| 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 |
| 19.1.272...391.1 |
$x^{19} - x^{18} + 2 x^{17} - 5 x^{16} + 8 x^{15} - 14 x^{14} + 13 x^{13} - 10 x^{12} - x^{11} + 9 x^{10} - 18 x^{9} + 25 x^{8} - 10 x^{7} - 4 x^{6} + 38 x^{5} - 42 x^{4} + 37 x^{3} - 16 x^{2} + 4 x + 1$ |
$19$ |
[1,9] |
$-\,311^{9}$ |
$1$ |
$15.1628639032$ |
$17.635192088548397$ |
|
|
? |
$D_{19}$ (as 19T2) |
trivial |
$2$ |
$9$ |
$2166.17030371$ |
| 19.1.990...639.1 |
$x^{19} - 2 x^{18} + 2 x^{17} - 2 x^{16} - 3 x^{15} + 14 x^{14} - 7 x^{13} - 22 x^{12} + 30 x^{11} - 9 x^{10} + 5 x^{9} - 2 x^{8} - 51 x^{7} + 90 x^{6} - 19 x^{5} - 91 x^{4} + 113 x^{3} - 59 x^{2} + 14 x - 1$ |
$19$ |
[1,9] |
$-\,359^{9}$ |
$1$ |
$16.2296030083$ |
$18.947295321496416$ |
|
|
? |
$D_{19}$ (as 19T2) |
trivial |
$2$ |
$9$ |
$4771.45184867$ |
| 19.1.193...555.1 |
$x^{19} - x - 1$ |
$19$ |
[1,9] |
$-\,5\cdot 659\cdot 588489604729898953429$ |
$3$ |
$18.9799223948$ |
$1392506103248.7495$ |
|
|
✓ |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$9$ |
$31427.0586812$ |
| 19.1.201...403.1 |
$x^{19} + x - 1$ |
$19$ |
[1,9] |
$-\,149\cdot 2063\cdot 6564253087266573169$ |
$3$ |
$19.0197028269$ |
$1420480926917.222$ |
|
|
✓ |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$9$ |
$40842.9289744$ |
| 19.1.756...064.1 |
$x^{19} - 2 x^{18} + 8 x^{17} - 12 x^{16} + 43 x^{15} - 74 x^{14} + 108 x^{13} - 18 x^{12} - 25 x^{11} + 338 x^{9} - 70 x^{8} - 264 x^{7} - 128 x^{6} + 120 x^{5} + 98 x^{4} + 43 x^{3} - 22 x^{2} - 31 x - 8$ |
$19$ |
[1,9] |
$-\,2^{18}\cdot 19^{16}$ |
$2$ |
$23.0160848178$ |
$27.39680150407798$ |
|
|
? |
$F_{19}$ (as 19T6) |
trivial |
$2$ |
$9$ |
$540383.098056$ |
| 19.3.146...972.1 |
$x^{19} - 2 x^{18} + 7 x^{16} - 10 x^{15} - x^{14} + 19 x^{13} - 19 x^{12} - 9 x^{11} + 33 x^{10} - 19 x^{9} - 20 x^{8} + 32 x^{7} - 9 x^{6} - 17 x^{5} + 17 x^{4} - 3 x^{3} - 5 x^{2} + 4 x - 1$ |
$19$ |
[3,8] |
$2^{2}\cdot 139\cdot 126311\cdot 1021043\cdot 2043393285469$ |
$5$ |
$23.8316032998$ |
|
|
|
✓ |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$10$ |
$737873.586636$ |
| 19.1.467...879.1 |
$x^{19} - 5 x^{18} + 10 x^{17} - 5 x^{16} + 9 x^{15} - 42 x^{14} + 51 x^{13} - 6 x^{12} - 23 x^{11} + 4 x^{10} - 29 x^{9} + 112 x^{8} - 63 x^{7} - 147 x^{6} + 183 x^{5} + 15 x^{4} - 77 x^{3} - 17 x^{2} + 37 x + 1$ |
$19$ |
[1,9] |
$-\,919^{9}$ |
$1$ |
$25.3323668457$ |
$30.315012782448235$ |
|
|
|
$D_{19}$ (as 19T2) |
trivial |
$2$ |
$9$ |
$1152808.1284$ |
| 19.1.714...419.1 |
$x^{19} + 19 x^{15} - 19 x^{14} - 19 x^{13} + 171 x^{12} + 19 x^{11} - 266 x^{10} + 19 x^{9} + 475 x^{8} + 741 x^{7} + 437 x^{6} + 38 x^{5} - 38 x^{4} - 19 x^{3} + 1$ |
$19$ |
[1,9] |
