| Label |
Dimension |
Base field |
Base char. |
Simple |
Geom. simple |
Primitive |
Ordinary |
Almost ordinary |
Supersingular |
Princ. polarizable |
Jacobian |
L-polynomial |
Newton slopes |
Newton elevation |
$p$-rank |
$p$-corank |
Angle rank |
Angle corank |
$\mathbb{F}_q$ points on curve |
$\mathbb{F}_{q^k}$ points on curve |
$\mathbb{F}_q$ points on variety |
$\mathbb{F}_{q^k}$ points on variety |
Jacobians |
Hyperelliptic Jacobians |
Num. twists |
Max. twist degree |
End. degree |
Number fields |
Galois groups |
Isogeny factors |
| 3.17.ay_jj_abzc |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 17 x^{2} )^{3}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$-6$ |
$[-6, 200, 4602, 82556, 1417434, 24134600, 410356122, 6975947516, 118589100474, 2016000461000]$ |
$1000$ |
$[1000, 17576000, 111284641000, 575930368000000, 2857545103792625000, 14061355882717286312000, 69094872316114708820849000, 339457920771989975334912000000, 1667728535147952717544489402849000, 8193492389449236510461529858617000000]$ |
$None$ |
$0$ |
$44$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
1.17.ai 3 |
| 3.17.ax_it_abvi |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 17 x^{2} )( 1 - 8 x + 17 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-5$ |
$[-5, 215, 4720, 83231, 1420475, 24145220, 410379755, 6975926591, 118588488880, 2015996127575]$ |
$1100$ |
$[1100, 18590000, 114014700800, 580602880000000, 2863668774319127500, 14067542823844590080000, 69098851702111695740092300, 339456902518053154897920000000, 1667719934190698704087815493049600, 8193474777369043784654087589998750000]$ |
$None$ |
$0$ |
$32$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-19}) \) |
$C_2$, $C_2$ |
1.17.ai 2 $\times$ 1.17.ah |
| 3.17.aw_id_abro |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 6 x + 17 x^{2} )( 1 - 8 x + 17 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-4$ |
$[-4, 228, 4796, 83452, 1420156, 24137316, 410328124, 6975721724, 118588094972, 2015997450468]$ |
$1200$ |
$[1200, 19468800, 115773044400, 582132695040000, 2863026403093230000, 14062938155043252134400, 69090157940066655684769200, 339446933264563329690501120000, 1667714394591111373386906873178800, 8193480153923986444472034069990720000]$ |
$None$ |
$0$ |
$32$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) |
$C_2$, $C_2$ |
1.17.ai 2 $\times$ 1.17.ag |
| 3.17.aw_ie_abrw |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 17 x^{2} )( 1 - 7 x + 17 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-4$ |
$[-4, 230, 4838, 83906, 1423516, 24155840, 410403388, 6975905666, 118587877286, 2015991794150]$ |
$1210$ |
$[1210, 19662500, 116811735040, 585313300000000, 2869805567767353050, 14073732487201587200000, 69102831317293749252509210, 339455884267170736837200000000, 1667711333277802308868335006883840, 8193457165326708586988665754614062500]$ |
$None$ |
$0$ |
$24$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-19}) \) |
$C_2$, $C_2$ |
1.17.ai $\times$ 1.17.ah 2 |
| 3.17.av_hn_abnu |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 17 x^{2} )( 1 - 8 x + 17 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-3$ |
$[-3, 239, 4836, 83375, 1418517, 24128516, 410310261, 6975804191, 118588973412, 2016001038239]$ |
$1300$ |
$[1300, 20212400, 116698488400, 581599682560000, 2859725944036032500, 14057811499495203814400, 69087150121674400053302900, 339450946279971108470784000000, 1667726748252020760301887447422800, 8193494735487199177140279846835310000]$ |
$None$ |
$0$ |
$32$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-43}) \) |
$C_2$, $C_2$ |
1.17.ai 2 $\times$ 1.17.af |
| 3.17.av_ho_aboc |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 17 x^{2} )( 1 - 13 x + 75 x^{2} - 221 x^{3} + 289 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-3$ |
$[-3, 241, 4875, 83753, 1420922, 24139297, 410342839, 6975849457, 118588840305, 2016000013536]$ |
$1310$ |
