↑

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 at least 1000)

Next   To download results, determine the number of results.
Label Polynomial Discriminant Galois group Class group Regulator
4.0.25281.1 $x^{4} - x^{3} + 14 x^{2} + 13 x + 169$ $3^{2}\cdot 53^{2}$ $C_2^2$ (as 4T2) $[5]$ $3.9314409433$
4.2.44944.1 $x^{4} - 7 x^{2} - 1$ $-\,2^{4}\cdot 53^{2}$ $D_{4}$ (as 4T3) trivial $9.5759588104$
4.4.47753.1 $x^{4} - x^{3} - 9 x^{2} - 2 x + 4$ $17\cdot 53^{2}$ $D_{4}$ (as 4T3) trivial $14.2302968307$
4.4.70225.1 $x^{4} - 29 x^{2} + 144$ $5^{2}\cdot 53^{2}$ $C_2^2$ (as 4T2) trivial $17.792129768$
4.0.81461.1 $x^{4} - x^{3} - 3 x^{2} - 5 x + 25$ $29\cdot 53^{2}$ $D_{4}$ (as 4T3) trivial $3.9314409433$
4.0.103933.1 $x^{4} - x^{3} + 20 x + 29$ $37\cdot 53^{2}$ $D_{4}$ (as 4T3) $[3]$ $3.9314409433$
4.2.123596.1 $x^{4} - x^{3} + x^{2} - 7 x - 4$ $-\,2^{2}\cdot 11\cdot 53^{2}$ $S_4$ (as 4T5) $[2]$ $24.6155390103$
4.2.132023.1 $x^{4} - x^{3} - 2 x^{2} + 21 x + 17$ $-\,47\cdot 53^{2}$ $D_{4}$ (as 4T3) trivial $18.9147181202$
4.2.176967.1 $x^{4} - x^{3} - 10 x^{2} + 25 x - 11$ $-\,3^{2}\cdot 7\cdot 53^{2}$ $D_{4}$ (as 4T3) trivial $27.5106616849$
4.0.179776.1 $x^{4} - 2 x^{3} - 21 x^{2} + 22 x + 227$ $2^{6}\cdot 53^{2}$ $C_2^2$ (as 4T2) $[3]$ $3.9314409433$
4.4.179776.1 $x^{4} - 2 x^{3} - 29 x^{2} + 30 x + 119$ $2^{6}\cdot 53^{2}$ $C_2^2$ (as 4T2) trivial $31.1455786519$
4.0.227529.1 $x^{4} - x^{3} + 3 x^{2} - 8 x + 11$ $3^{4}\cdot 53^{2}$ $A_4$ (as 4T4) $[2]$ $21.8968929894$
4.2.278091.1 $x^{4} - x^{3} - 4 x^{2} + 22 x + 7$ $-\,3^{2}\cdot 11\cdot 53^{2}$ $D_{4}$ (as 4T3) trivial $18.5184907213$
4.2.280900.1 $x^{4} - 11 x^{2} - 36$ $-\,2^{2}\cdot 5^{2}\cdot 53^{2}$ $D_{4}$ (as 4T3) $[2]$ $81.0574036826$
4.2.300563.1 $x^{4} - x^{3} - 8 x^{2} + 24 x - 7$ $-\,53^{2}\cdot 107$ $D_{4}$ (as 4T3) trivial $17.8083429212$
4.0.314608.1 $x^{4} + 9 x^{2} + 7$ $2^{4}\cdot 7\cdot 53^{2}$ $D_{4}$ (as 4T3) $[4]$ $3.9314409433$
4.4.314608.1 $x^{4} - 9 x^{2} + 7$ $2^{4}\cdot 7\cdot 53^{2}$ $D_{4}$ (as 4T3) trivial $43.0616212375$
4.0.317417.1 $x^{4} - 2 x^{3} + 17 x^{2} - 16 x + 11$ $53^{2}\cdot 113$ $D_{4}$ (as 4T3) $[5]$ $3.9314409433$
4.0.328653.2 $x^{4} + 7 x^{2} + 52$ $3^{2}\cdot 13\cdot 53^{2}$ $D_{4}$ (as 4T3) $[20]$ $6.06687521602$
4.0.328653.3 $x^{4} - 2 x^{3} + 24 x^{2} - 23 x + 13$ $3^{2}\cdot 13\cdot 53^{2}$ $D_{4}$ (as 4T3) $[4]$ $3.9314409433$
4.0.328653.4 $x^{4} - x^{3} - 92 x^{2} + 66 x + 2289$ $3^{2}\cdot 13\cdot 53^{2}$ $D_{4}$ (as 4T3) $[8]$ $7.81827419074$
4.2.334271.1 $x^{4} - 2 x^{3} + 15 x^{2} - 14 x - 4$ $-\,7\cdot 17\cdot 53^{2}$ $D_{4}$ (as 4T3) $[2]$ $19.3968587796$
4.2.334271.2 $x^{4} - x^{3} - 6 x^{2} + 23 x - 1$ $-\,7\cdot 17\cdot 53^{2}$ $D_{4}$ (as 4T3) $[4]$ $8.41726039121$
4.0.404496.1 $x^{4} + 25 x^{2} + 196$ $2^{4}\cdot 3^{2}\cdot 53^{2}$ $C_2^2$ (as 4T2) $[30]$ $2.63391579385$
4.4.404496.1 $x^{4} - 2 x^{3} - 31 x^{2} + 32 x + 97$ $2^{4}\cdot 3^{2}\cdot 53^{2}$ $C_2^2$ (as 4T2) trivial $40.807108307$
