| 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 |
| 2.17.aq_du |
$2$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 17 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$2$ |
$[2, 230, 4706, 82878, 1418242, 24135590, 410350306, 6975884158, 118588692482, 2015998274150]$ |
$100$ |
$[100, 67600, 23136100, 6922240000, 2013702902500, 582574494096400, 168382600473360100, 48662075833712640000, 14063181218281174560100, 4064240224008909221290000]$ |
$0$ |
$0$ |
$16$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
1.17.ai 2 |
| 2.17.ap_dm |
$2$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 17 x^{2} )( 1 - 7 x + 17 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$3$ |
$[3, 245, 4824, 83553, 1421283, 24146210, 410373939, 6975863233, 118588080888, 2015993940725]$ |
$110$ |
$[110, 71500, 23703680, 6978400000, 2018018233550, 582830824576000, 168392298144692270, 48661929864662400000, 14063108690397910183040, 4064231487841064613287500]$ |
$0$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-19}) \) |
$C_2$, $C_2$ |
1.17.ai $\times$ 1.17.ah |
| 2.17.ao_de |
$2$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 8 x + 17 x^{2} )( 1 - 6 x + 17 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$4$ |
$[4, 258, 4900, 83774, 1420964, 24138306, 410322308, 6975658366, 118587686980, 2015995263618]$ |
$120$ |
$[120, 74880, 24069240, 6996787200, 2017565556600, 582640049047680, 168371111648329080, 48660500749182566400, 14063061977523943296120, 4064234154788176529846400]$ |
$2$ |
$2$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) |
$C_2$, $C_2$ |
1.17.ai $\times$ 1.17.ag |
| 2.17.ao_df |
$2$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 7 x + 17 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$4$ |
$[4, 260, 4942, 84228, 1424324, 24156830, 410397572, 6975842308, 118587469294, 2015989607300]$ |
$121$ |
$[121, 75625, 24285184, 7035015625, 2022342812281, 583087267840000, 168401996374543129, 48661783896050015625, 14063036162888693026816, 4064222751691998577515625]$ |
$1$ |
$1$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-19}) \) |
$C_2$ |
1.17.ah 2 |
| 2.17.an_cw |
$2$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 8 x + 17 x^{2} )( 1 - 5 x + 17 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$5$ |
$[5, 269, 4940, 83697, 1419325, 24129506, 410304445, 6975740833, 118588565420, 2015998851389]$ |
$130$ |
$[130, 77740, 24261640, 6990380800, 2015239733650, 582427647143680, 168363781664704210, 48661076024196480000, 14063166150216570691720, 4064241387720474658254700]$ |
$1$ |
$1$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-43}) \) |
$C_2$, $C_2$ |
1.17.ai $\times$ 1.17.af |
| 2.17.an_cx |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 13 x + 75 x^{2} - 221 x^{3} + 289 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$5$ |
$[5, 271, 4979, 84075, 1421730, 24140287, 410337023, 6975786099, 118588432313, 2015997826686]$ |
$131$ |
$[131, 78469, 24460451, 7022112341, 2018655589936, 582687837815581, 168377148446907251, 48661391770783328069, 14063150365174514584619, 4064239321923284317498624]$ |
$1$ |
$1$ |
$2$ |
$2$ |
$1$ |
4.0.9725.1 |
$D_{4}$ |
simple |
| 2.17.an_cy |
$2$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 17 x^{2} )( 1 - 6 x + 17 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$5$ |
$[5, 273, 5018, 84449, 1424005, 24148926, 410345941, 6975637441, 118587075386, 2015990930193]$ |
$132$ |
$[132, 79200, 24659712, 7053552000, 2021889165252, 582896408371200, 168380808657984516, 48660354784857024000, 14062989450255637909248, 4064225418633377836476000]$ |
$0$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-2}) \) |
$C_2$, $C_2$ |
1.17.ah $\times$ 1.17.ag |
| 2.17.am_cn |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