$[1310, 20401940, 117654769310, 584239746771200, 2864573214898680800, 14064091612462796052980, 69092635107100447988896990, 339453148871579172236954035200, 1667724876330962724058452150259310, 8193490570848146294842676907133875200]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), 4.0.9725.1 |
$C_2$, $D_{4}$ |
1.17.ai $\times$ 2.17.an_cx |
| 3.17.av_hp_abok |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 17 x^{2} )( 1 - 7 x + 17 x^{2} )( 1 - 6 x + 17 x^{2} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-3$ |
$[-3, 243, 4914, 84127, 1423197, 24147936, 410351757, 6975700799, 118587483378, 2015993117043]$ |
$1320$ |
$[1320, 20592000, 118613214720, 586855526400000, 2869161819950850600, 14069125792364138496000, 69094137054548240645916840, 339445915043585153045299200000, 1667705793706784291608330625963520, 8193462541870094231518155220354800000]$ |
$None$ |
$0$ |
$16$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-2}) \) |
$C_2$, $C_2$, $C_2$ |
1.17.ai $\times$ 1.17.ah $\times$ 1.17.ag |
| 3.17.av_hq_abor |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 17 x^{2} )^{3}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$-3$ |
$[-3, 245, 4956, 84581, 1426557, 24166460, 410427021, 6975884741, 118587265692, 2015987460725]$ |
$1331$ |
$[1331, 20796875, 119677386752, 590061935546875, 2875955512259499571, 14079924873986048000000, 69106811161674068830276867, 339454866019342711990623046875, 1667702732409263303121011964379136, 8193439553322230836089729983966796875]$ |
$None$ |
$0$ |
$10$ |
$6$ |
$1$ |
\(\Q(\sqrt{-19}) \) |
$C_2$ |
1.17.ah 3 |
| 3.17.au_gw_abjs |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 17 x^{2} )( 1 - 12 x + 65 x^{2} - 204 x^{3} + 289 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-2$ |
$[-2, 246, 4810, 82818, 1415078, 24117792, 410299286, 6975799682, 118588284490, 2015993668086]$ |
$1390$ |
$[1390, 20635940, 116056526560, 577733681491200, 2852802639769683950, 14051565675319963182080, 69085302355515995271225710, 339450726757133479180975027200, 1667717059791063184198474216392160, 8193464781434832248200164247934257700]$ |
$None$ |
$0$ |
$16$ |
$12$ |
$6$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2$, $C_2^2$ |
1.17.ai $\times$ 2.17.am_cn |
| 3.17.au_gx_abka |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 17 x^{2} )( 1 - 8 x + 17 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-2$ |
$[-2, 248, 4846, 83132, 1416878, 24125816, 410334398, 6975986684, 118589373022, 2015999253368]$ |
$1400$ |
$[1400, 20820800, 116929849400, 579917578240000, 2856425484978835000, 14056238548361143534400, 69091214372502025546036600, 339459826768176230191595520000, 1667732368039867397642053408983800, 8193487481342686310134469133731720000]$ |
$None$ |
$0$ |
$32$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-13}) \) |
$C_2$, $C_2$ |
1.17.ai 2 $\times$ 1.17.ae |
| 3.17.au_gy_abki |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 17 x^{2} )( 1 - 12 x + 67 x^{2} - 204 x^{3} + 289 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 250, 4882, 83442, 1418558, 24132040, 410351534, 6976039202, 118589649394, 2016000582250]$ |
$1410$ |
$[1410, 21006180, 117805077000, 582076206316800, 2859808199511940050, 14059863180218240424000, 69094099444038594864717810, 339462382400086534041086899200, 1667736254718316778081453458533000, 8193492882238111600250015402244516900]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), 4.0.58896.2 |
$C_2$, $D_{4}$ |
1.17.ai $\times$ 2.17.am_cp |
| 3.17.au_gz_abkq |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 8 x + 17 x^{2} )( 1 - 12 x + 68 x^{2} - 204 x^{3} + 289 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$3$ |
$0$ |
$-2$ |
$[-2, 252, 4918, 83748, 1420118, 24136476, 410351198, 6975967868, 118589263294, 2015999230812]$ |
$1420$ |
$[1420, 21192080, 118682238220, 584209698508800, 2862951043395721100, 14062446853699257038480, 69094042636610998936022540, 339458911104667109599110758400, 1667730824915126211887334764041420, 8193487389668186603785407802680352400]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), 4.0.39168.3 |
$C_2$, $D_{4}$ |
1.17.ai $\times$ 2.17.am_cq |
