| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
| 30.0.457...771.1 |
x30 + 6x28 - x27 + 14x26 - x25 + 8x24 + 13x23 - 39x22 + 37x21 - 93x20 + 30x19 + 10x18 - 13x17 + 349x16 + 77x15 + 721x14 + 575x13 + 1026x12 + 1233x11 + 1137x10 + 993x9 + 501x8 - 41x7 - 253x6 - 186x5 - 58x4 + 6x3 + 14x2 + 6x + 1 |
$30$ |
[0,15] |
$-\,3^{20}\cdot 11^{27}$ |
$2$ |
$18.002559423165124$ |
|
|
not computed |
$C_{15}\times S_3$ (as 30T15) |
trivial |
$22$ |
$14$ |
$27376181.549941503$ |
| 30.0.131...536.1 |
x30 + 6x28 + 25x26 + 45x24 - 44x22 - 197x20 - 20x18 + 411x16 + 283x14 - 424x12 - 397x10 + 348x8 + 358x6 + 8x4 - 7x2 + 1 |
$30$ |
[0,15] |
$-\,2^{40}\cdot 11^{26}$ |
$2$ |
$20.13323926187899$ |
|
|
not computed |
$C_{10}\times S_3$ (as 30T12) |
trivial |
$4$ |
$14$ |
$18931497.119988322$ |
| 30.10.144...896.1 |
x30 - 15x28 + 104x26 - 482x24 + 1708x22 - 4753x20 + 10608x18 - 18925x16 + 26563x14 - 28460x12 + 22463x10 - 12716x8 + 5049x6 - 1331x4 + 198x2 - 11 |
$30$ |
[10,10] |
$2^{40}\cdot 11^{27}$ |
$2$ |
$21.808547634345086$ |
|
|
not computed |
$C_{10}\times S_3$ (as 30T12) |
trivial |
$2$ |
$19$ |
$397294072.2356694$ |
| 30.0.218...571.1 |
x30 - x29 - 7x28 + 10x27 + 7x26 - 19x25 + 56x24 - 38x23 - 238x22 + 196x21 + 1084x20 + 255x19 - 3219x18 - 4472x17 + 2252x16 + 12483x15 + 13641x14 + 1966x13 - 11281x12 - 13340x11 - 5077x10 + 3378x9 + 6156x8 + 4833x7 + 3411x6 + 3672x5 + 4671x4 + 4536x3 + 2997x2 + 1215x + 243 |
$30$ |
[0,15] |
$-\,3^{10}\cdot 7^{10}\cdot 11^{27}$ |
$3$ |
$23.877737944442764$ |
|
|
not computed |
$C_{10}\times S_3$ (as 30T12) |
trivial |
$22$ |
$14$ |
$2830009383.1065817$ |
| 30.0.107...171.1 |
x30 - x29 - 4x28 + 2x27 + 14x26 - 18x25 - 22x24 + 80x23 + 2x22 - 292x21 + 107x20 + 966x19 - 524x18 - 1689x17 + 1837x16 + 1003x15 - 6747x14 + 4493x13 + 13850x12 - 15662x11 - 11779x10 + 28372x9 - 4752x8 - 31522x7 + 29972x6 + 5164x5 - 25670x4 + 15150x3 + 3000x2 - 8125x + 3125 |
$30$ |
[0,15] |
$-\,11^{27}\cdot 31^{10}$ |
$2$ |
$27.18779466419903$ |
|
|
not computed |
$C_{15}\times S_3$ (as 30T15) |
trivial |
$22$ |
$14$ |
$10842704727.78492$ |
| 30.0.177...271.1 |
x30 - x29 + x28 - x27 + x26 - x25 + x24 - x23 + x22 - x21 + x20 - x19 + x18 - x17 + x16 - x15 + x14 - x13 + x12 - x11 + x10 - x9 + x8 - x7 + x6 - x5 + x4 - x3 + x2 - x + 1 |
$30$ |
[0,15] |
$-\,31^{29}$ |
$1$ |
$27.6471034373$ |
✓ |
✓ |
✓ |
$C_{30}$ (as 30T1) |
$[9]$ |
$62$ |
$14$ |
$4316173757.895952$ |
| 30.0.182...875.1 |
x30 - 10x27 - 54x25 + 90x24 + 315x23 + 15x22 - 240x21 + 504x20 - 4740x19 + 8375x18 - 14580x17 + 25140x16 - 34179x15 + 51465x14 - 61710x13 + 70215x12 - 67800x11 + 45276x10 - 22840x9 - 3240x8 + 16350x7 - 10730x6 + 4956x5 + 2280x4 - 4065x3 - 420x2 + 780x + 169 |