|
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 12 x + 65 x^{2} - 204 x^{3} + 289 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$6$ |
$[6, 276, 4914, 83140, 1415886, 24118782, 410293470, 6975736324, 118587876498, 2015991481236]$ |
$139$ |
$[139, 79369, 24128176, 6943914441, 2010360903259, 582168877086976, 168359278701453979, 48661044555091420809, 14063084451918975425584, 4064226529530741241632649]$ |
$2$ |
$2$ |
$4$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2^2$ |
simple |
| 2.17.am_co |
$2$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 8 x + 17 x^{2} )( 1 - 4 x + 17 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$6$ |
$[6, 278, 4950, 83454, 1417686, 24126806, 410328582, 6975923326, 118588965030, 2015997066518]$ |
$140$ |
$[140, 80080, 24309740, 6970163200, 2012913910700, 582362478377680, 168373686149659340, 48662349062661734400, 14063213539280935740620, 4064237789427522323016400]$ |
$4$ |
$4$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-13}) \) |
$C_2$, $C_2$ |
1.17.ai $\times$ 1.17.ae |
| 2.17.am_cp |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 12 x + 67 x^{2} - 204 x^{3} + 289 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$6$ |
$[6, 280, 4986, 83764, 1419366, 24133030, 410345718, 6975975844, 118589241402, 2015998395400]$ |
$141$ |
$[141, 80793, 24491700, 6996108249, 2015297698821, 582512650102800, 168380717002045269, 48662715418390124649, 14063246313837597011700, 4064240468448309770809353]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.58896.2 |
$D_{4}$ |
simple |
| 2.17.am_cq |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
|
✓ |
|
✓ |
✓ |
$1 - 12 x + 68 x^{2} - 204 x^{3} + 289 x^{4}$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$2$ |
$0$ |
$6$ |
$[6, 282, 5022, 84070, 1420926, 24137466, 410345382, 6975904510, 118588855302, 2015997043962]$ |
$142$ |
$[142, 81508, 24674062, 7021751184, 2017512450862, 582619693995556, 168380578563662446, 48662217800185909248, 14063200526825718750958, 4064237743953971910957988]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.39168.3 |
$D_{4}$ |
simple |
| 2.17.am_cr |
$2$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 7 x + 17 x^{2} )( 1 - 5 x + 17 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$6$ |
$[6, 284, 5058, 84372, 1422366, 24140126, 410328078, 6975719908, 118587953826, 2015994517964]$ |
$143$ |
$[143, 82225, 24856832, 7047093625, 2019558358103, 582683913011200, 168373478252203367, 48660930058145315625, 14063093622411016671488, 4064232651550128628338625]$ |
$3$ |
$3$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-43}) \) |
$C_2$, $C_2$ |
1.17.ah $\times$ 1.17.af |
| 2.17.am_cs |
$2$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 6 x + 17 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$6$ |
$[6, 286, 5094, 84670, 1423686, 24141022, 410294310, 6975432574, 118586681478, 2015992253086]$ |
$144$ |
$[144, 82944, 25040016, 7072137216, 2021435619984, 582705611375616, 168359623607186064, 48658925715634520064, 14062942737777746304144, 4064228085576507141325824]$ |
$6$ |
$6$ |
$8$ |
$8$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$C_2$ |
1.17.ag 2 |
| 2.17.al_cf |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 11 x + 57 x^{2} - 187 x^{3} + 289 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$7$ |
$[7, 283, 4903, 82899, 1415502, 24125131, 410336815, 6975811491, 118587509791, 2015990033118]$ |
$149$ |
$[149, 81205, 24077357, 6923944325, 2009816552704, 582322075016005, 168377063814286973, 48661568906378867525, 14063040965304164776373, 4064223610137057085542400]$ |
$1$ |
$1$ |
$2$ |
$2$ |
$1$ |
4.0.44573.1 |
$D_{4}$ |
simple |
| 2.17.al_cg |
