| 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 |
| 3.23.abb_ma_acxv |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 9 x + 23 x^{2} )^{3}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$-3$ |
$[-3, 425, 11844, 279341, 6439287, 148073900, 3405099849, 78312580661, 1801160708652, 41426546944625]$ |
$3375$ |
$[3375, 121287375, 1754049816000, 21875648690671875, 266757296587533703125, 3244984021819186454016000, 39474765326813393907880360875, 480260547919212498486209874796875, 5843237151886323572628557017104456000, 71094410111095246794693772521401657484375]$ |
$None$ |
$0$ |
$10$ |
$6$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$C_2$ |
1.23.aj 3 |
| 3.23.aba_li_acsy |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 23 x^{2} )( 1 - 9 x + 23 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-2$ |
$[-2, 442, 11992, 280242, 6443258, 148083964, 3405076358, 78312069794, 1801156630216, 41426523384682]$ |
$3600$ |
$[3600, 125452800, 1775575468800, 21946123203840000, 266921851464714690000, 3245204608356438746726400, 39474492984863372442103628400, 480257414928376694985956152320000, 5843223920785054029381351132026630400, 71094369678538432325821958680312461120000]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-7}) \) |
$C_2$, $C_2$ |
1.23.aj 2 $\times$ 1.23.ai |
| 3.23.az_kp_acns |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 9 x + 23 x^{2} )( 1 - 16 x + 108 x^{2} - 368 x^{3} + 529 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 455, 12044, 279967, 6437469, 148034600, 3404793923, 78310955407, 1801154426852, 41426531235775]$ |
$3810$ |
$[3810, 128496060, 1782882261000, 21924411514513200, 266681908802990270550, 3244122685618237790136000, 39471218661524051700437001690, 480250580780479167837626170060800, 5843216772734766184281269580383151000, 71094383152247762252138928556357953486300]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-14 +4 \sqrt{2}})\) |
$C_2$, $D_{4}$ |
1.23.aj $\times$ 2.23.aq_ee |
| 3.23.az_kq_acob |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 23 x^{2} )( 1 - 9 x + 23 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-1$ |
$[-1, 457, 12092, 280557, 6442429, 148065964, 3404946691, 78311508149, 1801155660116, 41426530907857]$ |
$3825$ |
$[3825, 129128175, 1790119828800, 21970761907111875, 266887498406748676875, 3244810077586313421926400, 39472989695789538488552414325, 480253970531619858359397768316875, 5843220773624882438138013139444670400, 71094382589486502645510538066686028104375]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-43}) \) |
$C_2$, $C_2$ |
1.23.aj 2 $\times$ 1.23.ah |
| 3.23.az_kr_acok |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 9 x + 23 x^{2} )( 1 - 8 x + 23 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-1$ |
$[-1, 459, 12140, 281143, 6447229, 148094028, 3405052867, 78311558927, 1801152551780, 41426499824739]$ |
$3840$ |
$[3840, 129761280, 1797365283840, 22016824757452800, 267086507851050067200, 3245425209888655603138560, 39474220644792276338578871040, 480254281957979029949825993932800, 5843210689713744256079199609096975360, 71094329246004612515011174616259880550400]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-7}) \) |
$C_2$, $C_2$ |
1.23.aj $\times$ 1.23.ai 2 |
| 3.23.ay_jw_acim |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 9 x + 23 x^{2} )( 1 - 15 x + 98 x^{2} - 345 x^{3} + 529 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$0$ |
$[0, 466, 12060, 279458, 6432000, 148005292, 3404714880, 78311004482, 1801155343860, 41426526544786]$ |
$4020$ |
$[4020, 131068080, 1785051927360, 21884576249764800, 266455388712937988100, 3243480420088754908508160, 39470302330561230206080853580, 480250881741851255738962989100800, 5843219747645175641319202733299515840, 71094375101771983017935112122225134340400]$ |
$None$ |
$0$ |
$8$ |
$12$ |
$6$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-3}, \sqrt{17})\) |