| 3.17.au_ha_abky |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 17 x^{2} )( 1 - 7 x + 17 x^{2} )( 1 - 5 x + 17 x^{2} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 254, 4954, 84050, 1421558, 24139136, 410333894, 6975783266, 118588361818, 2015996704814]$ |
$1430$ |
$[1430, 21378500, 119561361920, 586318189600000, 2865854288066062150, 14063996881107869696000, 69091129062926482007897830, 339449928046955302159440000000, 1667718147303982284748551815621120, 8193477123401963594542383899461962500]$ |
$None$ |
$0$ |
$16$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-43}) \) |
$C_2$, $C_2$, $C_2$ |
1.17.ai $\times$ 1.17.ah $\times$ 1.17.af |
| 3.17.au_hb_ablg |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 17 x^{2} )( 1 - 6 x + 17 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-2$ |
$[-2, 256, 4990, 84348, 1422878, 24140032, 410300126, 6975495932, 118587089470, 2015994439936]$ |
$1440$ |
$[1440, 21565440, 120442476960, 588401816371200, 2868518216538295200, 14064520605416465633280, 69085443885682725767187360, 339435946112778170260468531200, 1667700254154166849106874737926560, 8193467918417007961713369318448435200]$ |
$None$ |
$0$ |
$32$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) |
$C_2$, $C_2$ |
1.17.ai $\times$ 1.17.ag 2 |
| 3.17.au_hb_ablf |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 17 x^{2} )( 1 - 13 x + 75 x^{2} - 221 x^{3} + 289 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 256, 4993, 84428, 1423963, 24149917, 410366472, 6975828532, 118588228711, 2015995680111]$ |
$1441$ |
$[1441, 21578975, 120541102528, 588979672601375, 2870711946547676176, 14070279757300397523200, 69096614364249693747959873, 339452130631956368595814191375, 1667716275392578285516379284786624, 8193472958771862689434333350659168000]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-19}) \), 4.0.9725.1 |
$C_2$, $D_{4}$ |
1.17.ah $\times$ 2.17.an_cx |
| 3.17.au_hc_ablm |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 6 x + 17 x^{2} )( 1 - 7 x + 17 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-2$ |
$[-2, 258, 5032, 84802, 1426238, 24158556, 410375390, 6975679874, 118586871784, 2015988783618]$ |
$1452$ |
$[1452, 21780000, 121523060736, 591616674000000, 2875310384902381932, 14075316152221040640000, 69098116398199254793983468, 339444896825661279912072000000, 1667697192866814451961719157342208, 8193444929854059490172804189344500000]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-2}) \) |
$C_2$, $C_2$ |
1.17.ah 2 $\times$ 1.17.ag |
| 3.17.at_gg_abfy |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 17 x^{2} )( 1 - 11 x + 57 x^{2} - 187 x^{3} + 289 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 253, 4799, 82577, 1414694, 24124141, 410342631, 6975874849, 118587917783, 2015992219968]$ |
$1490$ |
$[1490, 21113300, 115812087170, 576072167840000, 2852030179114611200, 14055263349389805962900, 69092600378571042649328770, 339454384537750956761339520000, 1667711902788014511882358554354770, 8193458895948587701190219798251520000]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), 4.0.44573.1 |
$C_2$, $D_{4}$ |
1.17.ai $\times$ 2.17.al_cf |
| 3.17.at_gh_abgg |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 17 x^{2} )( 1 - 8 x + 17 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-1$ |
$[-1, 255, 4832, 82831, 1415959, 24129540, 410370967, 6976048991, 118588835744, 2015995901775]$ |
$1500$ |
$[1500, 21294000, 116605944000, 577833984000000, 2854574892011437500, 14058408055777158528000, 69097371955818735851533500, 339462858756135201325056000000, 1667724812201988801969148107576000, 8193473859663601203442385422716750000]$ |
$None$ |
$0$ |
$32$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-59}) \) |
$C_2$, $C_2$ |
1.17.ai 2 $\times$ 1.17.ad |
| 3.17.at_gi_abgo |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 17 x^{2} )( 1 - 11 x + 59 x^{2} - 187 x^{3} + 289 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 257, 4865, 83081, 1417114, 24133457, 410386213, 6976136369, 118589269595, 2015997009632]$ |