$2$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 8 x + 17 x^{2} )( 1 - 3 x + 17 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$7$ |
$[7, 285, 4936, 83153, 1416767, 24130530, 410365151, 6975985633, 118588427752, 2015993714925]$ |
$150$ |
$[150, 81900, 24242400, 6945120000, 2011609803750, 582452363001600, 168388692037314150, 48662783705128320000, 14063149824404621522400, 4064231032629148100947500]$ |
$3$ |
$3$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-59}) \) |
$C_2$, $C_2$ |
1.17.ai $\times$ 1.17.ad |
| 2.17.al_ch |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 11 x + 59 x^{2} - 187 x^{3} + 289 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$7$ |
$[7, 287, 4969, 83403, 1417922, 24134447, 410380397, 6976073011, 118588861603, 2015994822782]$ |
$151$ |
$[151, 82597, 24407791, 6965983189, 2013247390576, 582546874152541, 168394948323913903, 48663393247233584325, 14063201274021632223919, 4064233266062100403793152]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
4.0.185661.1 |
$D_{4}$ |
simple |
| 2.17.al_ci |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 11 x + 60 x^{2} - 187 x^{3} + 289 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$7$ |
$[7, 289, 5002, 83649, 1418967, 24136894, 410383015, 6976082433, 118588922026, 2015994388929]$ |
$152$ |
$[152, 83296, 24573536, 6986535296, 2014729448152, 582605904904192, 168396022413610136, 48663458974401709568, 14063208439519455792992, 4064232391420445724920416]$ |
$6$ |
$6$ |
$2$ |
$2$ |
$1$ |
4.0.43928.1 |
$D_{4}$ |
simple |
| 2.17.al_cj |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 11 x + 61 x^{2} - 187 x^{3} + 289 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$7$ |
$[7, 291, 5035, 83891, 1419902, 24137883, 410373467, 6976022659, 118588717327, 2015993387166]$ |
$153$ |
$[153, 83997, 24739641, 7006777749, 2016056118528, 582629752607373, 168392104113976497, 48663041996611347237, 14063184164576808156897, 4064230371874251183132672]$ |
$5$ |
$5$ |
$2$ |
$2$ |
$1$ |
4.0.134693.2 |
$D_{4}$ |
simple |
| 2.17.al_ck |
$2$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 7 x + 17 x^{2} )( 1 - 4 x + 17 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$7$ |
$[7, 293, 5068, 84129, 1420727, 24137426, 410352215, 6975902401, 118588353436, 2015992733093]$ |
$154$ |
$[154, 84700, 24906112, 7026712000, 2017227550954, 582618715571200, 168383383307588218, 48662203092791904000, 14063141011230982642048, 4064229053264910897713500]$ |
$4$ |
$4$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-13}) \) |
$C_2$, $C_2$ |
1.17.ah $\times$ 1.17.ae |
| 2.17.al_cl |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 11 x + 63 x^{2} - 187 x^{3} + 289 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$7$ |
$[7, 295, 5101, 84363, 1421442, 24135535, 410319721, 6975730323, 118587933907, 2015993284350]$ |
$155$ |
$[155, 85405, 25072955, 7046339525, 2018243902000, 582573093106645, 168370049959276355, 48661002711561767525, 14063091259929107805755, 4064230164591533262112000]$ |
$3$ |
$3$ |
$2$ |
$2$ |
$1$ |
4.0.29525.1 |
$D_{4}$ |
simple |
| 2.17.al_cm |
$2$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 6 x + 17 x^{2} )( 1 - 5 x + 17 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$7$ |
$[7, 297, 5134, 84593, 1422047, 24132222, 410276447, 6975515041, 118587559918, 2015995840857]$ |
$156$ |
$[156, 86112, 25240176, 7065661824, 2019105335676, 582493185570816, 168352294123689468, 48659500972028044800, 14063046909587100522864, 4064235318498004170329952]$ |
$0$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-43}) \) |
$C_2$, $C_2$ |
1.17.ag $\times$ 1.17.af |
| 2.17.ak_bx |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 10 x + 49 x^{2} - 170 x^{3} + 289 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$8$ |