$30$ |
[0,15] |
$-\,3^{35}\cdot 5^{38}$ |
$2$ |
$27.669637490247258$ |
|
|
not computed |
$D_{30}$ (as 30T14) |
trivial |
$6$ |
$14$ |
$17149795938.655872$ |
| 30.10.531...753.1 |
x30 - 7x29 + 24x28 - 23x27 - 141x26 + 633x25 - 1481x24 + 2556x23 - 3432x22 + 2970x21 + 2520x20 - 16434x19 + 36814x18 - 58793x17 + 75906x16 - 86484x15 + 87441x14 - 74977x13 + 56249x12 - 35409x11 + 19416x10 - 7865x9 + 726x8 + 1323x7 - 1451x6 + 413x5 - 168x4 + 17x3 - 15x2 + x + 1 |
$30$ |
[10,10] |
$3^{15}\cdot 7^{10}\cdot 11^{27}$ |
$3$ |
$28.6756579034896$ |
|
|
not computed |
$C_{10}\times S_3$ (as 30T12) |
trivial |
$2$ |
$19$ |
$26520700757.33144$ |
| 30.2.605...125.1 |
x30 - 4x29 - 4x28 + 32x27 + 29x26 - 207x25 - 80x24 + 808x23 + 324x22 - 2807x21 - 784x20 + 6744x19 + 2549x18 - 11743x17 - 5231x16 + 15441x15 + 10445x14 - 10233x13 - 7776x12 + 6706x11 + 5598x10 - 2410x9 - 2278x8 + 1045x7 + 940x6 - 185x5 - 176x4 + 44x3 + 30x2 - 6x - 1 |
$30$ |
[2,14] |
$5^{15}\cdot 239^{14}$ |
$2$ |
$28.80076493748214$ |
|
|
not computed |
$D_{30}$ (as 30T14) |
trivial |
$2$ |
$15$ |
$5581738694.683278$ |
| 30.0.141...987.1 |
x30 - 5x29 + 14x28 - 37x27 + 83x26 - 152x25 + 241x24 - 335x23 + 465x22 - 620x21 + 812x20 - 1084x19 + 1348x18 - 1578x17 + 1736x16 - 1826x15 + 1986x14 - 2009x13 + 2111x12 - 2179x11 + 1810x10 - 1551x9 + 1376x8 - 959x7 + 887x6 - 765x5 + 462x4 - 285x3 + 146x2 - 13x + 1 |
$30$ |
[0,15] |
$-\,3^{15}\cdot 439^{14}$ |
$2$ |
$29.628573118259904$ |
|
|
|
$D_{30}$ (as 30T14) |
$[2]$ |
$6$ |
$14$ |
$18103283853.50697$ |
| 30.0.203...531.1 |
x30 - x + 1 |
$30$ |
[0,15] |
$-\,7\cdot 4547\cdot 625861750823\cdot 40306090892659\cdot 253230129277627$ |
$5$ |
$29.9874531212$ |
|
|
✓ |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$14$ |
$11086740597.223595$ |
| 30.2.208...469.1 |
x30 - x - 1 |
$30$ |
[2,14] |
$4421\cdot 22659339443160463\cdot 2080906233684319160584903$ |
$3$ |
$30.0123965237$ |
|
|
✓ |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$15$ |
$12534500381.926157$ |
| 30.0.104...371.1 |
x30 - x29 + 3x28 - 4x27 + 9x26 - 14x25 + 28x24 - 47x23 + 89x22 - 155x21 + 286x20 + 132x19 + 285x18 + 265x17 + 437x16 + 378x15 + 761x14 + 432x13 + 1468x12 + 157x11 + 3211x10 - 1429x9 + 636x8 - 283x7 + 126x6 - 56x5 + 25x4 - 11x3 + 5x2 - 2x + 1 |
$30$ |
[0,15] |
$-\,7^{20}\cdot 11^{27}$ |
$2$ |
$31.670295092$ |
✓ |
✓ |
not computed |
$C_{30}$ (as 30T1) |
$[2, 2, 2, 2]$ |
$22$ |
$14$ |
$4697581952.048968$ |
| 30.0.132...687.1 |