$1510$ |
$[1510, 21475220, 117401474710, 579569801324800, 2856898709596872800, 14060689231732738049780, 69099939188552805330444470, 339467110812631579992888960000, 1667730913523807768584257754716310, 8193478362255694292866744510534169600]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), 4.0.185661.1 |
$C_2$, $D_{4}$ |
1.17.ai $\times$ 2.17.al_ch |
| 3.17.at_gj_abgw |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 17 x^{2} )( 1 - 11 x + 60 x^{2} - 187 x^{3} + 289 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 259, 4898, 83327, 1418159, 24135904, 410388831, 6976145791, 118589330018, 2015996575779]$ |
$1520$ |
$[1520, 21656960, 118198708160, 581279736627200, 2859001823400095600, 14062114032192422543360, 69100379935341420315750640, 339467569313578113160013414400, 1667731763267902182469313844294080, 8193476598981540670661570759888316800]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), 4.0.43928.1 |
$C_2$, $D_{4}$ |
1.17.ai $\times$ 2.17.al_ci |
| 3.17.at_gk_abhf |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 17 x^{2} )( 1 - 12 x + 65 x^{2} - 204 x^{3} + 289 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-1$ |
$[-1, 261, 4928, 83493, 1418119, 24128412, 410322919, 6975778757, 118587672896, 2015989334661]$ |
$1529$ |
$[1529, 21826475, 118903651328, 582420823738875, 2858916147276494569, 14057748308794626867200, 69089281190349546733111417, 339449708524776163892994598875, 1667708458892990897264617781771264, 8193447169413983516447799225972264875]$ |
$None$ |
$0$ |
$8$ |
$12$ |
$6$ |
\(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2$, $C_2^2$ |
1.17.ah $\times$ 2.17.am_cn |
| 3.17.at_gk_abhe |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 17 x^{2} )( 1 - 11 x + 61 x^{2} - 187 x^{3} + 289 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 261, 4931, 83569, 1419094, 24136893, 410379283, 6976086017, 118589125319, 2015995574016]$ |
$1530$ |
$[1530, 21839220, 118997673210, 582963908716800, 2860884434997158400, 14062689634188067004340, 69098772082676587533451530, 339464660551234965571887129600, 1667728884544097506166253991627530, 8193472527584314352812862508794265600]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), 4.0.134693.2 |
$C_2$, $D_{4}$ |
1.17.ai $\times$ 2.17.al_cj |
| 3.17.at_gl_abhn |
$3$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 19 x + 167 x^{2} - 871 x^{3} + 2839 x^{4} - 5491 x^{5} + 4913 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 263, 4961, 83731, 1418949, 24128135, 410304908, 6975697171, 118587649745, 2015991015043]$ |
$1539$ |
$[1539, 22009239, 119704308003, 584079445852119, 2860589054695744539, 14057587504917743941287, 69086248907084994281810112, 339445738539653123819405413575, 1667708133313937185248212225739627, 8193453998861993095068433326341729199]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.60699031.1 |
$S_4\times C_2$ |
simple |
| 3.17.at_gl_abhm |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 17 x^{2} )( 1 - 7 x + 17 x^{2} )( 1 - 4 x + 17 x^{2} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 263, 4964, 83807, 1419919, 24136436, 410358031, 6975965759, 118588761428, 2015994919943]$ |
$1540$ |
$[1540, 22022000, 119798398720, 584622438400000, 2862546756181273700, 14062423237881514496000, 69095193547826800445218820, 339458808508522093994803200000, 1667723767062846054657440060235520, 8193469869273043660173546516388550000]$ |
$None$ |
$0$ |
$16$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-13}) \) |
$C_2$, $C_2$, $C_2$ |
1.17.ai $\times$ 1.17.ah $\times$ 1.17.ae |
| 3.17.at_gm_abhv |
$3$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 19 x + 168 x^{2} - 879 x^{3} + 2856 x^{4} - 5491 x^{5} + 4913 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 265, 4994, 83965, 1419669, 24126424, 410275641, 6975563109, 118587555638, 2015993664765]$ |
$1549$ |