$[8, 288, 4874, 82676, 1415908, 24133302, 410357284, 6975725668, 118587062858, 2015991718128]$ |
$159$ |
$[159, 82521, 23939676, 6905439801, 2010392171439, 582519252414096, 168385462895412831, 48660970239290954025, 14062987964585295365724, 4064227007104482349060521]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
4.0.142400.3 |
$D_{4}$ |
simple |
| 2.17.ak_by |
$2$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 8 x + 17 x^{2} )( 1 - 2 x + 17 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$8$ |
$[8, 290, 4904, 82878, 1416808, 24137570, 410384584, 6975884158, 118587729608, 2015993900450]$ |
$160$ |
$[160, 83200, 24088480, 6922240000, 2011667984800, 582622284524800, 168396666261788320, 48662075833712640000, 14063067032705334535840, 4064231406646822197280000]$ |
$10$ |
$10$ |
$16$ |
$12$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.17.ai $\times$ 1.17.ac |
| 2.17.ak_bz |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
|
✓ |
|
✓ |
✓ |
$1 - 10 x + 51 x^{2} - 170 x^{3} + 289 x^{4}$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$2$ |
$0$ |
$8$ |
$[8, 292, 4934, 83076, 1417608, 24140638, 410402504, 6975985668, 118588075238, 2015994212772]$ |
$161$ |
$[161, 83881, 24237584, 6938720201, 2012801907361, 582696338646016, 168404020269239489, 48662783951221586825, 14063108020149657479696, 4064232036283697612305321]$ |
$6$ |
$6$ |
$2$ |
$2$ |
$1$ |
4.0.27200.2 |
$D_{4}$ |
simple |
| 2.17.ak_ca |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 10 x + 52 x^{2} - 170 x^{3} + 289 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$8$ |
$[8, 294, 4964, 83270, 1418308, 24142518, 410411464, 6976037374, 118588179848, 2015993321814]$ |
$162$ |
$[162, 84564, 24386994, 6954881616, 2013794032482, 582741707504436, 168407697256754418, 48663144646229873664, 14063120425706884270866, 4064230240118967136503924]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.467264.1 |
$D_{4}$ |
simple |
| 2.17.ak_cb |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 10 x + 53 x^{2} - 170 x^{3} + 289 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$8$ |
$[8, 296, 4994, 83460, 1418908, 24143222, 410411884, 6976046404, 118588121378, 2015991846536]$ |
$163$ |
$[163, 85249, 24536716, 6970725481, 2014644459643, 582758684476816, 168407869599292507, 48663207639232067529, 14063113492007835514444, 4064227265971277058006049]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
4.0.442944.2 |
$D_{4}$ |
simple |
| 2.17.ak_cc |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 10 x + 54 x^{2} - 170 x^{3} + 289 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$8$ |
$[8, 298, 5024, 83646, 1419408, 24142762, 410404184, 6976019838, 118587975608, 2015990358378]$ |
$164$ |
$[164, 85936, 24686756, 6986253056, 2015353294564, 582747563627056, 168404709712798436, 48663022317189017600, 14063096205542845055204, 4064224265858270698670896]$ |
$6$ |
$6$ |
$2$ |
$2$ |
$1$ |
4.0.23600.1 |
$D_{4}$ |
simple |
| 2.17.ak_cd |
$2$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 7 x + 17 x^{2} )( 1 - 3 x + 17 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$8$ |
$[8, 300, 5054, 83828, 1419808, 24141150, 410388784, 6975964708, 118587816158, 2015989381500]$ |
$165$ |
$[165, 86625, 24837120, 7001465625, 2015920649325, 582708639744000, 168398390059478205, 48662637733954715625, 14063077296683264424960, 4064222296481060552540625]$ |
$18$ |
$18$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-59}) \) |
$C_2$, $C_2$ |
1.17.ah $\times$ 1.17.ad |
| 2.17.ak_ce |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 10 x + 56 x^{2} - 170 x^{3} + 289 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$8$ |
$[8, 302, 5084, 84006, 1420108, 24138398, 410366104, 6975887998, 118587714488, 2015989393022]$ |
$166$ |