$-\,19^{21}$ |
$1$ |
$25.9035473939$ |
$29.474396900751216$ |
|
|
? |
$C_{19}:C_{6}$ (as 19T4) |
trivial |
$2$ |
$9$ |
$1437945.22979$ |
| 19.1.173...823.1 |
$x^{19} + 9 x^{17} - 10 x^{16} + 8 x^{15} - 45 x^{14} + 39 x^{13} + 7 x^{12} + 42 x^{11} - 36 x^{10} - 60 x^{9} + 9 x^{8} + 55 x^{7} + 63 x^{6} + 15 x^{5} - 88 x^{4} - 7 x^{3} + 27 x^{2} + 51 x + 1$ |
$19$ |
[1,9] |
$-\,1063^{9}$ |
$1$ |
$27.140698466$ |
$32.60368077380221$ |
|
|
|
$D_{19}$ (as 19T2) |
trivial |
$2$ |
$9$ |
$2724154.30052$ |
| 19.1.512...799.1 |
$x^{19} - 3 x^{18} + 17 x^{17} - 47 x^{16} + 135 x^{15} - 310 x^{14} + 709 x^{13} - 1319 x^{12} + 2423 x^{11} - 3757 x^{10} + 5497 x^{9} - 6561 x^{8} + 7142 x^{7} - 5699 x^{6} + 4212 x^{5} - 1490 x^{4} + 482 x^{3} + 408 x^{2} - 210 x + 49$ |
$19$ |
[1,9] |
$-\,11^{9}\cdot 109^{9}$ |
$2$ |
$28.7334671769$ |
$34.62657938636157$ |
|
|
? |
$D_{19}$ (as 19T2) |
trivial |
$2$ |
$9$ |
$2481320.5796$ |
| 19.3.787...824.1 |
$x^{19} - 2 x^{18} + 7 x^{16} - 10 x^{15} - x^{14} + 19 x^{13} - 19 x^{12} - 9 x^{11} + 33 x^{10} - 19 x^{9} - 20 x^{8} + 33 x^{7} - 9 x^{6} - 18 x^{5} + 17 x^{4} - 3 x^{3} - 5 x^{2} + 4 x - 1$ |
$19$ |
[3,8] |
$2^{8}\cdot 317\cdot 25373\cdot 137363\cdot 27854432176313$ |
$5$ |
$29.3922902441$ |
$13978832686367.559$ |
|
|
? |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$10$ |
$6223827.226$ |
| 19.1.206...091.1 |
$x^{19} + 2 x - 1$ |
$19$ |
[1,9] |
$-\,7\cdot 233\cdot 12649189464522827348824661$ |
$3$ |
$30.9198742421$ |
$143634355279775.34$ |
|
|
✓ |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$9$ |
$6403224.03446$ |
| 19.1.223...888.1 |
$x^{19} + 4 x - 4$ |
$19$ |
[1,9] |
$-\,2^{18}\cdot 1699471\cdot 109607929\cdot 458633653$ |
$4$ |
$31.0537295863$ |
$563633938950.1552$ |
|
|
? |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$9$ |
$8836400.64766$ |
| 19.1.473...375.1 |
$x^{19} - 6 x^{18} + 18 x^{17} - 22 x^{16} - 38 x^{15} + 219 x^{14} - 403 x^{13} + 380 x^{12} - 536 x^{11} + 1378 x^{10} - 1608 x^{9} + 691 x^{8} - 1073 x^{7} + 1881 x^{6} - 757 x^{5} + 716 x^{4} - 1464 x^{3} + 513 x^{2} - 10 x + 295$ |
$19$ |
[1,9] |
$-\,5^{9}\cdot 307^{9}$ |
$2$ |
$32.3004990658$ |
$39.179076048319466$ |
|
|
|
$D_{19}$ (as 19T2) |
trivial |
$2$ |
$9$ |
$26027741.7153$ |
| 19.1.495...343.1 |
$x^{19} - 9 x^{18} + 24 x^{17} - 6 x^{16} - 42 x^{15} + 4 x^{14} + 34 x^{13} + 74 x^{12} + 46 x^{11} - 238 x^{10} - 49 x^{9} + 181 x^{8} + 195 x^{7} + 116 x^{6} - 193 x^{5} - 275 x^{4} + 106 x^{3} - 8 x^{2} + 121 x - 1$ |
$19$ |
[1,9] |
$-\,1543^{9}$ |
$1$ |
$32.3801306357$ |
$39.28103868280471$ |
|
|
|
$D_{19}$ (as 19T2) |
trivial |
$2$ |
$9$ |
$17317158.8896$ |
| 19.1.101...431.1 |