$[1549, 22192523, 120506753716, 585712545896251, 2862041888529350509, 14056591922816030352176, 69081321536767900122835109, 339439215037455215858778247675, 1667706809882839102035109248407188, 8193464767937226482981787851157597203]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.36689200.1 |
$S_4\times C_2$ |
simple |
| 3.17.at_gm_abhu |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 17 x^{2} )( 1 - 11 x + 63 x^{2} - 187 x^{3} + 289 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 265, 4997, 84041, 1420634, 24134545, 410325537, 6975793681, 118588341899, 2015995471200]$ |
$1550$ |
$[1550, 22205300, 120600913550, 586255448480000, 2863989009133100000, 14061322067615985574100, 69089722281813776661533950, 339450434864168978385659520000, 1667717867141305573700753599239950, 8193472109703166059125597334377600000]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), 4.0.29525.1 |
$C_2$, $D_{4}$ |
1.17.ai $\times$ 2.17.al_cl |
| 3.17.at_gm_abht |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 17 x^{2} )( 1 - 12 x + 67 x^{2} - 204 x^{3} + 289 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 265, 5000, 84117, 1421599, 24142660, 410375167, 6976018277, 118589037800, 2015996248825]$ |
$1551$ |
$[1551, 22218075, 120695097600, 586798579384875, 2865936719814054711, 14066049464562332160000, 69098078785523504200560087, 339461364132766404227728618875, 1667727653721250712890146684883200, 8193475270156859614633246832723992875]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-19}) \), 4.0.58896.2 |
$C_2$, $D_{4}$ |
1.17.ah $\times$ 2.17.am_cp |
| 3.17.at_gn_abic |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 17 x^{2} )( 1 - 6 x + 17 x^{2} )( 1 - 5 x + 17 x^{2} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 267, 5030, 84271, 1421239, 24131232, 410282263, 6975578399, 118587967910, 2015998027707]$ |
$1560$ |
$[1560, 22389120, 121405246560, 587863063756800, 2865211426591027800, 14059393372984846049280, 69082436272515351664831320, 339439958998293453099171840000, 1667712607710330385239623781579360, 8193482499958445720244265981996809600]$ |
$None$ |
$0$ |
$16$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-43}) \) |
$C_2$, $C_2$, $C_2$ |
1.17.ai $\times$ 1.17.ag $\times$ 1.17.af |
| 3.17.at_gn_abib |
$3$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 19 x + 169 x^{2} - 885 x^{3} + 2873 x^{4} - 5491 x^{5} + 4913 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 267, 5033, 84347, 1422199, 24139167, 410328680, 6975765651, 118588354535, 2015996964167]$ |
$1561$ |
$[1561, 22401911, 121499499961, 588406107713879, 2867148565438580521, 14064015192052182673967, 69090251235684739706816576, 339449070803835833697247783847, 1667718044831873186753606933450761, 8193478177468797674726002809707485871]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.20569367.1 |
$A_4\times C_2$ |
simple |
| 3.17.at_gn_abia |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 7 x + 17 x^{2} )( 1 - 12 x + 68 x^{2} - 204 x^{3} + 289 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$3$ |
$0$ |
$-1$ |
$[-1, 267, 5036, 84423, 1423159, 24147096, 410374831, 6975946943, 118588651700, 2015994897387]$ |
$1562$ |
$[1562, 22414700, 121593777536, 588949380558000, 2869086298758792442, 14068634274849489843200, 69098021974824193970608858, 339457892847759640708959744000, 1667722223946063208438700990634368, 8193469777598741010044679559561203500]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-19}) \), 4.0.39168.3 |
$C_2$, $D_{4}$ |
1.17.ah $\times$ 2.17.am_cq |
| 3.17.at_go_abii |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 6 x + 17 x^{2} )( 1 - 13 x + 75 x^{2} - 221 x^{3} + 289 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 269, 5069, 84649, 1423644, 24142013, 410314841, 6975623665, 118587834803, 2015997003004]$ |
$1572$ |
$[1572, 22599072, 122400096804, 590531559428736, 2870067995414486592, 14065674192630303170976, 69087920883698231479683492, 339442161518608463527742679552, 1667710735805144240353688286685572, 8193478335325611986493693979366367232]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-2}) \), 4.0.9725.1 |
$C_2$, $D_{4}$ |
1.17.ag $\times$ 2.17.an_cx |