$C_2$, $C_2^2$ |
1.23.aj $\times$ 2.23.ap_du |
| 3.23.ay_jx_aciv |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 9 x + 23 x^{2} )( 1 - 15 x + 99 x^{2} - 345 x^{3} + 529 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 468, 12105, 279964, 6435825, 148027257, 3404821770, 78311528516, 1801158378795, 41426545959603]$ |
$4035$ |
$[4035, 131690295, 1791800160660, 21924256618472175, 266613847783369918800, 3243961753187570465632560, 39471541480625178516001929165, 480254095454378769774496163919375, 5843229593458532668083265549574417940, 71094408420642952346582854228973792121600]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-130 -30 \sqrt{13}})\) |
$C_2$, $C_4$ |
1.23.aj $\times$ 2.23.ap_dv |
| 3.23.ay_jy_acjf |
$3$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 24 x + 258 x^{2} - 1591 x^{3} + 5934 x^{4} - 12696 x^{5} + 12167 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 470, 12147, 280370, 6437910, 148028177, 3404731218, 78310535474, 1801151572380, 41426510432870]$ |
$4049$ |
$[4049, 132284879, 1797999381341, 21955948530241339, 266700114751222825759, 3243981869496650955929831, 39470491724589189231894276157, 480248005510337712627384494648883, 5843207512401460075208080250459387072, 71094347451212874617312867388120840938159]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.9100107.1 |
$A_4\times C_2$ |
simple |
| 3.23.ay_jy_acje |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 6 x + 23 x^{2} )( 1 - 9 x + 23 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$0$ |
$[0, 470, 12150, 280466, 6439500, 148046360, 3404891700, 78311690786, 1801158561450, 41426546481350]$ |
$4050$ |
$[4050, 132313500, 1798555557600, 21963644059500000, 266766123127155851250, 3244380389740894707072000, 39472352159874778349583094350, 480255090588400348474977438000000, 5843230186018253516901438344443936800, 71094409316042696870312945727498522937500]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-14}) \) |
$C_2$, $C_2$ |
1.23.aj 2 $\times$ 1.23.ag |
| 3.23.ay_jz_acjo |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 8 x + 23 x^{2} )( 1 - 16 x + 108 x^{2} - 368 x^{3} + 529 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 472, 12192, 280868, 6441440, 148044664, 3404770432, 78310444540, 1801150348416, 41426507675832]$ |
$4064$ |
$[4064, 132909056, 1804761744800, 21995043121823744, 266846417175622796384, 3244343213603839689574400, 39470946344042972177091717664, 480247447854664225297119452332032, 5843203541679642058554235714410418400, 71094342719706279721894470404325059741696]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14 +4 \sqrt{2}})\) |
$C_2$, $D_{4}$ |
1.23.ai $\times$ 2.23.aq_ee |
| 3.23.ay_jz_acjn |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 9 x + 23 x^{2} )( 1 - 15 x + 101 x^{2} - 345 x^{3} + 529 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 472, 12195, 280964, 6443025, 148062613, 3404925300, 78311508116, 1801156195575, 41426532263347]$ |
$4065$ |
$[4065, 132937695, 1805318190540, 22002739240712175, 266912217466704901200, 3244736599417922444454960, 39472741683008465581121151435, 480253970332403578458274201779375, 5843222510746695910142084840628206460, 71094384915721897391615761484393173881600]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-33 +6 \sqrt{5}})\) |
$C_2$, $D_{4}$ |
1.23.aj $\times$ 2.23.ap_dx |
| 3.23.ay_ka_acjw |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 9 x + 23 x^{2} )( 1 - 8 x + 23 x^{2} )( 1 - 7 x + 23 x^{2} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 474, 12240, 281458, 6446400, 148076028, 3404923200, 78310997282, 1801151581680, 41426507347914]$ |
$4080$ |
$[4080, 133562880, 1812088131840, 22041542836684800, 267052133601674084400, 3245030652299237537218560, 39472717366089844834779768720, 480250837583691795543968260300800, 5843207542560698919317652488486511360, 71094342156945340166822404397294527910400]$ |
$None$ |