$x^{19} - 5 x^{18} + 11 x^{17} - 10 x^{16} + 3 x^{15} + 3 x^{14} - 80 x^{13} + 481 x^{12} - 1180 x^{11} + 1220 x^{10} + 888 x^{9} - 5070 x^{8} + 8854 x^{7} - 9440 x^{6} + 6893 x^{5} - 3748 x^{4} + 2592 x^{3} - 2790 x^{2} + 2673 x - 1053$ |
$19$ |
[1,9] |
$-\,3^{9}\cdot 557^{9}$ |
$2$ |
$33.6258332676$ |
$40.87786687193939$ |
|
|
|
$D_{19}$ (as 19T2) |
trivial |
$2$ |
$9$ |
$191261859.157$ |
| 19.7.105...804.1 |
$x^{19} - 3 x^{18} - x^{17} + 15 x^{16} - 22 x^{15} - 6 x^{14} + 59 x^{13} - 70 x^{12} - 6 x^{11} + 106 x^{10} - 107 x^{9} + 92 x^{7} - 73 x^{6} - x^{5} + 35 x^{4} - 19 x^{3} - x^{2} + 4 x - 1$ |
$19$ |
[7,6] |
$2^{2}\cdot 131\cdot 149\cdot 397\cdot 20117\cdot 218819\cdot 773146117559$ |
$7$ |
$33.6928527152$ |
$324794707032692.7$ |
|
|
✓ |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$12$ |
$52861133.6694$ |
| 19.1.197...516.1 |
$x^{19} - 3 x^{18} + 2 x^{17} + 4 x^{16} - 8 x^{15} + 14 x^{13} - 9 x^{12} - 16 x^{11} + 21 x^{10} + 8 x^{9} - 25 x^{8} + 2 x^{7} + 16 x^{6} - 4 x^{5} - 8 x^{4} + 2 x^{3} + 3 x^{2} - x - 1$ |
$19$ |
[1,9] |
$-\,2^{2}\cdot 49323595893763542101396994379$ |
$2$ |
$34.8215535648$ |
$352544569446363.8$ |
|
|
✓ |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$9$ |
$20856736.7017$ |
| 19.1.231...871.1 |
$x^{19} - 6 x^{18} + 18 x^{17} - 39 x^{16} + 73 x^{15} - 200 x^{14} + 265 x^{13} + 305 x^{12} - 931 x^{11} + 1905 x^{10} - 5214 x^{9} + 10284 x^{8} - 13343 x^{7} + 12719 x^{6} - 8662 x^{5} + 4443 x^{4} - 1732 x^{3} + 614 x^{2} - 152 x + 39$ |
$19$ |
[1,9] |
$-\,1831^{9}$ |
$1$ |
$35.1142949338$ |
$42.790185790669334$ |
|
|
|
$D_{19}$ (as 19T2) |
trivial |
$2$ |
$9$ |
$34462435.5384$ |
| 19.1.239...368.1 |
$x^{19} - 3 x^{18} + 2 x^{17} + 4 x^{16} - 8 x^{15} + 14 x^{13} - 9 x^{12} - 16 x^{11} + 21 x^{10} + 8 x^{9} - 25 x^{8} + 2 x^{7} + 17 x^{6} - 4 x^{5} - 9 x^{4} + 2 x^{3} + 3 x^{2} - x - 1$ |
$19$ |
[1,9] |
$-\,2^{7}\cdot 7\cdot 60259\cdot 4440286064038502416537$ |
$4$ |
$35.180511669$ |
$173111311497788.5$ |
|
|
✓ |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$9$ |
$21087865.9745$ |
| 19.1.436...528.1 |
$x^{19} - 8 x - 8$ |
$19$ |
[1,9] |
$-\,2^{18}\cdot 17\cdot 8627\cdot 11343650175290580793$ |
$4$ |
$36.306051933$ |
$2487236508762.5366$ |
|
|
? |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$9$ |
$47279371.8637$ |
| 19.1.477...752.1 |
$x^{19} - 4 x - 4$ |
$19$ |
[1,9] |
$-\,2^{18}\cdot 593\cdot 10949399\cdot 280461391706269$ |
$4$ |
$36.4791875178$ |
$2602227976782.856$ |
|
|
? |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$9$ |
$25714895.7196$ |
| 19.1.498...864.1 |
$x^{19} - 2 x - 2$ |
$19$ |
[1,9] |
$-\,2^{18}\cdot 11\cdot 29\cdot 8255287577\cdot 721386928637$ |
