Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
4.2.6591.1 |
$x^{4} - x^{3} + 2 x^{2} - 9 x + 3$ |
$4$ |
[2,1] |
$-\,3\cdot 13^{3}$ |
$2$ |
$9.01027047203$ |
$11.858182817915045$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$4.0390075457$ |
4.0.19773.1 |
$x^{4} - x^{3} + 2 x^{2} + 4 x + 16$ |
$4$ |
[0,2] |
$3^{2}\cdot 13^{3}$ |
$2$ |
$11.8581828179$ |
$11.858182817915045$ |
|
|
|
$D_{4}$ (as 4T3) |
$[4]$ |
$2$ |
$1$ |
$3.38059247829$ |
4.2.35152.1 |
$x^{4} - 13$ |
$4$ |
[2,1] |
$-\,2^{4}\cdot 13^{3}$ |
$2$ |
$13.692650084$ |
$19.364331453687083$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$11.5237014669$ |
4.4.37349.1 |
$x^{4} - x^{3} - 11 x^{2} + 17 x + 3$ |
$4$ |
[4,0] |
$13^{3}\cdot 17$ |
$2$ |
$13.9017586555$ |
$28.228121295572286$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$13.6750389701$ |
4.0.54925.1 |
$x^{4} - x^{3} + 15 x^{2} + 17 x + 29$ |
$4$ |
[0,2] |
$5^{2}\cdot 13^{3}$ |
$2$ |
$15.30884819$ |
$15.308848190022635$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
$[2]$ |
$2$ |
$1$ |
$2.38952643457$ |
4.2.105456.1 |
$x^{4} - 13 x^{2} - 39$ |
$4$ |
[2,1] |
$-\,2^{4}\cdot 3\cdot 13^{3}$ |
$3$ |
$18.0205409441$ |
$23.71636563583009$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$2$ |
$13.2670532709$ |
4.4.107653.1 |
$x^{4} - x^{3} - 24 x^{2} - 22 x + 29$ |
$4$ |
[4,0] |
$7^{2}\cdot 13^{3}$ |
$2$ |
$18.1136734559$ |
$18.113673455906813$ |
|
✓ |
|
$C_4$ (as 4T1) |
trivial |
$2$ |
$3$ |
$13.2792379456$ |
4.0.140608.1 |
$x^{4} - 2 x^{3} + 8 x^{2} + 6 x + 9$ |
$4$ |
[0,2] |
$2^{6}\cdot 13^{3}$ |
$2$ |
$19.3643314537$ |
$19.364331453687083$ |
|
|
|
$D_{4}$ (as 4T3) |
$[4]$ |
$2$ |
$1$ |
$4.82258798237$ |
4.4.140608.1 |
$x^{4} - 26 x^{2} + 52$ |
$4$ |
[4,0] |
$2^{6}\cdot 13^{3}$ |
$2$ |
$19.3643314537$ |
$19.364331453687083$ |
|
✓ |
|
$C_4$ (as 4T1) |
trivial |
$2$ |
$3$ |
$56.3106022511$ |
4.0.140608.2 |
$x^{4} + 26 x^{2} + 52$ |
$4$ |
[0,2] |
$2^{6}\cdot 13^{3}$ |
$2$ |
$19.3643314537$ |
$19.364331453687083$ |
✓ |
✓ |
|
$C_4$ (as 4T1) |
$[2]$ |
$2$ |
$1$ |
$2.38952643457$ |
4.0.151593.1 |
$x^{4} - x^{3} + 15 x^{2} + 4 x + 68$ |
$4$ |
[0,2] |
$3\cdot 13^{3}\cdot 23$ |
$3$ |
$19.7319400321$ |
$56.86984696736222$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[2, 6]$ |
$2$ |
$1$ |
$2.38952643457$ |
4.4.151593.1 |
$x^{4} - x^{3} - 24 x^{2} + 43 x + 29$ |
$4$ |
[4,0] |
$3\cdot 13^{3}\cdot 23$ |
$3$ |
$19.7319400321$ |
$56.86984696736222$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$52.6995237561$ |
4.2.173563.1 |
$x^{4} - 2 x^{3} - 18 x^{2} + 19 x - 69$ |
$4$ |
[2,1] |
$-\,13^{3}\cdot 79$ |
$2$ |
$20.4110002041$ |
$60.85146801763715$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$21.3557697404$ |