$0$ |
$8$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-43}) \) |
$C_2$, $C_2$, $C_2$ |
1.23.aj $\times$ 1.23.ai $\times$ 1.23.ah |
| 3.23.ay_kb_acke |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 8 x + 23 x^{2} )^{3}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$0$ |
$[0, 476, 12288, 282044, 6451200, 148104092, 3405029376, 78311048060, 1801148473344, 41426476264796]$ |
$4096$ |
$[4096, 134217728, 1819422502912, 22087754082942976, 267251265809157902336, 3245645826416856346394624, 39473948306600092634336129024, 480251149008019370049148563750912, 5843197458672394184882865420726145024, 71094288813493787349183981230599876640768]$ |
$None$ |
$1$ |
$14$ |
$14$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$C_2$ |
1.23.ai 3 |
| 3.23.ax_je_acdp |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 9 x + 23 x^{2} )( 1 - 14 x + 89 x^{2} - 322 x^{3} + 529 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 477, 12088, 279277, 6430871, 148012164, 3404838809, 78311795189, 1801157883544, 41426528030757]$ |
$4245$ |
$[4245, 133781175, 1789206983280, 21870536455411875, 266408658624871575975, 3243631005102834877766400, 39471739028207398892139025785, 480255730867373739945930612916875, 5843227986782784329284038015386439120, 71094377651935416144764571977462463729375]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-34 +8 \sqrt{6}})\) |
$C_2$, $D_{4}$ |
1.23.aj $\times$ 2.23.ao_dl |
| 3.23.ax_jf_acdz |
$3$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 23 x + 239 x^{2} - 1455 x^{3} + 5497 x^{4} - 12167 x^{5} + 12167 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 479, 12127, 279611, 6432221, 148010123, 3404766800, 78311187203, 1801154183935, 41426506925759]$ |
$4259$ |
$[4259, 134367191, 1794937674977, 21896570024354599, 266464474854732220789, 3243586226293778010426431, 39470904213038541922027933888, 480252002295730338688144711687911, 5843215984668431085449503414474646483, 71094341432463566832133585915640919471911]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.8140239.1 |
$S_4\times C_2$ |
simple |
| 3.23.ax_jf_acdy |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 9 x + 23 x^{2} )( 1 - 14 x + 90 x^{2} - 322 x^{3} + 529 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 479, 12130, 279703, 6433671, 148025888, 3404900353, 78312134287, 1801160107990, 41426540933239]$ |
$4260$ |
$[4260, 134394480, 1795477893840, 21903902642476800, 266524621004524446300, 3243931737075909398280960, 39472452504325828128485815860, 480257810448077398389124518604800, 5843235203242345487203360003355776560, 71094399794614202139325727325839828300400]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-22 +2 \sqrt{5}})\) |
$C_2$, $D_{4}$ |
1.23.aj $\times$ 2.23.ao_dm |
| 3.23.ax_jg_acei |
$3$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 23 x + 240 x^{2} - 1464 x^{3} + 5520 x^{4} - 12167 x^{5} + 12167 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 481, 12169, 280033, 6434886, 148021621, 3404804943, 78311357745, 1801155619387, 41426518536936]$ |
$4274$ |
$[4274, 134981468, 1801214869682, 21929638935817696, 266574866025970910624, 3243838191668588945949404, 39471346408240616953393553674, 480253048182628836724965982470016, 5843220641504977607152125959539786826, 71094361359055536923016132378897451486208]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.160679224.1 |
$S_4\times C_2$ |
simple |
| 3.23.ax_jg_aceh |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 5 x + 23 x^{2} )( 1 - 9 x + 23 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$1$ |
$[1, 481, 12172, 280125, 6436331, 148037164, 3404933477, 78312227861, 1801160644036, 41426544006361]$ |
$4275$ |
$[4275, 135008775, 1801755316800, 21936971685481875, 266634802450805675625, 3244178828354112902246400, 39472836499819695414661403175, 480258384304872814233969050296875, 5843236942261644006048019415075102400, 71094405068573449695754901097817393869375]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-67}) \) |