x30 - x29 + 5x28 - 6x27 + 20x26 - 27x25 + 75x24 - 46x23 + 211x22 - 109x21 + 617x20 - 357x19 + 1911x18 - 1372x17 + 2909x16 - 2210x15 + 4354x14 - 2262x13 + 5693x12 + 2042x11 + 3092x10 + 1302x9 + 2375x8 + 290x7 + 1798x6 - 511x5 + 146x4 - 41x3 + 12x2 - 3x + 1 |
$30$ |
[0,15] |
$-\,7^{25}\cdot 11^{24}$ |
$2$ |
$34.4637486944$ |
✓ |
✓ |
not computed |
$C_{30}$ (as 30T1) |
$[2, 2, 2, 10]$ |
$14$ |
$14$ |
$4697581952.048968$ |
| 30.2.140...000.1 |
x30 - x29 + 11x28 + 4x27 + 44x26 - 6x25 - 74x24 - 446x23 - 1543x22 + 183x21 - 1721x20 + 7116x19 + 11884x18 - 3168x17 + 7664x16 - 18756x15 + 17109x14 - 3363x13 - 2431x12 + 11594x11 - 15080x10 + 6868x9 + 3884x8 - 3768x7 + 2512x6 - 1864x5 - 1696x4 + 656x3 + 448x2 + 16x - 16 |
$30$ |
[2,14] |
$2^{20}\cdot 5^{15}\cdot 131^{14}$ |
$3$ |
$34.53278493432046$ |
|
|
|
$D_{30}$ (as 30T14) |
$[2]$ |
$2$ |
$15$ |
$145673548066.95038$ |
| 30.0.290...763.1 |
x30 - 4x27 + 47x24 + 4x21 + 1159x18 - 1525x15 + 4898x12 + 2458x9 + 1824x6 - 42x3 + 1 |
$30$ |
[0,15] |
$-\,3^{45}\cdot 11^{24}$ |
$2$ |
$35.3831122505$ |
✓ |
✓ |
not computed |
$C_{30}$ (as 30T1) |
$[31]$ |
$18$ |
$14$ |
$15853905121.091976$ |
| 30.2.698...512.1 |
x30 - 16x28 + 152x26 - 960x24 + 4656x22 - 18272x20 + 59264x18 - 161280x16 + 368896x14 - 701952x12 + 1121280x10 - 1376256x8 + 1417216x6 - 884736x4 + 524288x2 - 32768 |
$30$ |
[2,14] |
$2^{45}\cdot 239^{14}$ |
$2$ |
$36.43040622302421$ |
|
|
not computed |
$D_{30}$ (as 30T14) |
not computed |
$2$ |
$15$ |
$$ |
| 30.0.159...171.1 |
x30 + 3x28 - x27 + 9x26 - 6x25 + 28x24 - 27x23 + 90x22 - 109x21 + 297x20 + 507x19 + 1000x18 + 1224x17 + 2493x16 + 2672x15 + 6255x14 + 5523x13 + 16093x12 + 10314x11 + 42756x10 + 14849x9 + 5157x8 + 1791x7 + 622x6 + 216x5 + 75x4 + 26x3 + 9x2 + 3x + 1 |
$30$ |
[0,15] |
$-\,3^{40}\cdot 11^{27}$ |
$2$ |
$37.4468326297$ |
✓ |
✓ |
not computed |
$C_{30}$ (as 30T1) |
$[93]$ |
$22$ |
$14$ |
$15853905121.091976$ |
| 30.2.301...125.1 |
x30 - 5x29 + 8x28 + 19x27 - 63x26 - 52x25 + 265x24 - 211x23 - 393x22 + 858x21 - 86x20 - 2380x19 + 4186x18 + 8272x17 - 3336x16 - 13036x15 + 7176x14 + 23259x13 + 6583x12 - 9115x11 - 7328x10 + 1279x9 + 4440x8 + 2429x7 - 349x6 - 1189x5 - 88x4 + 271x3 + 100x2 - 13x - 1 |
$30$ |
[2,14] |
$5^{15}\cdot 439^{14}$ |
$2$ |
$38.25032341963645$ |
|
|
|
$D_{30}$ (as 30T14) |
$[2]$ |
$2$ |
$15$ |
$748323688575.9082$ |
| 30.2.812...137.1 |
x30 - 9x29 + 29x28 - 62x27 + 140x26 - 289x25 + 749x24 - 2505x23 + 6556x22 - 13979x21 + 24020x20 - 33363x19 + 38542x18 - 41923x17 + 47672x16 - 60161x15 + 70650x14 - 64907x13 + 32243x12 + 11892x11 - 39347x10 + 39493x9 - 24068x8 + 9526x7 + 164x6 - 4686x5 + 4431x4 - 2269x3 + 729x2 - 213x + 43 |
$30$ |
[2,14] |
$17^{15}\cdot 127^{14}$ |
$2$ |
$39.53661926232569$ |
|
|
not computed |