$[166, 87316, 24987814, 7016364496, 2016346642486, 582642208379956, 168389083153342294, 48662102610748339200, 14063065239707569007926, 4064222319709011656766196]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.187200.1 |
$D_{4}$ |
simple |
| 2.17.ak_cf |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 10 x + 57 x^{2} - 170 x^{3} + 289 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$8$ |
$[8, 304, 5114, 84180, 1420308, 24134518, 410336564, 6975796644, 118587739898, 2015990823264]$ |
$167$ |
$[167, 88009, 25138844, 7030951001, 2016631399207, 582548565889936, 168376961566020983, 48661465336673635049, 14063068252832495135516, 4064225203064888872883449]$ |
$3$ |
$3$ |
$2$ |
$2$ |
$1$ |
4.0.94784.1 |
$D_{4}$ |
simple |
| 2.17.ak_cg |
$2$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 6 x + 17 x^{2} )( 1 - 4 x + 17 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$8$ |
$[8, 306, 5144, 84350, 1420408, 24129522, 410300584, 6975697534, 118587959528, 2015994055986]$ |
$168$ |
$[168, 88704, 25290216, 7045226496, 2016775051368, 582428009471616, 168362197932856872, 48660773969287839744, 14063094298249656917544, 4064231720210425246353024]$ |
$8$ |
$8$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-13}) \) |
$C_2$, $C_2$ |
1.17.ag $\times$ 1.17.ae |
| 2.17.ak_ch |
$2$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 5 x + 17 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$8$ |
$[8, 308, 5174, 84516, 1420408, 24123422, 410258584, 6975597508, 118588438358, 2015999428628]$ |
$169$ |
$[169, 89401, 25441936, 7059192361, 2016777737689, 582280837206016, 168344964959279641, 48660076235222375625, 14063151082168111575184, 4064242551432373300082521]$ |
$2$ |
$2$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-43}) \) |
$C_2$ |
1.17.af 2 |
| 2.17.aj_bp |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 9 x + 41 x^{2} - 153 x^{3} + 289 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$9$ |
$[9, 291, 4833, 82531, 1417014, 24139923, 410348241, 6975598339, 118587234249, 2015995427166]$ |
$169$ |
$[169, 83317, 23743993, 6893398629, 2011960631824, 582679036603573, 168381752616945673, 48660082030956511557, 14063008289407622370553, 4064234484501891974889472]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.328653.3 |
$D_{4}$ |
simple |
| 2.17.aj_bq |
$2$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 8 x + 17 x^{2} )( 1 - x + 17 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$9$ |
$[9, 293, 4860, 82689, 1417689, 24143906, 410374953, 6975726721, 118587672540, 2015997074693]$ |
$170$ |
$[170, 83980, 23876840, 6906515200, 2012918167850, 582775213895680, 168392714234005130, 48660977581413350400, 14063060265109115260520, 4064237805908290336693900]$ |
$2$ |
$2$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-67}) \) |
$C_2$, $C_2$ |
1.17.ai $\times$ 1.17.ab |
| 2.17.aj_br |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 9 x + 43 x^{2} - 153 x^{3} + 289 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$9$ |
$[9, 295, 4887, 82843, 1418274, 24146935, 410394987, 6975815443, 118587867669, 2015997236350]$ |
$171$ |
$[171, 84645, 24009939, 6919305525, 2013747767856, 582848352157005, 168400935545490819, 48661596480863715525, 14063083404869803766211, 4064238131807072897568000]$ |
$15$ |
$15$ |
$2$ |
$2$ |
$1$ |
4.0.10525.1 |
$D_{4}$ |
simple |
| 2.17.aj_bs |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
|
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 9 x + 44 x^{2} - 153 x^{3} + 289 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$9$ |
$[9, 297, 4914, 82993, 1418769, 24149022, 410408721, 6975870241, 118587876498, 2015996344857]$ |
$172$ |
$[172, 85312, 24143296, 6931770624, 2014449490252, 582898741743616, 168406571598364684, 48661978739878425600, 14063084451840828627904, 4064236334561133871365952]$ |