$C_2$, $C_2$ |
1.23.aj 2 $\times$ 1.23.af |
| 3.23.ax_jh_aces |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 8 x + 23 x^{2} )( 1 - 15 x + 98 x^{2} - 345 x^{3} + 529 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$1$ |
$[1, 483, 12208, 280359, 6435971, 148015356, 3404691389, 78310493615, 1801151265424, 41426502984843]$ |
$4288$ |
$[4288, 135569408, 1806958037248, 21955079523926016, 266619757351864728128, 3243700904414625914814464, 39470030019402046689305152448, 480247748814072984699441493573632, 5843206516583315293893099586494221056, 71094334669235078925275532301062062317568]$ |
$None$ |
$0$ |
$8$ |
$12$ |
$6$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{17})\) |
$C_2$, $C_2^2$ |
1.23.ai $\times$ 2.23.ap_du |
| 3.23.ax_jh_acer |
$3$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 23 x + 241 x^{2} - 1473 x^{3} + 5543 x^{4} - 12167 x^{5} + 12167 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 483, 12211, 280451, 6437411, 148030683, 3404815240, 78311296419, 1801155579973, 41426522753843]$ |
$4289$ |
$[4289, 135596735, 1807498648799, 21962411298569975, 266679478378081493999, 3244036783688524877654015, 39471465782985360090139173376, 480252672097995461155376821454375, 5843220513641392795144039931057467793, 71094368595923794346330351102325782734175]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.173393831.1 |
$A_4\times C_2$ |
simple |
| 3.23.ax_jh_aceq |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 9 x + 23 x^{2} )( 1 - 14 x + 92 x^{2} - 322 x^{3} + 529 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$3$ |
$0$ |
$1$ |
$[1, 483, 12214, 280543, 6438851, 148046004, 3404938769, 78312090383, 1801159729318, 41426540165163]$ |
$4290$ |
$[4290, 135624060, 1808039324520, 21969744191881200, 266739205154465707950, 3244372546491988002336960, 39472897837403617193938415370, 480257541194117605634752487193600, 5843233974769971834562226813683119960, 71094398476475424486958657923029006922300]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-40 -14 \sqrt{3}})\) |
$C_2$, $D_{4}$ |
1.23.aj $\times$ 2.23.ao_do |
| 3.23.ax_ji_acfb |
$3$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 23 x + 242 x^{2} - 1483 x^{3} + 5566 x^{4} - 12167 x^{5} + 12167 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 485, 12250, 280773, 6438361, 148022216, 3404679419, 78310290197, 1801150838146, 41426510249745]$ |
$4303$ |
$[4303, 136185647, 1813248244132, 21987555798375011, 266718802742136815993, 3243851264726561711301872, 39469891272095207054481770719, 480246501341871617048478345404075, 5843205130433243487209813955678625852, 71094347136938733286581902100190653252767]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.88032176.1 |
$S_4\times C_2$ |
simple |
| 3.23.ax_ji_acfa |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 8 x + 23 x^{2} )( 1 - 15 x + 99 x^{2} - 345 x^{3} + 529 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 485, 12253, 280865, 6439796, 148037321, 3404798279, 78311017649, 1801154300359, 41426522399660]$ |
$4304$ |
$[4304, 136212992, 1813789084688, 21994887726770176, 266778314171123801344, 3244182270233356521972224, 39471269160916924675667467024, 480250962505635770440652925542400, 5843216362374378008408379484224743696, 71094367988087099265650410260656908009472]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-130 -30 \sqrt{13}})\) |
$C_2$, $C_4$ |
1.23.ai $\times$ 2.23.ap_dv |
| 3.23.ax_ji_acez |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 9 x + 23 x^{2} )( 1 - 14 x + 93 x^{2} - 322 x^{3} + 529 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 485, 12256, 280957, 6441231, 148052420, 3404916817, 78311736277, 1801157598448, 41426532228925]$ |
$4305$ |