$D_{30}$ (as 30T14) |
trivial |
$2$ |
$15$ |
$1232398776399.036$ |
| 30.0.893...671.1 |
x30 - 3x29 - 5x28 + 23x27 - 7x26 - 43x25 + 380x24 - 1004x23 - 505x22 + 4147x21 - 3960x20 + 145x19 + 33797x18 - 104422x17 + 76694x16 + 164546x15 - 470105x14 + 125016x13 + 1685293x12 - 1720079x11 - 1513677x10 - 5549753x9 + 23270864x8 - 21911244x7 + 5984424x6 - 15339818x5 + 45492605x4 - 53109297x3 + 35921397x2 - 13035410x + 2348809 |
$30$ |
[0,15] |
$-\,3^{15}\cdot 7^{15}\cdot 11^{27}$ |
$3$ |
$39.66094555677728$ |
|
✓ |
not computed |
$C_5\times S_3$ (as 30T2) |
$[2, 22]$ |
$2$ |
$14$ |
$9800307802.95059$ |
| 30.0.109...375.1 |
x30 - 7x29 + 48x28 - 257x27 + 1124x26 - 4108x25 + 12894x24 - 35106x23 + 82734x22 - 166828x21 + 288975x20 - 424231x19 + 515389x18 - 443551x17 + 184757x16 + 79835x15 - 29816x14 - 348911x13 + 993639x12 - 2148173x11 + 1765791x10 + 384577x9 - 1489368x8 + 2068027x7 - 1731374x6 - 444980x5 + 2213182x4 - 1190713x3 - 21588x2 + 127306x + 52081 |
$30$ |
[0,15] |
$-\,3^{15}\cdot 5^{25}\cdot 47^{14}$ |
$3$ |
$39.93447365182815$ |
|
|
not computed |
$D_{30}$ (as 30T14) |
not computed |
$2$ |
$14$ |
$$ |
| 30.2.110...000.1 |
x30 - 3x29 + 21x28 - 42x27 + 225x26 - 359x25 + 651x24 - 2808x23 - 1822x22 - 11536x21 - 10414x20 - 26496x19 - 25330x18 - 33066x17 - 28312x16 - 19700x15 - 18200x14 + 6446x13 - 8210x12 + 13412x11 - 5750x10 + 6200x9 - 4422x8 + 1276x7 - 711x6 + 161x5 - 113x4 - 42x3 + 3x2 - 3x - 1 |
$30$ |
[2,14] |
$2^{20}\cdot 5^{15}\cdot 179^{14}$ |
$3$ |
$39.94873948168138$ |
|
|
|
$D_{30}$ (as 30T14) |
$[3, 3]$ |
$2$ |
$15$ |
$383760855207.4596$ |
| 30.0.337...000.1 |
x30 - 2x15 + 2 |
$30$ |
[0,15] |
$-\,2^{44}\cdot 3^{30}\cdot 5^{30}$ |
$3$ |
$41.457386399$ |
|
|
✓ |
$C_2\times S_3\times F_5$ (as 30T51) |
trivial |
$4$ |
$14$ |
$4813633304417.372$ |
| 30.0.607...847.1 |
x30 - 6x29 + 38x28 - 178x27 + 694x26 - 2325x25 + 6840x24 - 17890x23 + 42428x22 - 92148x21 + 185209x20 - 348333x19 + 617591x18 - 1037914x17 + 1659175x16 - 2519432x15 + 3620042x14 - 4892313x13 + 6168845x12 - 7195888x11 + 7698034x10 - 7475970x9 + 6524456x8 - 5050948x7 + 3416179x6 - 1976201x5 + 950326x4 - 363451x3 + 103267x2 - 19350x + 1849 |
$30$ |
[0,15] |
$-\,17^{14}\cdot 127^{15}$ |
$2$ |
$42.277700430231675$ |
|
|
not computed |
$D_{30}$ (as 30T14) |
$[5]$ |
$2$ |
$14$ |
$588337897727.5111$ |
| 30.0.822...187.1 |
x30 - x29 + 15x28 - 12x27 + 131x26 - 92x25 + 755x24 - 449x23 + 3202x22 - 1648x21 + 10173x20 - 4368x19 + 24856x18 - 8980x17 + 46255x16 - 13276x15 + 65515x14 - 15154x13 + 68312x12 - 11198x11 + 51310x10 - 6592x9 + 25719x8 - 1518x7 + 8148x6 - 588x5 + 1330x4 + 56x3 + 92x2 - 8x + 1 |
$30$ |
[0,15] |