4.2.191139.1 |
$x^{4} - 2 x^{3} + 8 x^{2} - 7 x - 69$ |
$4$ |
[2,1] |
$-\,3\cdot 13^{3}\cdot 29$ |
$3$ |
$20.9091956981$ |
$63.85826878760316$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$2$ |
$15.4383167029$ |
4.2.191139.2 |
$x^{4} - x^{3} + 2 x^{2} + 30 x - 75$ |
$4$ |
[2,1] |
$-\,3\cdot 13^{3}\cdot 29$ |
$3$ |
$20.9091956981$ |
$63.85826878760316$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$2$ |
$6.83337035508$ |
4.0.219700.1 |
$x^{4} - 2 x^{3} + 8 x^{2} + 6 x + 35$ |
$4$ |
[0,2] |
$2^{2}\cdot 5^{2}\cdot 13^{3}$ |
$3$ |
$21.6499807346$ |
$31.777825866337707$ |
|
|
|
$S_4$ (as 4T5) |
$[8]$ |
$2$ |
$1$ |
$7.69716897285$ |
4.0.221897.1 |
$x^{4} - 2 x^{3} + 21 x^{2} - 20 x + 87$ |
$4$ |
[0,2] |
$13^{3}\cdot 101$ |
$2$ |
$21.7039038938$ |
$68.80471513409687$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[10]$ |
$2$ |
$1$ |
$2.38952643457$ |
4.2.235079.1 |
$x^{4} - x^{3} + 2 x^{2} - 35 x - 75$ |
$4$ |
[2,1] |
$-\,13^{3}\cdot 107$ |
$2$ |
$22.0192974723$ |
$70.81893690370119$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$66.6619406148$ |
4.0.265837.1 |
$x^{4} - x^{3} + 2 x^{2} - 22 x + 29$ |
$4$ |
[0,2] |
$11^{2}\cdot 13^{3}$ |
$2$ |
$22.7066913572$ |
$33.86252232274932$ |
|
|
✓ |
$S_4$ (as 4T5) |
$[8]$ |
$2$ |
$1$ |
$2.88120016789$ |
4.4.265837.1 |
$x^{4} - x^{3} - 37 x^{2} - 35 x + 81$ |
$4$ |
[4,0] |
$11^{2}\cdot 13^{3}$ |
$2$ |
$22.7066913572$ |
$22.70669135720461$ |
|
✓ |
|
$C_4$ (as 4T1) |
trivial |
$2$ |
$3$ |
$70.5048065217$ |
4.0.283413.1 |
$x^{4} - 2 x^{3} + 34 x^{2} - 33 x + 113$ |
$4$ |
[0,2] |
$3\cdot 13^{3}\cdot 43$ |
$3$ |
$23.0730465254$ |
$77.75930483841216$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[2, 2]$ |
$2$ |
$1$ |
$2.38952643457$ |
4.4.283413.1 |
$x^{4} - x^{3} - 24 x^{2} + 30 x + 81$ |
$4$ |
[4,0] |
$3\cdot 13^{3}\cdot 43$ |
$3$ |
$23.0730465254$ |
$77.75930483841216$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$53.0356035619$ |
4.2.287807.1 |
$x^{4} - 2 x^{3} - 5 x^{2} + 6 x - 108$ |
$4$ |
[2,1] |
$-\,13^{3}\cdot 131$ |
$2$ |
$23.1619616469$ |
$78.35977170790618$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$75.6230718059$ |
4.2.305383.1 |
$x^{4} - 2 x^{3} + 21 x^{2} - 20 x - 108$ |
$4$ |
[2,1] |
$-\,13^{3}\cdot 139$ |
$2$ |
$23.5077581657$ |
$80.71698182392245$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$44.2002599804$ |
4.2.316368.1 |
$x^{4} - 117$ |
$4$ |
[2,1] |
$-\,2^{4}\cdot 3^{2}\cdot 13^{3}$ |
$3$ |
$23.7163656358$ |
$33.54000593239012$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2, 2]$ |
$2$ |
$2$ |
$7.36109382858$ |
4.0.316368.1 |
$x^{4} + 13 x^{2} + 52$ |
$4$ |
[0,2] |
$2^{4}\cdot 3^{2}\cdot 13^{3}$ |
$3$ |