$[4305, 136240335, 1814329989360, 22002220775841075, 266837831376550576275, 3244513159378067756256000, 39472643340755411955757410045, 480255369579683167363482050829675, 5843227061888887236240622663388489040, 71094384856645752858025824689556577523175]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-41 -14 \sqrt{2}})\) |
$C_2$, $D_{4}$ |
1.23.aj $\times$ 2.23.ao_dp |
| 3.23.ax_jj_acfk |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 23 x^{2} )( 1 - 16 x + 108 x^{2} - 368 x^{3} + 529 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 487, 12292, 281183, 6440611, 148026664, 3404640765, 78309882895, 1801149378316, 41426515199007]$ |
$4318$ |
$[4318, 136802876, 1819545179800, 22019736747021104, 266812073826110743018, 3243948787556459503774400, 39469443190034239532520905702, 480244003529391045774537458429952, 5843200394530446652676150204822883400, 71094355630649454237829073958243677685596]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-14 +4 \sqrt{2}})\) |
$C_2$, $D_{4}$ |
1.23.ah $\times$ 2.23.aq_ee |
| 3.23.ax_jj_acfj |
$3$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 23 x + 243 x^{2} - 1491 x^{3} + 5589 x^{4} - 12167 x^{5} + 12167 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 487, 12295, 281275, 6442041, 148041547, 3404754648, 78310535811, 1801152012187, 41426520202047]$ |
$4319$ |
$[4319, 136830239, 1820086249709, 22027068841289239, 266871375736225550969, 3244274919526491386657303, 39470763366698892874593903424, 480248007577073856125790598347079, 5843208939193425169832804792706814103, 71094364216640454180667327545885818704559]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.29174551.1 |
$A_4\times C_2$ |
simple |
| 3.23.ax_jj_acfi |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 9 x + 23 x^{2} )( 1 - 8 x + 23 x^{2} )( 1 - 6 x + 23 x^{2} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 487, 12298, 281367, 6443471, 148056424, 3404868209, 78311179919, 1801154483014, 41426522921407]$ |
$4320$ |
$[4320, 136857600, 1820627383680, 22034402058240000, 266930683449174381600, 3244600935244629105868800, 39472079834573534510445771360, 480251957633165569244762603520000, 5843216954932757097946377932903829120, 71094368883486334560863301268141559040000]$ |
$None$ |
$0$ |
$8$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) |
$C_2$, $C_2$, $C_2$ |
1.23.aj $\times$ 1.23.ai $\times$ 1.23.ag |
| 3.23.ax_jk_acfr |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 9 x + 23 x^{2} )( 1 - 7 x + 23 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$1$ |
$[1, 489, 12340, 281773, 6445571, 148058028, 3404793533, 78310435637, 1801150611580, 41426514871089]$ |
$4335$ |
$[4335, 137475855, 1826931579840, 22066288666668675, 267017763776291771925, 3244636142677552911298560, 39471214144636089055811753835, 480247393234107545944812499545675, 5843204395409348639061291504154647360, 71094355067888412483703841674889995754775]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-43}) \) |
$C_2$, $C_2$ |
1.23.aj $\times$ 1.23.ah 2 |
| 3.23.ax_jk_acfq |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 23 x^{2} )( 1 - 15 x + 101 x^{2} - 345 x^{3} + 529 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 489, 12343, 281865, 6446996, 148072677, 3404901809, 78310997249, 1801152117139, 41426508703404]$ |
$4336$ |
$[4336, 137503232, 1827473007472, 22073623188350976, 267076867910104960256, 3244957169135969968669184, 39472469355019846936115252336, 480250837384476815234872348876800, 5843209279678578949287087454703881264, 71094344483179411944713742576450050588672]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-33 +6 \sqrt{5}})\) |
$C_2$, $D_{4}$ |
1.23.ai $\times$ 2.23.ap_dx |
| 3.23.ax_jl_acfy |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 23 x^{2} )( 1 - 8 x + 23 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$1$ |
$[1, 491, 12388, 282359, 6450371, 148086092, 3404899709, 78310486415, 1801147503244, 41426483787971]$ |
$4352$ |
