| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
Unit signature rank |
Max $p$ |
| 4.0.84872.2 |
$x^{4} - 5 x^{2} + 32$ |
$4$ |
(0, 2) |
$2^{3}\cdot 103^{2}$ |
$2$ |
$17.0683330718$ |
$28.705400188814647$ |
|
|
|
$D_{4}$ (as 4T3) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$3.6205473006$ |
$0$ |
$103$ |
| 4.0.169744.1 |
$x^{4} - 51 x^{2} + 676$ |
$4$ |
(0, 2) |
$2^{4}\cdot 103^{2}$ |
$2$ |
$20.2977831302$ |
$20.29778313018444$ |
✓ |
✓ |
|
$C_2^2$ (as 4T2) |
$[5]$ |
$[5]$ |
$4$ |
$1$ |
$13.0281757673$ |
$0$ |
$103$ |
| 4.0.265225.1 |
$x^{4} + 49 x^{2} + 729$ |
$4$ |
(0, 2) |
$5^{2}\cdot 103^{2}$ |
$2$ |
$22.6936114358$ |
$22.693611435820433$ |
✓ |
✓ |
|
$C_2^2$ (as 4T2) |
$[15]$ |
$[15]$ |
$2$ |
$1$ |
$0.962423650119$ |
$0$ |
$103$ |
| 4.2.286443.1 |
$x^{4} - 3 x^{2} - 75$ |
$4$ |
(2, 1) |
$-\,3^{3}\cdot 103^{2}$ |
$2$ |
$23.1344699429$ |
$23.134469942896533$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$[2]$ |
$2$ |
$2$ |
$40.9609493027$ |
$1$ |
$103$ |
| 4.0.297052.1 |
$x^{4} - 3 x^{2} + 28$ |
$4$ |
(0, 2) |
$2^{2}\cdot 7\cdot 103^{2}$ |
$3$ |
$23.3457655706$ |
$53.70288632839021$ |
|
|
|
$D_{4}$ (as 4T3) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$16.2076103095$ |
$0$ |
$103$ |
| 4.0.307661.1 |
$x^{4} - x^{3} + 18 x^{2} + 4 x + 16$ |
$4$ |
(0, 2) |
$29\cdot 103^{2}$ |
$2$ |
$23.5514750097$ |
$54.653453687758834$ |
|
|
|
$D_{4}$ (as 4T3) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$9.87296039254$ |
$0$ |
$103$ |
| 4.0.434969.1 |
$x^{4} - 2 x^{3} + 11 x^{2} - 10 x + 128$ |
$4$ |
(0, 2) |
$41\cdot 103^{2}$ |
$2$ |
$25.681156447$ |
$64.98461356351979$ |
|
|
|
$D_{4}$ (as 4T3) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$33.4438757009$ |
$0$ |
$103$ |
| 4.2.466796.3 |
$x^{4} - x^{3} + 2 x^{2} + 12 x - 62$ |
$4$ |
(2, 1) |
$-\,2^{2}\cdot 11\cdot 103^{2}$ |
$3$ |
$26.1385674208$ |
$53.43202316085161$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$121.303415523$ |
$1$ |
$103$ |
| 4.0.519841.1 |
$x^{4} + 55 x^{2} + 576$ |
$4$ |
(0, 2) |
$7^{2}\cdot 103^{2}$ |
$2$ |
$26.8514431642$ |
$26.851443164195103$ |
✓ |
✓ |
|
$C_2^2$ (as 4T2) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$38.1568136047$ |
$0$ |
$103$ |
| 4.0.594104.1 |
$x^{4} - x^{3} + 28 x^{2} - x + 1$ |
$4$ |
(0, 2) |
$2^{3}\cdot 7\cdot 103^{2}$ |
$3$ |
$27.7629505218$ |
$75.9473501841901$ |
|
|
|
$D_{4}$ (as 4T3) |
$[15]$ |
$[15]$ |
$2$ |