$-\,3^{15}\cdot 31^{28}$ |
$2$ |
$42.7069157518$ |
✓ |
✓ |
not computed |
$C_{30}$ (as 30T1) |
$[755]$ |
$6$ |
$14$ |
$4316173757.895952$ |
| 30.0.112...787.1 |
x30 - x29 + 23x28 - 12x27 + 335x26 - 144x25 + 2773x24 - 863x23 + 16295x22 - 4775x21 + 62257x20 - 15750x19 + 170334x18 - 52802x17 + 293956x16 - 111720x15 + 369164x14 - 135917x13 + 276687x12 - 78965x11 + 139349x10 - 31906x9 + 42847x8 - 4541x7 + 8009x6 - 477x5 + 1036x4 + 2x3 + 63x2 - 6x + 1 |
$30$ |
[0,15] |
$-\,3^{15}\cdot 7^{20}\cdot 11^{24}$ |
$3$ |
$43.1592082322$ |
✓ |
✓ |
not computed |
$C_{30}$ (as 30T1) |
$[2, 2, 2, 122]$ |
$6$ |
$14$ |
$4697581952.048968$ |
| 30.2.119...125.1 |
x30 - 5x29 + 11x28 - 4x27 - 19x26 + 37x25 + 129x24 - 1314x23 + 6565x22 - 21133x21 + 56331x20 - 116407x19 + 192164x18 - 249788x17 + 240591x16 - 123362x15 + 65684x14 - 91823x13 + 137991x12 - 356197x11 - 307772x10 + 22452x9 + 102955x8 + 347102x7 + 442668x6 - 57105x5 - 325253x4 - 81893x3 + 80109x2 + 46065x + 6845 |
$30$ |
[2,14] |
$5^{15}\cdot 571^{14}$ |
$2$ |
$43.2429373044137$ |
|
|
|
$D_{30}$ (as 30T14) |
$[5]$ |
$2$ |
$15$ |
$9816173974474.957$ |
| 30.0.131...875.1 |
x30 + 3 |
$30$ |
[0,15] |
$-\,3^{59}\cdot 5^{30}$ |
$2$ |
$43.3818903138$ |
|
|
|
$S_3\times F_5$ (as 30T32) |
trivial |
$6$ |
$14$ |
$19051205214911.367$ |
| 30.30.175...397.1 |
x30 - x29 - 30x28 + 29x27 + 405x26 - 377x25 - 3250x24 + 2901x23 + 17249x22 - 14697x21 - 63734x20 + 51590x19 + 168035x18 - 128611x17 - 318629x16 + 229651x15 + 432159x14 - 292608x13 - 411241x12 + 261924x11 + 264472x10 - 159873x9 - 107406x8 + 63143x7 + 24051x6 - 14609x5 - 2010x4 + 1562x3 - 72x2 - 24x + 1 |
$30$ |
[30,0] |
$7^{25}\cdot 11^{27}$ |
$2$ |
$43.8027909818$ |
|
✓ |
✓ |
$C_{30}$ (as 30T1) |
trivial |
$2$ |
$29$ |
$864355592506536.0$ |
| 30.2.305...688.1 |
x30 - 24x28 + 342x26 - 3240x24 + 23571x22 - 138753x20 + 675054x18 - 2755620x16 + 9454401x14 - 26985393x12 + 64658655x10 - 119042784x8 + 183878586x6 - 172186884x4 + 153055008x2 - 14348907 |
$30$ |
[2,14] |
$2^{30}\cdot 3^{15}\cdot 239^{14}$ |
$3$ |
$44.61795318436113$ |
|
|
not computed |
$D_{30}$ (as 30T14) |
not computed |
$2$ |
$15$ |
$$ |
| 30.0.380...059.1 |
x30 - 6x29 + 25x28 - 72x27 + 234x26 - 520x25 + 1111x24 - 2189x23 + 3903x22 - 4957x21 + 4623x20 - 10333x19 + 8702x18 + 8683x17 - 6137x16 + 9595x15 - 28557x14 + 23199x13 - 20007x12 + 4195x11 + 12906x10 - 27137x9 + 36711x8 - 24629x7 + 24367x6 - 23558x5 + 11264x4 + 26568x3 - 14144x2 - 4128x + 4928 |
$30$ |
[0,15] |
$-\,11^{12}\cdot 19^{29}$ |
$2$ |
$44.94543157691572$ |
|
|
|
$C_6\times D_5$ (as 30T5) |
$[11]$ |
$2$ |
$14$ |
$2589248825821.8447$ |
| 30.30.387...553.1 |