$[4352, 138149888, 1834326029312, 22112551793852416, 267216870355299580672, 3245251242006322425626624, 39472445038268992026527026432, 480247704656201591283019658821632, 5843194311526475086466814808153447424, 71094301724427172337293757030955705171968]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-43}) \) |
$C_2$, $C_2$ |
1.23.ai 2 $\times$ 1.23.ah |
| 3.23.aw_il_abyj |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 9 x + 23 x^{2} )( 1 - 13 x + 79 x^{2} - 299 x^{3} + 529 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$2$ |
$[2, 484, 12047, 278604, 6428017, 148014097, 3404890876, 78311684612, 1801154198417, 41426505443059]$ |
$4455$ |
$[4455, 135400815, 1783198341540, 21817987023088575, 266290481393365532400, 3243673368503450417692080, 39472342624913945550597719145, 480255052723877579508676433177775, 5843216031655719281393437880977393380, 71094338887917438648797169764002520851200]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-29 +2 \sqrt{37}})\) |
$C_2$, $D_{4}$ |
1.23.aj $\times$ 2.23.an_db |
| 3.23.aw_im_abys |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 9 x + 23 x^{2} )( 1 - 13 x + 80 x^{2} - 299 x^{3} + 529 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$2$ |
$[2, 486, 12086, 278962, 6430162, 148025016, 3404956942, 78312156386, 1801157202314, 41426520561846]$ |
$4470$ |
$[4470, 136004220, 1788990337440, 21845982486952800, 266379289777152535350, 3243912648770318047902720, 39473108555003491979848812810, 480257945969618293622382624393600, 5843225776768365182277811583496048480, 71094364834113573421699535163954054191100]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-166 +26 \sqrt{33}})\) |
$C_2$, $D_{4}$ |
1.23.aj $\times$ 2.23.an_dc |
| 3.23.aw_in_abzc |
$3$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 22 x + 221 x^{2} - 1328 x^{3} + 5083 x^{4} - 11638 x^{5} + 12167 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$2$ |
$[2, 488, 12122, 279228, 6430862, 148020344, 3404892262, 78311707388, 1801154415770, 41426501643288]$ |
$4484$ |
$[4484, 136582640, 1794262228508, 21866694911609600, 266408201234571699844, 3243810220245572661555440, 39472358691463371921423321884, 480255192404117184487391560908800, 5843216736785530192711518591494178116, 71094332366924153092974716813848523145200]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.2343728.1 |
$S_4\times C_2$ |
simple |
| 3.23.aw_in_abzb |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 9 x + 23 x^{2} )( 1 - 13 x + 81 x^{2} - 299 x^{3} + 529 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$2$ |
$[2, 488, 12125, 279316, 6432177, 148033853, 3405000986, 78312451924, 1801159013045, 41426528017843]$ |
$4485$ |
$[4485, 136608615, 1794788122140, 21873676490812575, 266462721100059790800, 3244106296809452250736560, 39473619170681505538855064055, 480259758414341313913185619599375, 5843231651065839470915034402216080460, 71094377629768809752407581386782007059200]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-170 +26 \sqrt{29}})\) |
$C_2$, $D_{4}$ |
1.23.aj $\times$ 2.23.an_dd |
| 3.23.aw_io_abzl |
$3$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 22 x + 222 x^{2} - 1337 x^{3} + 5106 x^{4} - 11638 x^{5} + 12167 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$2$ |
$[2, 490, 12161, 279578, 6432752, 148027321, 3404919282, 78311902642, 1801155908972, 41426509622670]$ |
$4499$ |
$[4499, 137188007, 1800065686991, 21894088246506971, 266486467838989230569, 3243963113127485945717807, 39472671948250986119517469891, 480256389840624485641092893769075, 5843221580966327469378901602517414208, 71094346060786271174886236411051512486367]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.1006556771.2 |
$S_4\times C_2$ |
simple |
| 3.23.aw_io_abzk |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 4 x + 23 x^{2} )( 1 - 9 x + 23 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$2$ |
$[2, 490, 12164, 279666, 6434062, 148040620, 3405023554, 78312583586, 1801159816172, 41426529895450]$ |