| 3.17.at_go_abih |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 17 x^{2} )( 1 - 7 x + 17 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-1$ |
$[-1, 269, 5072, 84725, 1424599, 24149756, 410357527, 6975762341, 118587750224, 2015992371389]$ |
$1573$ |
$[1573, 22611875, 122494468096, 591074977796875, 2871995765033053373, 14070184984264048640000, 69095108233338016330070141, 339448909816993835468710546875, 1667709546400301379905221633589248, 8193459511354585550926232641155921875]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-43}) \) |
$C_2$, $C_2$ |
1.17.ah 2 $\times$ 1.17.af |
| 3.17.at_gp_abio |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 17 x^{2} )( 1 - 6 x + 17 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-1$ |
$[-1, 271, 5108, 85023, 1425919, 24150652, 410323759, 6975475007, 118586477876, 2015990106511]$ |
$1584$ |
$[1584, 22809600, 123397198848, 593175508992000, 2874665402258666544, 14070708939009274675200, 69089422728667434395437872, 339434927924757570608136192000, 1667691653342766080663901601281024, 8193450306389416222337910418589568000]$ |
$None$ |
$0$ |
$16$ |
$8$ |
$1$ |
\(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-2}) \) |
$C_2$, $C_2$ |
1.17.ah $\times$ 1.17.ag 2 |
| 3.17.as_fq_abce |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 17 x^{2} )( 1 - 10 x + 49 x^{2} - 170 x^{3} + 289 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 258, 4770, 82354, 1415100, 24132312, 410363100, 6975789026, 118587470850, 2015993904978]$ |
$1590$ |
$[1590, 21455460, 115149841560, 574532591443200, 2852847010880512950, 14060022537433021231680, 69096046895232101476151190, 339450208343426814339438720000, 1667705617523687051701156306820760, 8193465744221625717997923166899483300]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), 4.0.142400.3 |
$C_2$, $D_{4}$ |
1.17.ai $\times$ 2.17.ak_bx |
| 3.17.as_fr_abcm |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 2 x + 17 x^{2} )( 1 - 8 x + 17 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$0$ |
$[0, 260, 4800, 82556, 1416000, 24136580, 410390400, 6975947516, 118588137600, 2015996087300]$ |
$1600$ |
$[1600, 21632000, 115865588800, 575930368000000, 2854657453830440000, 14062509380215597184000, 69100644134893734658356800, 339457920771989975334912000000, 1667714994076400346276816021121600, 8193474613681768762695268702544000000]$ |
$None$ |
$1$ |
$44$ |
$12$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.17.ai 2 $\times$ 1.17.ac |
| 3.17.as_fs_abcu |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 8 x + 17 x^{2} )( 1 - 10 x + 51 x^{2} - 170 x^{3} + 289 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$3$ |
$0$ |
$0$ |
$[0, 262, 4830, 82754, 1416800, 24139648, 410408320, 6976049026, 118588483230, 2015996399622]$ |
$1610$ |
$[1610, 21809060, 116582779040, 577301520723200, 2856266546640627050, 14064296793436656865280, 69103661811330740801565610, 339462860472837730782840960000, 1667719854707108233578245646715040, 8193475883027246019183879468970523300]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), 4.0.27200.2 |
$C_2$, $D_{4}$ |
1.17.ai $\times$ 2.17.ak_bz |
| 3.17.as_ft_abdc |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 8 x + 17 x^{2} )( 1 - 10 x + 52 x^{2} - 170 x^{3} + 289 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 264, 4860, 82948, 1417500, 24141528, 410417280, 6976100732, 118588587840, 2015995508664]$ |
$1620$ |
$[1620, 21986640, 117301441140, 578646150451200, 2857674421793582100, 14065391842517419868880, 69105170642897290709456820, 339465376616578994286703411200, 1667721325860857901264963426668340, 8193472261966177233709195785096565200]$ |
$None$ |
$1$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), 4.0.467264.1 |
$C_2$, $D_{4}$ |
1.17.ai $\times$ 2.17.ak_ca |
| 3.17.as_fu_abdl |
$3$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
|
✓ |
|
✓ |
? |
$1 - 18 x + 150 x^{2} - 765 x^{3} + 2550 x^{4} - 5202 x^{5} + 4913 x^{6}$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$3$ |
$0$ |
$0$ |