$1$ |
$3.32973098252$ |
$0$ |
$103$ |
| 4.0.647149.1 |
$x^{4} - x^{3} + 15 x^{2} - 46 x + 56$ |
$4$ |
(0, 2) |
$61\cdot 103^{2}$ |
$2$ |
$28.3629285621$ |
$79.26537705707328$ |
|
|
|
$D_{4}$ (as 4T3) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$17.7602150607$ |
$0$ |
$103$ |
| 4.0.678976.2 |
$x^{4} - 2 x^{3} + 57 x^{2} - 56 x + 578$ |
$4$ |
(0, 2) |
$2^{6}\cdot 103^{2}$ |
$2$ |
$28.7054001888$ |
$28.705400188814647$ |
✓ |
✓ |
|
$C_2^2$ (as 4T2) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$11.6874668344$ |
$0$ |
$103$ |
| 4.0.763848.2 |
$x^{4} - x^{3} + 17 x^{2} - 47 x + 46$ |
$4$ |
(0, 2) |
$2^{3}\cdot 3^{2}\cdot 103^{2}$ |
$3$ |
$29.5632200808$ |
$49.71921157862421$ |
|
|
|
$D_{4}$ (as 4T3) |
$[10]$ |
$[10]$ |
$2$ |
$1$ |
$15.9164260581$ |
$0$ |
$103$ |
| 4.0.806284.2 |
$x^{4} - x^{3} - 4 x^{2} + 15 x + 225$ |
$4$ |
(0, 2) |
$2^{2}\cdot 19\cdot 103^{2}$ |
$3$ |
$29.9655332402$ |
$88.47598544237866$ |
|
|
|
$D_{4}$ (as 4T3) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$10.3015251031$ |
$0$ |
$103$ |
| 4.0.976028.2 |
$x^{4} - x^{3} + 4 x^{2} + 11 x + 121$ |
$4$ |
(0, 2) |
$2^{2}\cdot 23\cdot 103^{2}$ |
$3$ |
$31.4315334307$ |
$97.34474818910365$ |
|
|
|
$D_{4}$ (as 4T3) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$5.02865042105$ |
$0$ |
$103$ |
| 4.2.1050291.1 |
$x^{4} - 2 x^{3} - 14 x^{2} + 15 x - 21$ |
$4$ |
(2, 1) |
$-\,3^{2}\cdot 11\cdot 103^{2}$ |
$3$ |
$32.0130763942$ |
$58.30094338859364$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$[2]$ |
$2$ |
$2$ |
$66.2718263192$ |
$1$ |
$103$ |
| 4.2.1050291.2 |
$x^{4} - 2 x^{3} - 16 x^{2} + 17 x - 5$ |
$4$ |
(2, 1) |
$-\,3^{2}\cdot 11\cdot 103^{2}$ |
$3$ |
$32.0130763942$ |
$58.30094338859364$ |
|
|
✓ |
$D_{4}$ (as 4T3) |
trivial |
$[2]$ |
$2$ |
$2$ |
$77.3444898262$ |
$1$ |
$103$ |
| 4.0.1103336.1 |
$x^{4} + x^{2} + 26$ |
$4$ |
(0, 2) |
$2^{3}\cdot 13\cdot 103^{2}$ |
$3$ |
$32.409844489$ |
$103.49879226348489$ |
|
|
|
$D_{4}$ (as 4T3) |
$[10]$ |
$[10]$ |
$2$ |
$1$ |
$5.21372257561$ |
$0$ |
$103$ |
| 4.0.1103336.2 |
$x^{4} + 2 x^{2} + 104$ |
$4$ |
(0, 2) |
$2^{3}\cdot 13\cdot 103^{2}$ |
$3$ |
$32.409844489$ |
$103.49879226348489$ |
|
|
|
$D_{4}$ (as 4T3) |
$[10]$ |
$[10]$ |
$2$ |
$1$ |
$15.5260723581$ |
$0$ |
$103$ |
| 4.0.1410997.1 |
$x^{4} - x^{3} + 2 x^{2} + 12 x + 144$ |
$4$ |
(0, 2) |
$7\cdot 19\cdot 103^{2}$ |
$3$ |
$34.4652571041$ |
$117.04272724095249$ |