$4500$ |
$[4500, 137214000, 1800591768000, 21901069575000000, 266540777012295562500, 3244254578261976964608000, 39473880803843878445301679500, 480260565857341590256158300000000, 5843234256537895635557271282005448000, 71094380852037326861596837323207336750000]$ |
$None$ |
$1$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-19}) \) |
$C_2$, $C_2$ |
1.23.aj 2 $\times$ 1.23.ae |
| 3.23.aw_ip_abzv |
$3$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 22 x + 223 x^{2} - 1347 x^{3} + 5129 x^{4} - 11638 x^{5} + 12167 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$2$ |
$[2, 492, 12197, 279836, 6433207, 148019145, 3404825216, 78311319396, 1801153175195, 41426497145507]$ |
$4513$ |
$[4513, 137768351, 1805348874844, 21914201142006719, 266505266925446872048, 3243783930808944944698928, 39471581442512643698256350471, 480252812996839244202985639633775, 5843212712169828261728714380882050364, 71094324648032871498566508650751646712576]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.1392115799.1 |
$S_4\times C_2$ |
simple |
| 3.23.aw_ip_abzu |
$3$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 22 x + 223 x^{2} - 1346 x^{3} + 5129 x^{4} - 11638 x^{5} + 12167 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$2$ |
$[2, 492, 12200, 279924, 6434512, 148032240, 3404925358, 78311945564, 1801156556138, 41426513634792]$ |
$4514$ |
$[4514, 137794364, 1805875078646, 21921181198999344, 266559360698935288594, 3244070905245034752951644, 39472742392793622001634813302, 480256653071887456952740347065088, 5843223680473010013450927992397349706, 71094352946211809253640820466758799848444]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.1192782528.1 |
$S_4\times C_2$ |
simple |
| 3.23.aw_ip_abzt |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 9 x + 23 x^{2} )( 1 - 13 x + 83 x^{2} - 299 x^{3} + 529 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$2$ |
$[2, 492, 12203, 280012, 6435817, 148045329, 3405025192, 78312563684, 1801159794449, 41426528197107]$ |
$4515$ |
$[4515, 137820375, 1806401347380, 21928162286559375, 266613459226638913200, 3244357759024573999038000, 39473899786985947310825588805, 480260443804406065546525132959375, 5843234186065367837900250045030505620, 71094377937417127735866067458289490400000]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-178 +26 \sqrt{21}})\) |
$C_2$, $D_{4}$ |
1.23.aj $\times$ 2.23.an_df |
| 3.23.aw_iq_acaf |
$3$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
|
✓ |
|
✓ |
? |
$1 - 22 x + 224 x^{2} - 1357 x^{3} + 5152 x^{4} - 11638 x^{5} + 12167 x^{6}$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$3$ |
$0$ |
$2$ |
$[2, 494, 12233, 280090, 6433542, 148009337, 3404719292, 78310712194, 1801150931324, 41426491442554]$ |
$4527$ |
$[4527, 138349647, 1810637756847, 21934015707770091, 266519120057740247337, 3243569015935875165105519, 39470353499691040171776659343, 480249089259888664611606612705075, 5843205432707769285217698795771582144, 71094314860876793356590512459045722260447]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.411022075.2 |
$S_4\times C_2$ |
simple |
| 3.23.aw_iq_acae |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 8 x + 23 x^{2} )( 1 - 14 x + 89 x^{2} - 322 x^{3} + 529 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$2$ |
$[2, 494, 12236, 280178, 6434842, 148022228, 3404815318, 78311284322, 1801153805108, 41426504470814]$ |
$4528$ |
$[4528, 138375680, 1811164083904, 21940994499020800, 266572998437355700208, 3243851499665128188354560, 39471466707136236537504191696, 480252597907962085965781934284800, 5843214755702267736827889984870572608, 71094337219397061732343776641749734310400]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-34 +8 \sqrt{6}})\) |
$C_2$, $D_{4}$ |
1.23.ai $\times$ 2.23.ao_dl |
| 3.23.aw_iq_acad |
$3$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 22 x + 224 x^{2} - 1355 x^{3} + 5152 x^{4} - 11638 x^{5} + 12167 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$2$ |