x30 - 30x28 - x27 + 405x26 + 27x25 - 3250x24 - 324x23 + 17250x22 + 2278x21 - 63756x20 - 10416x19 + 168244x18 + 32508x17 - 319752x16 - 70720x15 + 435915x14 + 107592x13 - 419353x12 - 113139x11 + 275835x10 + 79936x9 - 117504x8 - 36027x7 + 29442x6 + 9423x5 - 3555x4 - 1173x3 + 108x2 + 36x + 1 |
$30$ |
[30,0] |
$3^{45}\cdot 11^{27}$ |
$2$ |
$44.9712851592$ |
|
✓ |
✓ |
$C_{30}$ (as 30T1) |
trivial |
$2$ |
$29$ |
$1458908175124897.5$ |
| 30.2.515...625.1 |
x30 - 10x29 + 36x28 - 34x27 - 129x26 + 673x25 - 2345x24 + 3400x23 + 8195x22 - 23985x21 - 13829x20 + 36240x19 + 94321x18 + 102411x17 + 62946x16 + 325659x15 + 1299805x14 + 3826146x13 + 7335516x12 + 9580506x11 + 8499204x10 + 5247290x9 + 1937111x8 + 388946x7 - 47819x6 - 74039x5 - 43685x4 - 5057x3 + 3493x2 + 123x + 169 |
$30$ |
[2,14] |
$3^{15}\cdot 5^{25}\cdot 47^{15}$ |
$3$ |
$45.40300106204512$ |
|
|
not computed |
$D_{30}$ (as 30T14) |
not computed |
$2$ |
$15$ |
$$ |
| 30.0.675...203.1 |
x30 - x29 + 12x28 - 45x27 + 210x26 - 744x25 + 2465x24 - 6965x23 + 19758x22 - 48686x21 + 121619x20 - 306546x19 + 810012x18 - 2087415x17 + 5002572x16 - 11311375x15 + 24424402x14 - 49257771x13 + 88022499x12 - 134078913x11 + 172501038x10 - 188691174x9 + 176841252x8 - 141293241x7 + 95362353x6 - 55362204x5 + 28414476x4 - 12173571x3 + 3774762x2 - 708588x + 59049 |
$30$ |
[0,15] |
$-\,3^{15}\cdot 1117^{14}$ |
$2$ |
$45.81265290342043$ |
|
|
|
$D_{30}$ (as 30T14) |
trivial |
$6$ |
$14$ |
$3232250515402658.0$ |
| 30.2.114...125.1 |
x30 - 3x29 + 9x28 + 14x27 - 113x26 + 370x25 - 643x24 - 15x23 + 3880x22 - 13302x21 + 28770x20 - 44390x19 + 53641x18 - 46319x17 + 35868x16 - 26390x15 + 12095x14 + 43878x13 + 45313x12 - 6914x11 - 59831x10 - 94496x9 - 64150x8 - 2932x7 + 54993x6 + 69070x5 + 52989x4 + 26576x3 + 8569x2 + 484x - 121 |
$30$ |
[2,14] |
$5^{15}\cdot 11^{14}\cdot 61^{14}$ |
$3$ |
$46.62535787186501$ |
|
|
|
$D_{30}$ (as 30T14) |
$[2]$ |
$2$ |
$15$ |
$16637349953072.254$ |
| 30.0.214...923.1 |
x30 - 6x29 + 7x28 + 64x27 - 269x26 + 169x25 + 1697x24 - 5426x23 + 2993x22 + 23602x21 - 68143x20 + 32587x19 + 255113x18 - 722972x17 + 638195x16 + 912175x15 - 3578530x14 + 6806701x13 - 13186196x12 + 20272003x11 - 4641245x10 - 65229024x9 + 170166391x8 - 258098865x7 + 369027093x6 - 495862722x5 + 471214449x4 - 297134325x3 + 130881204x2 - 35973639x + 5861241 |
$30$ |
[0,15] |
$-\,3^{15}\cdot 1213^{14}$ |
$2$ |
$47.609724432602746$ |
|
|
|
$D_{30}$ (as 30T14) |
$[7]$ |
$6$ |
$14$ |
$828216417792195.4$ |
| 30.0.249...171.1 |
x30 - x29 + 5x28 - 10x27 + 31x26 - 76x25 + 210x24 - 545x23 + 1461x22 - 3851x21 + 10240x20 + 18326x19 + 26485x18 + 36579x17 + 51035x16 + 68796x15 + 98765x14 + 125384x13 + 200880x12 + 201891x11 + 476245x10 + 130439x9 + 35726x8 + 9785x7 + 2680x6 + 734x5 + 201x4 + 55x3 + 15x2 + 4x + 1 |