$23.7163656358$ |
$23.71636563583009$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2, 4]$ |
$2$ |
$1$ |
$11.104336892$ |
4.0.336141.1 |
$x^{4} - x^{3} + 28 x^{2} - 48 x + 159$ |
$4$ |
[0,2] |
$3^{2}\cdot 13^{3}\cdot 17$ |
$3$ |
$24.0785523058$ |
$48.892540286148204$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[2, 2, 2]$ |
$2$ |
$1$ |
$2.38952643457$ |
4.2.349323.1 |
$x^{4} - x^{3} + 15 x^{2} + 43 x - 127$ |
$4$ |
[2,1] |
$-\,3\cdot 13^{3}\cdot 53$ |
$3$ |
$24.3112223454$ |
$86.32887400159964$ |
|
|
|
$D_{4}$ (as 4T3) |
$[4]$ |
$2$ |
$2$ |
$10.1084254513$ |
4.2.349323.2 |
$x^{4} - 2 x^{3} + 34 x^{2} - 33 x - 121$ |
$4$ |
[2,1] |
$-\,3\cdot 13^{3}\cdot 53$ |
$3$ |
$24.3112223454$ |
$86.32887400159964$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$2$ |
$8.89146508938$ |
4.0.380081.1 |
$x^{4} - x^{3} + 28 x^{2} + 17 x + 159$ |
$4$ |
[0,2] |
$13^{3}\cdot 173$ |
$2$ |
$24.82956094$ |
$90.0493465746338$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[14]$ |
$2$ |
$1$ |
$2.38952643457$ |
4.4.397657.1 |
$x^{4} - 2 x^{3} - 31 x^{2} + 32 x + 139$ |
$4$ |
[4,0] |
$13^{3}\cdot 181$ |
$2$ |
$25.1117603416$ |
$92.10788321944418$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$38.8868565015$ |
4.2.402051.1 |
$x^{4} - 2 x^{3} + 8 x^{2} - 7 x - 147$ |
$4$ |
[2,1] |
$-\,3\cdot 13^{3}\cdot 61$ |
$3$ |
$25.1808442414$ |
$92.61536851046283$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$2$ |
$20.3258249859$ |
4.2.402051.2 |
$x^{4} - x^{3} - 24 x^{2} - 48 x - 153$ |
$4$ |
[2,1] |
$-\,3\cdot 13^{3}\cdot 61$ |
$3$ |
$25.1808442414$ |
$92.61536851046283$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$2$ |
$22.7224625474$ |
4.2.419627.1 |
$x^{4} - x^{3} + 15 x^{2} - 61 x - 127$ |
$4$ |
[2,1] |
$-\,13^{3}\cdot 191$ |
$2$ |
$25.4516449404$ |
$94.61809455372205$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$14.4952807612$ |
4.0.421824.1 |
$x^{4} + 26 x^{2} + 156$ |
$4$ |
[0,2] |
$2^{6}\cdot 3\cdot 13^{3}$ |
$3$ |
$25.4848934044$ |
$47.43273127166018$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[2, 8]$ |
$2$ |
$1$ |
$2.38952643457$ |
4.4.421824.1 |
$x^{4} - 26 x^{2} + 156$ |
$4$ |
[4,0] |
$2^{6}\cdot 3\cdot 13^{3}$ |
$3$ |
$25.4848934044$ |
$47.43273127166018$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$41.6037745628$ |
4.2.463567.1 |
$x^{4} - x^{3} - 11 x^{2} + 56 x - 192$ |
$4$ |
[2,1] |
$-\,13^{3}\cdot 211$ |
$2$ |
$26.093247163$ |
$99.44861561931228$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$53.6080748809$ |
4.2.492128.1 |
$x^{4} - 2 x^{3} - 5 x^{2} - 20 x + 74$ |
$4$ |
[2,1] |
$-\,2^{5}\cdot 7\cdot 13^{3}$ |
$3$ |
$26.4861917476$ |
$72.45469382362725$ |
|
|
|
$S_4$ (as 4T5) |