$8$ |
$8$ |
$4$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}, \sqrt{41})\) |
$C_2^2$ |
simple |
| 2.17.aj_bt |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 9 x + 45 x^{2} - 153 x^{3} + 289 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$9$ |
$[9, 299, 4941, 83139, 1419174, 24150179, 410416533, 6975896803, 118587753945, 2015994794654]$ |
$173$ |
$[173, 85981, 24276917, 6943911541, 2015023398608, 582926673437437, 168409777454100173, 48662164034104184613, 14063069918615304820709, 4064233209360549492822016]$ |
$3$ |
$3$ |
$2$ |
$2$ |
$1$ |
4.0.1003477.1 |
$D_{4}$ |
simple |
| 2.17.aj_bu |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 9 x + 46 x^{2} - 153 x^{3} + 289 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$9$ |
$[9, 301, 4968, 83281, 1419489, 24150418, 410418801, 6975900769, 118587552984, 2015992942141]$ |
$174$ |
$[174, 86652, 24410808, 6955729344, 2015469561774, 582932438477568, 168410708192052318, 48662191704444602112, 14063046087231918221688, 4064229474706288087398972]$ |
$10$ |
$10$ |
$2$ |
$2$ |
$1$ |
4.0.971388.2 |
$D_{4}$ |
simple |
| 2.17.aj_bv |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 9 x + 47 x^{2} - 153 x^{3} + 289 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$9$ |
$[9, 303, 4995, 83419, 1419714, 24149751, 410415903, 6975887731, 118587324645, 2015991105918]$ |
$175$ |
$[175, 87325, 24544975, 6967225125, 2015788054000, 582916328592325, 168409518913049575, 48662100757270657125, 14063019009180656508175, 4064225772894002499616000]$ |
$9$ |
$9$ |
$2$ |
$2$ |
$1$ |
4.0.10933.1 |
$D_{4}$ |
simple |
| 2.17.aj_bw |
$2$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 7 x + 17 x^{2} )( 1 - 2 x + 17 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$9$ |
$[9, 305, 5022, 83553, 1419849, 24148190, 410408217, 6975863233, 118587118014, 2015989567025]$ |
$176$ |
$[176, 88000, 24679424, 6978400000, 2015978955056, 582878636032000, 168406364743212464, 48661929864662400000, 14062994505410958119936, 4064222670497930690200000]$ |
$7$ |
$7$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.17.ah $\times$ 1.17.ac |
| 2.17.aj_bx |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 9 x + 49 x^{2} - 153 x^{3} + 289 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$9$ |
$[9, 307, 5049, 83683, 1419894, 24145747, 410396121, 6975832771, 118586980233, 2015988569182]$ |
$177$ |
$[177, 88677, 24814161, 6989255109, 2016042350352, 582819653602341, 168401400838004049, 48661717364683726725, 14062978166342579447409, 4064220658854933316042752]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.609021.1 |
$D_{4}$ |
simple |
| 2.17.aj_by |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 9 x + 50 x^{2} - 153 x^{3} + 289 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$9$ |
$[9, 309, 5076, 83809, 1419849, 24142434, 410379993, 6975801793, 118586956500, 2015988319029]$ |
$178$ |
$[178, 89356, 24949192, 6999791616, 2015978331058, 582739674698752, 168394782386517298, 48661501261692100608, 14062975351879497100744, 4064220154548700275695116]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.447372.1 |
$D_{4}$ |
simple |
| 2.17.aj_bz |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
|
✓ |
|
✓ |
✓ |
$1 - 9 x + 51 x^{2} - 153 x^{3} + 289 x^{4}$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$2$ |
$0$ |
$9$ |
$[9, 311, 5103, 83931, 1419714, 24138263, 410360211, 6975775699, 118587090069, 2015988986366]$ |
$179$ |
$[179, 90037, 25084523, 7010010709, 2015786994224, 582638993341213, 168386664616004363, 48661319226685136517, 14062991191427179169723, 4064221499894161540617472]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.290173.1 |
$D_{4}$ |
simple |
| 2.17.aj_ca |