$30$ |
[0,15] |
$-\,11^{27}\cdot 13^{20}$ |
$2$ |
$47.8500414346$ |
✓ |
✓ |
not computed |
$C_{30}$ (as 30T1) |
$[427]$ |
$22$ |
$14$ |
$85915831770.81862$ |
| 30.30.254...797.1 |
x30 - x29 - 30x28 + 30x27 + 404x26 - 404x25 - 3223x24 + 3223x23 + 16927x22 - 16927x21 - 61503x20 + 61503x19 + 158101x18 - 158101x17 - 288950x16 + 288950x15 + 371908x14 - 371908x13 - 329002x12 + 329002x11 + 191674x10 - 191674x9 - 68664x8 + 68664x7 + 13548x6 - 13548x5 - 1208x4 + 1208x3 + 32x2 - 32x + 1 |
$30$ |
[30,0] |
$3^{15}\cdot 31^{29}$ |
$2$ |
$47.8861878355$ |
|
✓ |
✓ |
$C_{30}$ (as 30T1) |
trivial |
$2$ |
$29$ |
$3165460564789336.0$ |
| 30.2.347...912.1 |
x30 - 6x28 + 68x26 - 536x24 + 1904x22 - 4192x20 + 2240x18 + 23936x16 - 82432x14 + 138752x12 + 235520x10 - 1073152x8 + 2486272x6 - 2449408x4 + 2015232x2 - 32768 |
$30$ |
[2,14] |
$2^{45}\cdot 439^{14}$ |
$2$ |
$48.38325729765269$ |
|
|
|
$D_{30}$ (as 30T14) |
not computed |
$2$ |
$15$ |
$$ |
| 30.2.553...125.1 |
x30 - 5x29 + 2x28 + 21x27 + 40x26 - 46x25 + 39x24 - 296x23 - 1612x22 - 2561x21 + 962x20 + 4669x19 + 19325x18 + 55780x17 + 98099x16 + 110152x15 + 94739x14 + 50734x13 + 40862x12 + 44242x11 + 25838x10 + 20656x9 + 3131x8 + 2527x7 + 6736x6 + 1305x5 + 3768x4 - 512x3 + 661x2 - 25x - 1 |
$30$ |
[2,14] |
$5^{15}\cdot 751^{14}$ |
$2$ |
$49.14171468572467$ |
|
|
|
$D_{30}$ (as 30T14) |
$[4]$ |
$2$ |
$15$ |
$26934148162576.97$ |
| 30.0.615...784.1 |
x30 + 29x28 + 378x26 + 2925x24 + 14950x22 + 53130x20 + 134596x18 + 245157x16 + 319770x14 + 293930x12 + 184756x10 + 75582x8 + 18564x6 + 2380x4 + 120x2 + 1 |
$30$ |
[0,15] |
$-\,2^{30}\cdot 31^{28}$ |
$2$ |
$49.3136986111$ |
✓ |
✓ |
✓ |
$C_{30}$ (as 30T1) |
$[2, 2542]$ |
$4$ |
$14$ |
$4316173757.895952$ |
| 30.0.843...984.1 |
x30 + 45x28 + 850x26 + 8863x24 + 56474x22 + 230106x20 + 610963x18 + 1061766x16 + 1203495x14 + 883132x12 + 414061x10 + 121105x8 + 21162x6 + 2035x4 + 90x2 + 1 |
$30$ |
[0,15] |
$-\,2^{30}\cdot 7^{20}\cdot 11^{24}$ |
$3$ |
$49.8359609817$ |
✓ |
✓ |
not computed |
$C_{30}$ (as 30T1) |
$[2, 2, 2, 362]$ |
$4$ |
$14$ |
$4697581952.048968$ |
| 30.0.266...291.1 |
x30 - 5x29 + 23x28 - 62x27 + 198x26 - 367x25 + 397x24 + 1188x23 - 7770x22 + 27186x21 - 70571x20 + 106780x19 + 113195x18 - 1691169x17 + 8127778x16 - 29421234x15 + 90493414x14 - 242325966x13 + 570478488x12 - 1182396448x11 + 2168615679x10 - 3480425904x9 + 4808261059x8 - 5571332106x7 + 5293750647x6 - 4028704993x5 + 2404982206x4 - 1088744723x3 + 357808383x2 - 76833878x + 8961073 |
$30$ |
[0,15] |