$5$ |
$36.5605029997$ |
$2657858713225.0776$ |
|
|
✓ |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$9$ |
$44496889.6897$ |
| 19.1.518...552.1 |
$x^{19} - x - 2$ |
$19$ |
[1,9] |
$-\,2^{19}\cdot 821\cdot 883013\cdot 15385297\cdot 88689509$ |
$5$ |
$36.6386877755$ |
|
|
|
✓ |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$9$ |
$42948347.6249$ |
| 19.1.518...855.1 |
$x^{19} - x - 4$ |
$19$ |
[1,9] |
$-\,5\cdot 103726168442653430174403870371$ |
$2$ |
$36.6386879218$ |
$720160289250432.9$ |
|
|
? |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$9$ |
$53039958.1922$ |
| 19.1.518...976.1 |
$x^{19} - 2$ |
$19$ |
[1,9] |
$-\,2^{18}\cdot 19^{19}$ |
$2$ |
$36.6386879218$ |
$42.41345857356653$ |
|
|
✓ |
$F_{19}$ (as 19T6) |
trivial |
$2$ |
$9$ |
$47980973.6594$ |
| 19.1.539...088.1 |
$x^{19} + 2 x - 2$ |
$19$ |
[1,9] |
$-\,2^{18}\cdot 7\cdot 47\cdot 1031\cdot 108139\cdot 56081694178207$ |
$6$ |
$36.7139803836$ |
$2765765342919.86$ |
|
|
✓ |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$9$ |
$30572994.7677$ |
| 19.1.601...424.1 |
$x^{19} + 8 x - 8$ |
$19$ |
[1,9] |
$-\,2^{18}\cdot 46553428447\cdot 49259334849493$ |
$3$ |
$36.9245102701$ |
$2920158458207.675$ |
|
|
? |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$9$ |
$28122221.8245$ |
| 19.9.159...156.1 |
$x^{19} - 3 x^{18} - 8 x^{17} + 30 x^{16} + 16 x^{15} - 115 x^{14} + 31 x^{13} + 208 x^{12} - 175 x^{11} - 165 x^{10} + 280 x^{9} + 5 x^{8} - 206 x^{7} + 82 x^{6} + 75 x^{5} - 54 x^{4} - 13 x^{3} + 13 x^{2} + x - 1$ |
$19$ |
[9,5] |
$-\,2^{2}\cdot 937\cdot 971\cdot 4676220259\cdot 93910895860973$ |
$5$ |
$38.8744917393$ |
|
|
|
✓ |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$13$ |
$222480440.47$ |
| 19.1.207...120.1 |
$x^{19} - 4 x - 8$ |
$19$ |
[1,9] |
$-\,2^{20}\cdot 5\cdot 928238261\cdot 426273972622159$ |
$4$ |
$39.4118910595$ |
|
|
|
? |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$9$ |
$110775507.502$ |
| 19.1.386...375.1 |
$x^{19} + 19 x^{17} + 152 x^{15} + 665 x^{13} + 1729 x^{11} + 2717 x^{9} + 2508 x^{7} + 1254 x^{5} + 285 x^{3} + 19 x - 1$ |
$19$ |
[1,9] |
$-\,5^{9}\cdot 19^{19}$ |
$2$ |
$40.7234586539$ |
$49.18156889081904$ |
|
|
✓ |
$F_{19}$ (as 19T6) |
trivial |
$2$ |
$9$ |
$123041861.807$ |
| 19.7.832...904.1 |
$x^{19} - 3 x^{18} - x^{17} + 15 x^{16} - 22 x^{15} - 6 x^{14} + 59 x^{13} - 70 x^{12} - 6 x^{11} + 106 x^{10} - 107 x^{9} - x^{8} + 92 x^{7} - 72 x^{6} - x^{5} + 35 x^{4} - 19 x^{3} - x^{2} + 4 x - 1$ |
$19$ |
[7,6] |
$2^{10}\cdot 2746819\cdot 2958679616604904629509$ |
$3$ |
$42.4014216337$ |
$254981683825377.03$ |
|
|
✓ |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$12$ |