$[0, 266, 4887, 83066, 1417230, 24135053, 410371164, 6975849650, 118587199176, 2015987720126]$ |
$1629$ |
$[1629, 22152771, 117931573917, 579453774865299, 2857125538204837749, 14061617545058513571699, 69097404483873753824299797, 339453158271501239813385141507, 1667701796980722714621051250483008, 8193440607584264956161817090737098931]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.2119203.1 |
$A_4\times C_2$ |
simple |
| 3.17.as_fu_abdk |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 8 x + 17 x^{2} )( 1 - 10 x + 53 x^{2} - 170 x^{3} + 289 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 266, 4890, 83138, 1418100, 24142232, 410417700, 6976109762, 118588529370, 2015994033386]$ |
$1630$ |
$[1630, 22164740, 118021603960, 579964360019200, 2858881220456399150, 14065801608569427529280, 69105241362708188145736430, 339465816044473952695802803200, 1667720503605382539296010576173560, 8193466266096070983124449923732077700]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), 4.0.442944.2 |
$C_2$, $D_{4}$ |
1.17.ai $\times$ 2.17.ak_cb |
| 3.17.as_fv_abdt |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 7 x + 17 x^{2} )( 1 - 11 x + 57 x^{2} - 187 x^{3} + 289 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 268, 4917, 83252, 1417735, 24134761, 410366264, 6975853924, 118587306189, 2015987886543]$ |
$1639$ |
$[1639, 22331375, 118653215296, 580745830259375, 2858142031251384064, 14061447609826475936000, 69096579633720165693361679, 339453366294421590783536559375, 1667703301916538377647006313286208, 8193441283940389943013618881676800000]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-19}) \), 4.0.44573.1 |
$C_2$, $D_{4}$ |
1.17.ah $\times$ 2.17.al_cf |
| 3.17.as_fv_abds |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 8 x + 17 x^{2} )( 1 - 10 x + 54 x^{2} - 170 x^{3} + 289 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 268, 4920, 83324, 1418600, 24141772, 410410000, 6976083196, 118588383600, 2015992545228]$ |
$1640$ |
$[1640, 22343360, 118743296360, 581256254259200, 2859887092651044200, 14065533189289527308480, 69103944720696320693217640, 339464523271111346505646080000, 1667718453633154424290521706985960, 8193460217879988704864763646385220800]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), 4.0.23600.1 |
$C_2$, $D_{4}$ |
1.17.ai $\times$ 2.17.ak_cc |
| 3.17.as_fw_abeb |
$3$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 18 x + 152 x^{2} - 781 x^{3} + 2584 x^{4} - 5202 x^{5} + 4913 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 270, 4947, 83434, 1418140, 24133317, 410353650, 6975829026, 118587386472, 2015988380530]$ |
$1649$ |
$[1649, 22510499, 119376414833, 582011675415379, 2858957755494151289, 14060606607516459830411, 69094455839721555103226657, 339452154724772619172732534819, 1667704430930840526354077019735104, 8193443291612344246363751405981342459]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.825389491.2 |
$S_4\times C_2$ |
simple |
| 3.17.as_fw_abea |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 8 x + 17 x^{2} )( 1 - 7 x + 17 x^{2} )( 1 - 3 x + 17 x^{2} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 270, 4950, 83506, 1419000, 24140160, 410394600, 6976028066, 118588224150, 2015991568350]$ |
$1650$ |
$[1650, 22522500, 119466547200, 582521940000000, 2860692197424641250, 14064593699872235520000, 69101351485777653696840450, 339461840487386171514960000000, 1667716211263935095049052736870400, 8193456247623238632476276074296562500]$ |
$None$ |
$0$ |
$16$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-59}) \) |
$C_2$, $C_2$, $C_2$ |
1.17.ai $\times$ 1.17.ah $\times$ 1.17.ad |
| 3.17.as_fw_abdz |
$3$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 18 x + 152 x^{2} - 779 x^{3} + 2584 x^{4} - 5202 x^{5} + 4913 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 270, 4953, 83578, 1419860, 24146997, 410435298, 6976221762, 118588985580, 2015993933290]$ |
$1651$ |