$2$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 6 x + 17 x^{2} )( 1 - 3 x + 17 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$9$ |
$[9, 313, 5130, 84049, 1419489, 24133246, 410337153, 6975759841, 118587422250, 2015990704393]$ |
$180$ |
$[180, 90720, 25220160, 7019913600, 2015468442900, 582517904209920, 168377202796652820, 48661208597686003200, 14063030583913576802880, 4064224963422141102261600]$ |
$9$ |
$9$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-59}) \) |
$C_2$, $C_2$ |
1.17.ag $\times$ 1.17.ad |
| 2.17.aj_cb |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 9 x + 53 x^{2} - 153 x^{3} + 289 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$9$ |
$[9, 315, 5157, 84163, 1419174, 24127395, 410311197, 6975759523, 118587992409, 2015993569950]$ |
$181$ |
$[181, 91405, 25356109, 7029501525, 2015022786256, 582376702681645, 168366552246613909, 48661206380169639525, 14063098197814205215261, 4064230740364296550912000]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.51525.2 |
$D_{4}$ |
simple |
| 2.17.aj_cc |
$2$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 17 x^{2} )( 1 - 4 x + 17 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$9$ |
$[9, 317, 5184, 84273, 1418769, 24120722, 410282721, 6975780001, 118588837968, 2015997643757]$ |
$182$ |
$[182, 92092, 25492376, 7038775744, 2014450139702, 582215684866816, 168354868337287814, 48661349247531820800, 14063198471181701378264, 4064238953138390667693052]$ |
$0$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-13}) \) |
$C_2$, $C_2$ |
1.17.af $\times$ 1.17.ae |
| 2.17.ai_bg |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
|
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 8 x + 32 x^{2} - 136 x^{3} + 289 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$10$ |
$[10, 290, 4762, 82374, 1417850, 24137570, 410290730, 6975432574, 118587392074, 2015993900450]$ |
$178$ |
$[178, 82948, 23402194, 6880370704, 2013144841618, 582622191933700, 168358154431328242, 48658925715634520064, 14063027005371573629746, 4064231406644218986637828]$ |
$2$ |
$2$ |
$8$ |
$24$ |
$4$ |
\(\Q(\zeta_{8})\) |
$C_2^2$ |
simple |
| 2.17.ai_bh |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 8 x + 33 x^{2} - 136 x^{3} + 289 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$10$ |
$[10, 292, 4786, 82500, 1418490, 24142366, 410320186, 6975560580, 118587959314, 2015997159012]$ |
$179$ |
$[179, 83593, 23519168, 6890821769, 2014054099699, 582738000449536, 168370241098946387, 48659818633199903753, 14063094273277609256384, 4064237975893985628512713]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.39593.1 |
$D_{4}$ |
simple |
| 2.17.ai_bi |
$2$ |
$\F_{17}$ |
$17$ |
|
|
✓ |
|
✓ |
|
✓ |
✓ |
$( 1 - 8 x + 17 x^{2} )( 1 + 17 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$10$ |
$[10, 294, 4810, 82622, 1419050, 24146406, 410344490, 6975653758, 118588284490, 2015998927014]$ |
$180$ |
$[180, 84240, 23636340, 6900940800, 2014849494900, 582835555345680, 168380213909806260, 48660468604600320000, 14063132835209808916020, 4064241540180178760317200]$ |
$16$ |
$16$ |
$4$ |
$4$ |
$2$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-17}) \) |
$C_2$, $C_2$ |
1.17.ai $\times$ 1.17.a |
| 2.17.ai_bj |
$2$ |
$\F_{17}$ |
$17$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 8 x + 35 x^{2} - 136 x^{3} + 289 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$10$ |
$[10, 296, 4834, 82740, 1419530, 24149702, 410363978, 6975716644, 118588409218, 2015999525336]$ |
$181$ |
$[181, 84889, 23753716, 6910728601, 2015531053261, 582915145476496, 168388210681200061, 48660907271948114409, 14063147626378708671604, 4064242746395381032085449]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.1472400.1 |
$D_{4}$ |
simple |