$409832342.529$ |
| 19.5.896...328.1 |
$x^{19} - 2 x^{18} - 3 x^{17} + 9 x^{16} + x^{15} - 16 x^{14} + 5 x^{13} + 17 x^{12} - 10 x^{11} - 12 x^{10} + 10 x^{9} + x^{8} + 3 x^{6} - 9 x^{5} + 2 x^{4} + 6 x^{3} - 5 x^{2} - x + 1$ |
$19$ |
[5,7] |
$-\,2^{4}\cdot 3947\cdot 1431584761\cdot 99216821342546749$ |
$4$ |
$42.5690720688$ |
|
|
|
✓ |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$11$ |
$363184844.905$ |
| 19.5.239...200.1 |
$x^{19} - x^{18} - 6 x^{17} + 7 x^{16} + 13 x^{15} - 21 x^{14} - 16 x^{13} + 41 x^{12} + 10 x^{11} - 51 x^{10} + 5 x^{9} + 43 x^{8} - 19 x^{7} - 24 x^{6} + 18 x^{5} + 5 x^{4} - 11 x^{3} + 2 x^{2} + 3 x - 1$ |
$19$ |
[5,7] |
$-\,2^{3}\cdot 5^{2}\cdot 430709\cdot 19005923\cdot 14610723851226353$ |
$5$ |
$44.824396879$ |
|
|
|
✓ |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$11$ |
$840306267.085$ |
| 19.1.331...008.1 |
$x^{19} + 4 x - 8$ |
$19$ |
[1,9] |
$-\,2^{24}\cdot 311\cdot 13913\cdot 49356007\cdot 9263974663$ |
$5$ |
$45.6039040723$ |
|
|
|
? |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$9$ |
$844213349.401$ |
| 19.3.457...029.1 |
$x^{19} - 3 x - 1$ |
$19$ |
[3,8] |
$15451\cdot 1192721\cdot 1892107519\cdot 1311498030721$ |
$4$ |
$46.37957716$ |
$6762456062138603.0$ |
|
|
✓ |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$10$ |
$278595712.583$ |
| 19.1.457...987.1 |
$x^{19} + 3 x - 1$ |
$19$ |
[1,9] |
$-\,577\cdot 70079\cdot 1130954781811714100492789$ |
$3$ |
$46.3795773712$ |
$6762456354697933.0$ |
|
|
✓ |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$9$ |
$356764768.985$ |
| 19.1.462...984.1 |
$x^{19} + 3 x - 2$ |
$19$ |
[1,9] |
$-\,2^{19}\cdot 613\cdot 7331\cdot 3070062337\cdot 6393898213$ |
$5$ |
$46.407113236$ |
$48720814800694.0$ |
|
|
✓ |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$9$ |
$1011018071.22$ |
| 19.1.629...707.1 |
$x^{19} - 9 x - 9$ |
$19$ |
[1,9] |
$-\,3^{18}\cdot 125471\cdot 142573\cdot 90800058249161$ |
$4$ |
$53.2421064555$ |
$3608635332174.5854$ |
|
|
? |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$9$ |
$682842465.233$ |
| 19.1.720...723.1 |
$x^{19} - 3 x - 3$ |
$19$ |
[1,9] |
$-\,3^{18}\cdot 30011\cdot 461269\cdot 134390022739373$ |
$4$ |
$53.6237363277$ |
$3861984185831.2554$ |
|
|
✓ |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$9$ |
$1413210922.08$ |
| 19.1.766...619.1 |
$x^{19} - 2 x - 3$ |
$19$ |
[1,9] |
$-\,3^{18}\cdot 109\cdot 2111\cdot 2503\cdot 3435034858449743$ |
$5$ |
$53.7975620938$ |
|
|
|
✓ |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$9$ |
$1389263095.55$ |
| 19.1.766...307.1 |
$x^{19} - x - 3$ |
$19$ |
[1,9] |
$-\,3^{18}\cdot 733\cdot 5827\cdot 8053\cdot 2874523\cdot 20009947$ |