|
|
|
$D_{4}$ (as 4T3) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$28.0164543925$ |
$0$ |
$103$ |
| 4.0.1442824.1 |
$x^{4} - x^{3} + 8 x^{2} + 9 x + 81$ |
$4$ |
(0, 2) |
$2^{3}\cdot 17\cdot 103^{2}$ |
$3$ |
$34.657987396$ |
$118.35539700410793$ |
|
|
|
$D_{4}$ (as 4T3) |
$[10]$ |
$[10]$ |
$2$ |
$1$ |
$8.04045747463$ |
$0$ |
$103$ |
| 4.0.1442824.2 |
$x^{4} - x^{3} + 18 x^{2} + 107 x + 119$ |
$4$ |
(0, 2) |
$2^{3}\cdot 17\cdot 103^{2}$ |
$3$ |
$34.657987396$ |
$118.35539700410793$ |
|
|
|
$D_{4}$ (as 4T3) |
$[20]$ |
$[20]$ |
$2$ |
$1$ |
$3.83518969944$ |
$0$ |
$103$ |
| 4.4.1527696.1 |
$x^{4} - 53 x^{2} + 625$ |
$4$ |
(4, 0) |
$2^{4}\cdot 3^{2}\cdot 103^{2}$ |
$3$ |
$35.1567916625$ |
$35.156791662493895$ |
|
✓ |
|
$C_2^2$ (as 4T2) |
trivial |
$[2]$ |
$2$ |
$3$ |
$146.287970966$ |
$3$ |
$103$ |
| 4.0.1527696.1 |
$x^{4} - 2 x^{3} + 47 x^{2} - 46 x + 838$ |
$4$ |
(0, 2) |
$2^{4}\cdot 3^{2}\cdot 103^{2}$ |
$3$ |
$35.1567916625$ |
$35.156791662493895$ |
✓ |
✓ |
|
$C_2^2$ (as 4T2) |
$[30]$ |
$[30]$ |
$2$ |
$1$ |
$2.63391579385$ |
$0$ |
$103$ |
| 4.0.1527696.2 |
$x^{4} + 155 x^{2} + 5929$ |
$4$ |
(0, 2) |
$2^{4}\cdot 3^{2}\cdot 103^{2}$ |
$3$ |
$35.1567916625$ |
$35.156791662493895$ |
✓ |
✓ |
|
$C_2^2$ (as 4T2) |
$[6]$ |
$[6]$ |
$4$ |
$1$ |
$17.052305787$ |
$0$ |
$103$ |
| 4.2.1559523.2 |
$x^{4} + 23 x^{2} - 48$ |
$4$ |
(2, 1) |
$-\,3\cdot 7^{2}\cdot 103^{2}$ |
$3$ |
$35.3384865587$ |
$46.50806381693394$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$[2]$ |
$2$ |
$2$ |
$456.781704877$ |
$1$ |
$103$ |
| 4.0.1612568.2 |
$x^{4} + 14 x^{2} + 152$ |
$4$ |
(0, 2) |
$2^{3}\cdot 19\cdot 103^{2}$ |
$3$ |
$35.6352253341$ |
$125.12393855693642$ |
|
|
|
$D_{4}$ (as 4T3) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$9.48358867072$ |
$0$ |
$103$ |
| 4.0.1708049.2 |
$x^{4} - x^{3} - 12 x^{2} + 19 x + 361$ |
$4$ |
(0, 2) |
$7\cdot 23\cdot 103^{2}$ |
$3$ |
$36.1513967457$ |
$128.77499757328673$ |
|
|
|
$D_{4}$ (as 4T3) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$7.25810198829$ |
$0$ |
$103$ |
| 4.0.1952056.1 |
$x^{4} + 9 x^{2} + 46$ |
$4$ |
(0, 2) |
$2^{3}\cdot 23\cdot 103^{2}$ |
$3$ |
$37.3786031912$ |
$137.66626311482418$ |
|
|
|
$D_{4}$ (as 4T3) |
$[5, 5]$ |
$[5, 5]$ |
$2$ |
$1$ |
$11.5805562523$ |
$0$ |
$103$ |
| 4.2.2036928.1 |
$x^{4} - 40 x^{2} - 12$ |
$4$ |
(2, 1) |
$-\,2^{6}\cdot 3\cdot 103^{2}$ |
$3$ |
$37.7784312199$ |