4.0.404496.3 $x^{4} - 53 x^{2} + 2809$ $2^{4}\cdot 3^{2}\cdot 53^{2}$ $C_2^2$ (as 4T2) $[6]$ $15.7631195489$
4.4.418541.1 $x^{4} - 2 x^{3} - 8 x^{2} + 9 x + 7$ $53^{2}\cdot 149$ $D_{4}$ (as 4T3) trivial $40.8159073036$
4.0.474721.1 $x^{4} - x^{3} + 23 x^{2} - 18 x + 59$ $13^{2}\cdot 53^{2}$ $A_4$ (as 4T4) $[2]$ $19.0606458596$
4.2.491575.1 $x^{4} - x^{3} - 33 x + 29$ $-\,5^{2}\cdot 7\cdot 53^{2}$ $D_{4}$ (as 4T3) $[2]$ $15.527396385$
4.2.494384.2 $x^{4} - 2 x^{3} - 12 x^{2} - 40 x - 24$ $-\,2^{4}\cdot 11\cdot 53^{2}$ $S_4$ (as 4T5) $[4]$ $15.9508677088$
4.0.494384.1 $x^{4} + 16 x^{2} + 11$ $2^{4}\cdot 11\cdot 53^{2}$ $D_{4}$ (as 4T3) $[6]$ $3.9314409433$
4.4.494384.1 $x^{4} - 16 x^{2} + 11$ $2^{4}\cdot 11\cdot 53^{2}$ $D_{4}$ (as 4T3) trivial $39.549818322$
4.2.525283.1 $x^{4} - 2 x^{3} + 4 x^{2} - 3 x - 11$ $-\,11\cdot 17\cdot 53^{2}$ $D_{4}$ (as 4T3) $[2]$ $8.24298542103$
4.2.525283.2 $x^{4} - x^{3} - 17 x^{2} + 55 x - 49$ $-\,11\cdot 17\cdot 53^{2}$ $D_{4}$ (as 4T3) $[4]$ $7.64862389123$
4.0.553373.1 $x^{4} - x^{3} + x^{2} - 7 x + 49$ $53^{2}\cdot 197$ $D_{4}$ (as 4T3) $[5]$ $3.9314409433$
4.2.570227.1 $x^{4} - 2 x^{3} + x - 13$ $-\,7\cdot 29\cdot 53^{2}$ $D_{4}$ (as 4T3) trivial $28.5789466338$
4.2.570227.2 $x^{4} - x^{3} - 21 x^{2} - 49 x - 37$ $-\,7\cdot 29\cdot 53^{2}$ $D_{4}$ (as 4T3) $[3]$ $8.18271010289$
4.2.584272.1 $x^{4} - x^{2} - 13$ $-\,2^{4}\cdot 13\cdot 53^{2}$ $D_{4}$ (as 4T3) $[2]$ $9.34816172906$
4.2.584272.2 $x^{4} + x^{2} - 13$ $-\,2^{4}\cdot 13\cdot 53^{2}$ $D_{4}$ (as 4T3) $[2]$ $22.8938704098$
4.0.606744.1 $x^{4} + 15 x^{2} + 96$ $2^{3}\cdot 3^{3}\cdot 53^{2}$ $D_{4}$ (as 4T3) $[10]$ $14.8026199874$
4.4.620789.1 $x^{4} - x^{3} - 18 x^{2} - 24 x - 7$ $13\cdot 17\cdot 53^{2}$ $D_{4}$ (as 4T3) $[2]$ $27.7225437824$
4.4.620789.2 $x^{4} - x^{3} - 21 x^{2} + 57 x - 37$ $13\cdot 17\cdot 53^{2}$ $D_{4}$ (as 4T3) $[2]$ $13.1207937783$
4.0.632025.3 $x^{4} + 77 x^{2} + 1681$ $3^{2}\cdot 5^{2}\cdot 53^{2}$ $C_2^2$ (as 4T2) $[20]$ $0.962423650119$
4.0.632025.4 $x^{4} - x^{3} + 67 x^{2} + 66 x + 4356$ $3^{2}\cdot 5^{2}\cdot 53^{2}$ $C_2^2$ (as 4T2) $[4]$ $18.8091810128$
4.2.637643.1 $x^{4} - 2 x^{3} + 22 x^{2} - 21 x - 9$ $-\,53^{2}\cdot 227$ $D_{4}$ (as 4T3) trivial $18.0285991832$
4.0.643261.2 $x^{4} - 2 x^{3} + 12 x^{2} - 11 x + 17$ $53^{2}\cdot 229$ $D_{4}$ (as 4T3) $[5]$ $3.9314409433$
4.0.643261.3 $x^{4} - x^{3} + 3 x^{2} + 45 x + 64$ $53^{2}\cdot 229$ $S_4$ (as 4T5) $[2]$ $58.2422707496$
4.4.676969.1 $x^{4} - 2 x^{3} - 15 x^{2} + 16 x + 11$ $53^{2}\cdot 241$ $D_{4}$ (as 4T3) trivial $74.4563957645$
4.0.707868.1 $x^{4} - 17 x^{2} + 112$ $2^{2}\cdot 3^{2}\cdot 7\cdot 53^{2}$ $D_{4}$ (as 4T3) $[10]$ $26.0669003528$
4.0.707868.2 $x^{4} + 17 x^{2} + 112$ $2^{2}\cdot 3^{2}\cdot 7\cdot 53^{2}$ $D_{4}$ (as 4T3) $[10]$ $17.7797110909$
Next   To download results, determine the number of results.