$-\,11^{15}\cdot 19^{28}$ |
$2$ |
$51.784490002099986$ |
|
✓ |
|
$C_3\times D_5$ (as 30T4) |
$[2, 2]$ |
$2$ |
$14$ |
$22790934759037.23$ |
| 30.2.275...081.1 |
x30 - 4x - 1 |
$30$ |
[2,14] |
$1657\cdot 56091358577718162989\cdot 29663564839667553243668426797$ |
$3$ |
$51.8419577315$ |
|
|
not computed |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$15$ |
$72802108759548.89$ |
| 30.2.275...456.1 |
x30 - 2x - 1 |
$30$ |
[2,14] |
$2^{31}\cdot 309259\cdot 14808181703558627\cdot 280341823437737461079$ |
$4$ |
$51.8419578606$ |
|
|
✓ |
$S_{30}$ (as 30T5712) |
trivial |
$2$ |
$15$ |
$90634957909906.56$ |
| 30.2.493...181.1 |
x30 - 9x29 + 51x28 - 225x27 + 938x26 - 3065x25 + 9027x24 - 23897x23 + 55855x22 - 110855x21 + 206236x20 - 276419x19 + 363187x18 - 228654x17 - 26451x16 + 1021780x15 - 676090x14 + 4072978x13 + 297137x12 + 7819653x11 - 19045735x10 + 54647605x9 - 99924364x8 + 139085676x7 - 209111579x6 + 87062190x5 - 13968112x4 - 6858710x3 - 581573x2 - 428582x - 60395 |
$30$ |
[2,14] |
$3^{15}\cdot 7^{25}\cdot 47^{14}$ |
$3$ |
$52.85929028008203$ |
|
|
|
$D_{30}$ (as 30T14) |
not computed |
$2$ |
$15$ |
$$ |
| 30.30.595...341.1 |
x30 - x29 - 29x28 + 28x27 + 378x26 - 351x25 - 2925x24 + 2600x23 + 14950x22 - 12650x21 - 53130x20 + 42504x19 + 134596x18 - 100947x17 - 245157x16 + 170544x15 + 319770x14 - 203490x13 - 293930x12 + 167960x11 + 184756x10 - 92378x9 - 75582x8 + 31824x7 + 18564x6 - 6188x5 - 2380x4 + 560x3 + 120x2 - 15x - 1 |
$30$ |
[30,0] |
$61^{29}$ |
$1$ |
$53.1886344501$ |
|
✓ |
✓ |
$C_{30}$ (as 30T1) |
trivial |
$2$ |
$29$ |
$17190292874679612$ |
| 30.0.885...327.1 |
x30 - 4x29 - 32x28 + 92x27 + 588x26 - 752x25 - 6717x24 - 805x23 + 44049x22 + 54263x21 - 93757x20 - 350454x19 - 591742x18 + 307201x17 + 3600412x16 + 5669890x15 - 632841x14 - 17605194x13 - 34361042x12 - 23087625x11 + 45815379x10 + 119941341x9 + 85868062x8 - 30516460x7 - 62011703x6 + 46150369x5 + 155790202x4 + 147686157x3 + 67768188x2 + 10788948x + 751689 |
$30$ |
[0,15] |
$-\,3^{14}\cdot 7^{25}\cdot 53^{14}$ |
$3$ |
$53.8973018694987$ |
|
|
|
$D_{30}$ (as 30T14) |
$[3]$ |
$2$ |
$14$ |
$44958053496730.96$ |
| 30.30.150...497.1 |
x30 - x29 - 52x28 + 51x27 + 1142x26 - 1092x25 - 13898x24 + 12856x23 + 103478x22 - 91664x21 - 491678x20 + 412467x19 + 1512708x18 - 1191563x17 - 3007832x16 + 2225799x15 + 3819257x14 - 2692049x13 - 3042474x12 + 2079355x11 + 1471733x10 - 992749x9 - 403229x8 + 274849x7 + 52970x6 - 38754x5 - 1790x4 + 2057x3 - 72x2 - 24x + 1 |
$30$ |
[30,0] |
$3^{15}\cdot 7^{20}\cdot 11^{27}$ |
$3$ |
$54.8545601901$ |
|
✓ |
not computed |
$C_{30}$ (as 30T1) |
trivial |
$2$ |
$29$ |
$25852981457107600$ |