$49.71921157862421$ |
|
|
|
$D_{4}$ (as 4T3) |
$[3]$ |
$[6]$ |
$2$ |
$2$ |
$76.8533765166$ |
$1$ |
$103$ |
| 4.0.2206672.1 |
$x^{4} - 27 x^{2} + 208$ |
$4$ |
(0, 2) |
$2^{4}\cdot 13\cdot 103^{2}$ |
$3$ |
$38.5420176624$ |
$73.18469785412795$ |
|
|
|
$D_{4}$ (as 4T3) |
$[30]$ |
$[30]$ |
$2$ |
$1$ |
$4.73338769304$ |
$0$ |
$103$ |
| 4.2.2291544.1 |
$x^{4} - x^{3} - 30 x^{2} + 28 x - 40$ |
$4$ |
(2, 1) |
$-\,2^{3}\cdot 3^{3}\cdot 103^{2}$ |
$3$ |
$38.9073856876$ |
$103.42012769959115$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$617.546830105$ |
$1$ |
$103$ |
| 4.0.2376416.1 |
$x^{4} - 11 x^{2} + 56$ |
$4$ |
(0, 2) |
$2^{5}\cdot 7\cdot 103^{2}$ |
$3$ |
$39.2627411594$ |
$107.40577265678041$ |
|
|
|
$D_{4}$ (as 4T3) |
$[10]$ |
$[10]$ |
$2$ |
$1$ |
$12.1364333258$ |
$0$ |
$103$ |
| 4.4.2387025.1 |
$x^{4} - 157 x^{2} + 5776$ |
$4$ |
(4, 0) |
$3^{2}\cdot 5^{2}\cdot 103^{2}$ |
$3$ |
$39.3064880141$ |
$39.30648801406709$ |
|
✓ |
|
$C_2^2$ (as 4T2) |
trivial |
$[2]$ |
$2$ |
$3$ |
$158.574499922$ |
$3$ |
$103$ |
| 4.0.2387025.1 |
$x^{4} + 59 x^{2} + 484$ |
$4$ |
(0, 2) |
$3^{2}\cdot 5^{2}\cdot 103^{2}$ |
$3$ |
$39.3064880141$ |
$39.30648801406709$ |
✓ |
✓ |
|
$C_2^2$ (as 4T2) |
$[10]$ |
$[10]$ |
$2$ |
$1$ |
$38.6495056383$ |
$0$ |
$103$ |
| 4.0.2387025.2 |
$x^{4} - x^{3} + 28 x^{2} - 207 x + 2679$ |
$4$ |
(0, 2) |
$3^{2}\cdot 5^{2}\cdot 103^{2}$ |
$3$ |
$39.3064880141$ |
$39.30648801406709$ |
✓ |
✓ |
|
$C_2^2$ (as 4T2) |
$[6]$ |
$[6]$ |
$2$ |
$1$ |
$17.052305787$ |
$0$ |
$103$ |
| 4.0.2503724.2 |
$x^{4} + 29 x^{2} + 236$ |
$4$ |
(0, 2) |
$2^{2}\cdot 59\cdot 103^{2}$ |
$3$ |
$39.7783361148$ |
$155.91023058157538$ |
|
|
|
$D_{4}$ (as 4T3) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$19.3862321404$ |
$0$ |
$103$ |
| 4.2.2577987.1 |
$x^{4} - x^{3} + 13 x - 37$ |
$4$ |
(2, 1) |
$-\,3^{5}\cdot 103^{2}$ |
$2$ |
$40.0700773473$ |
$76.05730150292834$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$406.471976095$ |
$1$ |
$103$ |
| 4.0.2673468.2 |
$x^{4} + 9 x^{2} + 252$ |
$4$ |
(0, 2) |
$2^{2}\cdot 3^{2}\cdot 7\cdot 103^{2}$ |
$4$ |
$40.4360521099$ |
$93.01612763386788$ |
|
|
|
$D_{4}$ (as 4T3) |
$[10]$ |
$[10]$ |
$2$ |
$1$ |
$8.6621866877$ |
$0$ |
$103$ |
| 4.0.2715904.1 |
$x^{4} + 104 x^{2} + 2601$ |
$4$ |
(0, 2) |
$2^{8}\cdot 103^{2}$ |
$2$ |
$40.5955662604$ |
$40.59556626036888$ |
✓ |
✓ |
|
$C_2^2$ (as 4T2) |
$[20]$ |
$[20]$ |
$2$ |
$1$ |
$13.0281757673$ |