$[2]$ |
$2$ |
$2$ |
$56.0954180327$ |
4.4.494325.1 |
$x^{4} - x^{3} - 50 x^{2} - 48 x + 159$ |
$4$ |
[4,0] |
$3^{2}\cdot 5^{2}\cdot 13^{3}$ |
$3$ |
$26.5157028705$ |
$26.51570287047805$ |
|
✓ |
|
$C_4$ (as 4T1) |
$[2]$ |
$2$ |
$3$ |
$21.1826002409$ |
4.0.511901.1 |
$x^{4} - x^{3} + 28 x^{2} + 4 x + 211$ |
$4$ |
[0,2] |
$13^{3}\cdot 233$ |
$2$ |
$26.7483190332$ |
$104.50461623000403$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[10]$ |
$2$ |
$1$ |
$2.38952643457$ |
4.0.564629.1 |
$x^{4} - x^{3} + 28 x^{2} - 22 x + 237$ |
$4$ |
[0,2] |
$13^{3}\cdot 257$ |
$2$ |
$27.4120045393$ |
$109.75493980375184$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[10]$ |
$2$ |
$1$ |
$2.38952643457$ |
4.2.577811.1 |
$x^{4} - x^{3} + 41 x^{2} - 113 x - 153$ |
$4$ |
[2,1] |
$-\,13^{3}\cdot 263$ |
$2$ |
$27.5706148483$ |
$111.02873416738291$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$2$ |
$81.6567203654$ |
4.0.597584.1 |
$x^{4} + 39 x^{2} + 221$ |
$4$ |
[0,2] |
$2^{4}\cdot 13^{3}\cdot 17$ |
$3$ |
$27.803517311$ |
$56.45624259114457$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[2, 6]$ |
$2$ |
$1$ |
$2.38952643457$ |
4.0.608569.1 |
$x^{4} - x^{3} + 41 x^{2} - 74 x + 276$ |
$4$ |
[0,2] |
$13^{3}\cdot 277$ |
$2$ |
$27.9304193633$ |
$113.94555780260073$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[34]$ |
$2$ |
$1$ |
$2.38952643457$ |
4.4.634933.1 |
$x^{4} - 2 x^{3} - 18 x^{2} + 19 x + 35$ |
$4$ |
[4,0] |
$13^{3}\cdot 17^{2}$ |
$2$ |
$28.2281212956$ |
$28.228121295572286$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$3$ |
$30.9446292887$ |
4.0.678873.1 |
$x^{4} - x^{3} + 41 x^{2} + 30 x + 276$ |
$4$ |
[0,2] |
$3\cdot 13^{3}\cdot 103$ |
$3$ |
$28.7043114815$ |
$120.34741157805948$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[2, 6]$ |
$2$ |
$1$ |
$2.38952643457$ |
4.4.678873.1 |
$x^{4} - 2 x^{3} - 31 x^{2} + 32 x + 243$ |
$4$ |
[4,0] |
$3\cdot 13^{3}\cdot 103$ |
$3$ |
$28.7043114815$ |
$120.34741157805948$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$125.248662951$ |
4.4.740389.1 |
$x^{4} - x^{3} - 37 x^{2} + 43 x + 237$ |
$4$ |
[4,0] |
$13^{3}\cdot 337$ |
$2$ |
$29.3335745973$ |
$125.68182103155466$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$2$ |
$3$ |
$123.382891227$ |
4.2.744783.1 |
$x^{4} - x^{3} + 2 x^{2} - 61 x - 257$ |
$4$ |
[2,1] |
$-\,3\cdot 13^{3}\cdot 113$ |
$3$ |
$29.3769996971$ |
$126.05421242850157$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$2$ |
$21.2843554996$ |
4.2.744783.2 |
$x^{4} - x^{3} + 15 x^{2} - 74 x - 244$ |
$4$ |
[2,1] |
$-\,3\cdot 13^{3}\cdot 113$ |
$3$ |
$29.3769996971$ |
$126.05421242850157$ |
|
|
|
$D_{4}$ (as 4T3) |
$[2]$ |
$2$ |
$2$ |
$47.3957798631$ |