$[1651, 22534499, 119556704371, 583032411021619, 2862427104360083611, 14068577792869914560987, 69108205000027940467405243, 339471266324891180103162100003, 1667726919363414894464084609258176, 8193465859284239300215359525908189819]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.17448067.1 |
$A_4\times C_2$ |
simple |
| 3.17.as_fx_abej |
$3$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 18 x + 153 x^{2} - 789 x^{3} + 2601 x^{4} - 5202 x^{5} + 4913 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 272, 4977, 83612, 1418445, 24130733, 410333742, 6975781940, 118587511539, 2015989682087]$ |
$1659$ |
$[1659, 22690143, 120101201388, 583251419153151, 2859572879081533104, 14059101671575423259328, 69091103892283571509631283, 339449863434287694954471372879, 1667706189735204178829696080325196, 8193448581431826109679057465980432128]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.925152759.1 |
$S_4\times C_2$ |
simple |
| 3.17.as_fx_abei |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 8 x + 17 x^{2} )( 1 - 10 x + 56 x^{2} - 170 x^{3} + 289 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 272, 4980, 83684, 1419300, 24137408, 410371920, 6975951356, 118588122480, 2015991579872]$ |
$1660$ |
$[1660, 22702160, 120191385340, 583761526067200, 2861296703019758300, 14062990273939478390480, 69097532448125835426860060, 339458107563792568156815360000, 1667714781447871237918235552867740, 8193456294450697174590741706904910800]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), 4.0.187200.1 |
$C_2$, $D_{4}$ |
1.17.ai $\times$ 2.17.ak_ce |
| 3.17.as_fx_abeh |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 7 x + 17 x^{2} )( 1 - 11 x + 59 x^{2} - 187 x^{3} + 289 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 272, 4983, 83756, 1420155, 24144077, 410409846, 6976115444, 118588658001, 2015992676207]$ |
$1661$ |
$[1661, 22714175, 120281594048, 584271839977375, 2863020994911614416, 14066875879536238035200, 69103918866366544387714069, 339466092531127881630136959375, 1667722312554287784598119399199424, 8193460750205653307709302203194464000]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-19}) \), 4.0.185661.1 |
$C_2$, $D_{4}$ |
1.17.ah $\times$ 2.17.al_ch |
| 3.17.as_fy_abes |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 6 x + 17 x^{2} )( 1 - 12 x + 65 x^{2} - 204 x^{3} + 289 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$0$ |
$[0, 274, 5004, 83714, 1417800, 24120508, 410271288, 6975573890, 118587278988, 2015990657554]$ |
$1668$ |
$[1668, 22858272, 120737392704, 583955428830336, 2858274842148354948, 14053146845990131408896, 69080588632430911962721668, 339439739482561295978887721472, 1667702919331520610764845840828992, 8193452545950809846958672593112198432]$ |
$None$ |
$0$ |
$8$ |
$12$ |
$6$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2$, $C_2^2$ |
1.17.ag $\times$ 2.17.am_cn |
| 3.17.as_fy_aber |
$3$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 18 x + 154 x^{2} - 797 x^{3} + 2618 x^{4} - 5202 x^{5} + 4913 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 274, 5007, 83786, 1418650, 24127021, 410306960, 6975719602, 118587750744, 2015992224414]$ |
$1669$ |
$[1669, 22870307, 120827603821, 584465172289331, 2859987579527518669, 14056939954817672849075, 69086594605434367819914773, 339446829977922302405792590275, 1667709553675385531183275643844928, 8193458914028400893447210695966163267]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.695126003.1 |
$S_4\times C_2$ |
simple |
| 3.17.as_fy_abeq |
$3$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 8 x + 17 x^{2} )( 1 - 10 x + 57 x^{2} - 170 x^{3} + 289 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 274, 5010, 83858, 1419500, 24133528, 410342380, 6975860002, 118588147890, 2015993010114]$ |
$1670$ |
$[1670, 22882340, 120917839640, 584975123283200, 2861700787044693350, 14060730064487711458880, 69092558421558481598433670, 339453662054046946186423219200, 1667715138769187181447112510946840, 8193462107284863935742340252929097700]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), 4.0.94784.1 |
$C_2$, $D_{4}$ |
1.17.ai $\times$ 2.17.ak_cf |
