_{4}$ (as 4T3) $[2]$ $7.24847935197$
4.2.26871.2 $x^{4} - x^{3} - x^{2} + 12 x - 12$ $-\,3\cdot 13^{2}\cdot 53$ $D_{4}$ (as 4T3) $[2]$ $4.3460994676$
4.4.29237.1 $x^{4} - 2 x^{3} - 6 x^{2} + 7 x + 9$ $13^{2}\cdot 173$ $D_{4}$ (as 4T3) trivial $11.8867910971$
4.0.30589.1 $x^{4} - x^{3} + 6 x^{2} + 2 x + 17$ $13^{2}\cdot 181$ $D_{4}$ (as 4T3) trivial $2.38952643457$
4.2.30927.1 $x^{4} - 2 x^{3} - x^{2} + 2 x - 12$ $-\,3\cdot 13^{2}\cdot 61$ $D_{4}$ (as 4T3) $[2]$ $7.82312113144$
4.2.30927.2 $x^{4} - x^{3} + 6 x^{2} + 15 x - 9$ $-\,3\cdot 13^{2}\cdot 61$ $D_{4}$ (as 4T3) $[2]$ $7.93493201484$
4.2.32279.1 $x^{4} - x^{3} + 3 x^{2} - 16 x - 4$ $-\,13^{2}\cdot 191$ $D_{4}$ (as 4T3) trivial $7.35197021222$
4.0.32448.1 $x^{4} + 10 x^{2} + 12$ $2^{6}\cdot 3\cdot 13^{2}$ $D_{4}$ (as 4T3) $[2]$ $2.38952643457$
4.4.32448.1 $x^{4} - 10 x^{2} + 12$ $2^{6}\cdot 3\cdot 13^{2}$ $D_{4}$ (as 4T3) trivial $18.2793947124$
4.2.35659.3 $x^{4} - x^{3} - 8 x^{2} + 22 x - 23$ $-\,13^{2}\cdot 211$ $D_{4}$ (as 4T3) trivial $9.10263290773$
4.0.38025.1 $x^{4} - x^{3} - x^{2} + 25 x + 40$ $3^{2}\cdot 5^{2}\cdot 13^{2}$ $C_2^2$ (as 4T2) $[8]$ $5.55294456145$
4.0.38025.2 $x^{4} + x^{2} + 49$ $3^{2}\cdot 5^{2}\cdot 13^{2}$ $C_2^2$ (as 4T2) $[2, 2]$ $2.38952643457$
4.0.38025.3 $x^{4} + 17 x^{2} + 121$ $3^{2}\cdot 5^{2}\cdot 13^{2}$ $C_2^2$ (as 4T2) $[8]$ $0.962423650119$
4.4.39377.1 $x^{4} - 2 x^{3} - 9 x^{2} + 10 x + 12$ $13^{2}\cdot 233$ $D_{4}$ (as 4T3) trivial $19.1731032049$
4.0.43264.1 $x^{4} - 12 x^{2} + 49$ $2^{8}\cdot 13^{2}$ $C_2^2$ (as 4T2) $[2]$ $4.62487668255$
4.0.43264.2 $x^{4} + 12 x^{2} + 49$ $2^{8}\cdot 13^{2}$ $C_2^2$ (as 4T2) $[6]$ $1.76274717404$
4.4.43433.1 $x^{4} - x^{3} - 14 x^{2} + 25 x + 1$ $13^{2}\cdot 257$ $D_{4}$ (as 4T3) trivial $20.2378324211$
4.2.44447.1 $x^{4} - x^{3} - x^{2} - 14 x - 12$ $-\,13^{2}\cdot 263$ $D_{4}$ (as 4T3) trivial $24.6514243541$
4.4.45968.1 $x^{4} - 9 x^{2} + 17$ $2^{4}\cdot 13^{2}\cdot 17$ $D_{4}$ (as 4T3) trivial $18.0810087504$
4.4.46813.1 $x^{4} - x^{3} - 10 x^{2} + 10 x + 9$ $13^{2}\cdot 277$ $D_{4}$ (as 4T3) trivial $25.1624107449$
4.0.52221.1 $x^{4} - x^{3} + 12 x^{2} + 12 x + 27$ $3\cdot 13^{2}\cdot 103$ $D_{4}$ (as 4T3) $[4]$ $2.38952643457$
4.4.52221.1 $x^{4} - 2 x^{3} - 8 x^{2} + 9 x + 17$ $3\cdot 13^{2}\cdot 103$ $D_{4}$ (as 4T3) trivial $11.5995762707$
4.2.56615.1 $x^{4} - x^{3} - 2 x^{2} - 7 x - 16$ $-\,5\cdot 13^{2}\cdot 67$ $S_4$ (as 4T5) $[2]$ $9.77772225919$
4.0.56953.1 $x^{4} - x^{3} + 11 x^{2} - 20 x + 36$ $13^{2}\cdot 337$ $D_{4}$ (as 4T3) $[9]$ $2.38952643457$
Next   displayed columns for results