$6$ |
$53.7976382997$ |
|
|
|
✓ |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$9$ |
$1320313121.52$ |
| 19.1.766...731.1 |
$x^{19} - 3$ |
$19$ |
[1,9] |
$-\,3^{18}\cdot 19^{19}$ |
$2$ |
$53.7976382998$ |
$62.27689998761435$ |
|
|
✓ |
$F_{19}$ (as 19T6) |
trivial |
$2$ |
$9$ |
$1832073247.14$ |
| 19.1.766...155.1 |
$x^{19} + x - 3$ |
$19$ |
[1,9] |
$-\,3^{18}\cdot 5\cdot 11\cdot 277\cdot 1202769413\cdot 107967633989$ |
$6$ |
$53.7976382999$ |
|
|
|
✓ |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$9$ |
$1322096028.33$ |
| 19.13.801...664.1 |
$x^{19} - 2 x^{18} - 18 x^{17} + 32 x^{16} + 132 x^{15} - 202 x^{14} - 502 x^{13} + 645 x^{12} + 1045 x^{11} - 1122 x^{10} - 1176 x^{9} + 1078 x^{8} + 700 x^{7} - 557 x^{6} - 220 x^{5} + 151 x^{4} + 34 x^{3} - 20 x^{2} - 2 x + 1$ |
$19$ |
[13,3] |
$-\,2^{3}\cdot 13^{2}\cdot 17\cdot 3229\cdot 34365587\cdot 85132367\cdot 3692009831$ |
$7$ |
$53.9247520599$ |
$1.2041290670651694e+16$ |
|
|
✓ |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$15$ |
$23798894722.8$ |
| 19.1.812...739.1 |
$x^{19} + 3 x - 3$ |
$19$ |
[1,9] |
$-\,3^{18}\cdot 581393\cdot 3605923841336588507$ |
$3$ |
$53.9619752737$ |
$4099706665433.8364$ |
|
|
✓ |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$9$ |
$1119576153.28$ |
| 19.1.903...755.1 |
$x^{19} + 9 x - 9$ |
$19$ |
[1,9] |
$-\,3^{18}\cdot 5\cdot 7\cdot 11\cdot 17\cdot 293990087\cdot 1212233453773$ |
$7$ |
$54.2658868088$ |
$4324380606930.263$ |
|
|
? |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$9$ |
$1386849912.1$ |
| 19.9.138...476.1 |
$x^{19} - 2 x^{18} - 14 x^{17} + 23 x^{16} + 83 x^{15} - 104 x^{14} - 274 x^{13} + 234 x^{12} + 555 x^{11} - 274 x^{10} - 708 x^{9} + 162 x^{8} + 554 x^{7} - 50 x^{6} - 246 x^{5} + 17 x^{4} + 56 x^{3} - 7 x^{2} - 5 x + 1$ |
$19$ |
[9,5] |
$-\,2^{2}\cdot 34\!\cdots\!19$ |
$2$ |
$55.505833971$ |
$2.9571521810644656e+16$ |
|
|
✓ |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$13$ |
$8259829376.29$ |
| 19.1.171...279.1 |
$x^{19} + 7 x - 4$ |
$19$ |
[1,9] |
$-\,17\!\cdots\!79$ |
$1$ |
$56.1208431643$ |
$4.1369453059951304e+16$ |
|
|
? |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$9$ |
$3321587861.16$ |
| 19.13.610...484.1 |
$x^{19} - 3 x^{18} - 12 x^{17} + 40 x^{16} + 52 x^{15} - 216 x^{14} - 88 x^{13} + 614 x^{12} + 8 x^{11} - 987 x^{10} + 143 x^{9} + 904 x^{8} - 163 x^{7} - 461 x^{6} + 72 x^{5} + 128 x^{4} - 14 x^{3} - 18 x^{2} + x + 1$ |
$19$ |
[13,3] |
$-\,2^{2}\cdot 90313\cdot 16881409121807\cdot 1000636759045331$ |
$4$ |
$60.0045203941$ |
$7.811738632783035e+16$ |
|
|
✓ |
$S_{19}$ (as 19T8) |
trivial |
$2$ |
$15$ |
$61782008553.5$ |