$0$ |
$103$ |
| 4.0.2715904.2 |
$x^{4} + 10609$ |
$4$ |
(0, 2) |
$2^{8}\cdot 103^{2}$ |
$2$ |
$40.5955662604$ |
$40.59556626036888$ |
✓ |
✓ |
|
$C_2^2$ (as 4T2) |
$[20]$ |
$[20]$ |
$4$ |
$1$ |
$11.6874668344$ |
$0$ |
$103$ |
| 4.0.2768949.1 |
$x^{4} - x^{3} - x^{2} - 38 x + 208$ |
$4$ |
(0, 2) |
$3^{2}\cdot 29\cdot 103^{2}$ |
$3$ |
$40.7923513101$ |
$94.66255859631093$ |
|
|
|
$D_{4}$ (as 4T3) |
$[10]$ |
$[10]$ |
$2$ |
$1$ |
$15.6089792296$ |
$0$ |
$103$ |
| 4.0.2885648.1 |
$x^{4} - 2 x^{3} + 29 x^{2} - 28 x + 93$ |
$4$ |
(0, 2) |
$2^{4}\cdot 17\cdot 103^{2}$ |
$3$ |
$41.2155252029$ |
$83.68990381163071$ |
✓ |
|
|
$D_{4}$ (as 4T3) |
$[4]$ |
$[4]$ |
$2$ |
$1$ |
$26.0563515346$ |
$0$ |
$103$ |
| 4.0.2885648.2 |
$x^{4} + 13 x^{2} + 68$ |
$4$ |
(0, 2) |
$2^{4}\cdot 17\cdot 103^{2}$ |
$3$ |
$41.2155252029$ |
$83.68990381163071$ |
|
|
|
$D_{4}$ (as 4T3) |
$[20]$ |
$[20]$ |
$2$ |
$1$ |
$6.13749323561$ |
$0$ |
$103$ |
| 4.0.2885648.3 |
$x^{4} - 51 x^{2} - 206 x + 11285$ |
$4$ |
(0, 2) |
$2^{4}\cdot 17\cdot 103^{2}$ |
$3$ |
$41.2155252029$ |
$83.68990381163071$ |
|
|
|
$D_{4}$ (as 4T3) |
$[8]$ |
$[8]$ |
$4$ |
$1$ |
$9.27002322329$ |
$0$ |
$103$ |
| 4.2.2917475.1 |
$x^{4} - x^{3} - 26 x^{2} - 180 x - 7255$ |
$4$ |
(2, 1) |
$-\,5^{2}\cdot 11\cdot 103^{2}$ |
$3$ |
$41.3287039118$ |
$75.26619427073486$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$[2]$ |
$2$ |
$2$ |
$77.6613408436$ |
$1$ |
$103$ |
| 4.2.3182700.2 |
$x^{4} - x^{3} - 9 x^{2} + 69 x + 126$ |
$4$ |
(2, 1) |
$-\,2^{2}\cdot 3\cdot 5^{2}\cdot 103^{2}$ |
$4$ |
$42.2375701455$ |
$81.59168580314125$ |
|
|
|
$S_4$ (as 4T5) |
trivial |
$[2]$ |
$2$ |
$2$ |
$636.263506988$ |
$1$ |
$103$ |
| 4.2.3341835.3 |
$x^{4} + 13 x^{2} - 35$ |
$4$ |
(2, 1) |
$-\,3^{2}\cdot 5\cdot 7\cdot 103^{2}$ |
$4$ |
$42.755919508$ |
$103.99519219656263$ |
|
|
|
$D_{4}$ (as 4T3) |
$[3]$ |
$[6]$ |
$2$ |
$2$ |
$67.97363303$ |
$1$ |
$103$ |
| 4.2.3341835.4 |
$x^{4} - x^{3} - 48 x^{2} + 140 x + 133$ |
$4$ |
(2, 1) |
$-\,3^{2}\cdot 5\cdot 7\cdot 103^{2}$ |
$4$ |
$42.755919508$ |
$103.99519219656263$ |
|
|
|
$D_{4}$ (as 4T3) |
trivial |
$[2]$ |
$2$ |
$2$ |
$123.837678385$ |
$1$ |
$103$ |
| 4.0.3352444.2 |
$x^{4} - x^{3} - 14 x^{2} + 123 x + 503$ |
$4$ |
(0, 2) |
$2^{2}\cdot 79\cdot 103^{2}$ |
$3$ |
$42.7898124554$ |
$180.41064270158788$ |
|
|
|
$D_{4}$ (as 4T3) |
$[5]$ |
$[5]$ |
$2$ |
$1$ |
$14.4103148047$ |
$0$ |
$103$ |