$[2, 494, 12239, 280266, 6436142, 148035113, 3404911036, 78311848418, 1801156537268, 41426515604034]$ |
$4529$ |
$[4529, 138401711, 1811690475833, 21947974322835659, 266626881589741158199, 3244133862753538254620351, 39472576358216165996879891081, 480256057310318463409012826556851, 5843223619253027295158151496887621824, 71094356325736190868731173178776674170111]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.1321324619.1 |
$A_4\times C_2$ |
simple |
| 3.23.aw_iq_acac |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 9 x + 23 x^{2} )( 1 - 13 x + 84 x^{2} - 299 x^{3} + 529 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$2$ |
$[2, 494, 12242, 280354, 6437442, 148047992, 3405006446, 78312404482, 1801159127822, 41426524843534]$ |
$4530$ |
$[4530, 138427740, 1812216932640, 21954955179247200, 266680769519212183650, 3244416105258170524154880, 39473682453246859480811247870, 480259467467949711807513449942400, 5843232023420446476138172014453542880, 71094372182162290755840586044159739388700]$ |
$None$ |
$1$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-182 +26 \sqrt{17}})\) |
$C_2$, $D_{4}$ |
1.23.aj $\times$ 2.23.an_dg |
| 3.23.aw_ir_acao |
$3$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 22 x + 225 x^{2} - 1366 x^{3} + 5175 x^{4} - 11638 x^{5} + 12167 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$2$ |
$[2, 496, 12272, 280428, 6435052, 148010596, 3404693938, 78310609820, 1801151680046, 41426503189036]$ |
$4542$ |
$[4542, 138957948, 1816458854922, 21960510012207216, 266581691987972792142, 3243596627864919477833244, 39470059593764327916287932458, 480248461449294341158084920880896, 5843207861674666241771931654862245654, 71094335019665046439306034548883099739708]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.1108246464.1 |
$S_4\times C_2$ |
simple |
| 3.23.aw_ir_acan |
$3$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 22 x + 225 x^{2} - 1365 x^{3} + 5175 x^{4} - 11638 x^{5} + 12167 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$2$ |
$[2, 496, 12275, 280516, 6436347, 148023277, 3404785554, 78311120628, 1801153925099, 41426511212091]$ |
$4543$ |
$[4543, 138983999, 1816985370508, 21967488578046319, 266635359771532381168, 3243874500256400201904944, 39471121664207816317658420189, 480251594036143765878840599355631, 5843215144968184778878353052784930236, 71094348788475867567602845815142109598464]$ |
$None$ |
$1$ |
$2$ |
$2$ |
$1$ |
6.0.1812258679.1 |
$S_4\times C_2$ |
simple |
| 3.23.aw_ir_acam |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 8 x + 23 x^{2} )( 1 - 14 x + 90 x^{2} - 322 x^{3} + 529 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$2$ |
$[2, 496, 12278, 280604, 6437642, 148035952, 3404876862, 78311623420, 1801156029554, 41426517373296]$ |
$4544$ |
$[4544, 139010048, 1817511950912, 21974468178477056, 266689032350853700544, 3244152252081269342019584, 39472180178332293828683799616, 480254677475099551401650832801792, 5843221972145488345017783228569415104, 71094359362063254822390494808856716320768]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-22 +2 \sqrt{5}})\) |
$C_2$, $D_{4}$ |
1.23.ai $\times$ 2.23.ao_dm |
| 3.23.aw_ir_acal |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 9 x + 23 x^{2} )( 1 - 13 x + 85 x^{2} - 299 x^{3} + 529 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$2$ |
$[2, 496, 12281, 280692, 6438937, 148048621, 3404967862, 78312118196, 1801157993429, 41426521673971]$ |
$4545$ |
$[4545, 139036095, 1818038596140, 21981448813532175, 266742709730253471600, 3244429883396733155158320, 39473235136455346558249073235, 480257711767160190726785430108975, 5843228343266986326257979405330678780, 71094366742695305772458221652309737593600]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-186 +26 \sqrt{13}})\) |
$C_2$, $D_{4}$ |
1.23.aj $\times$ 2.23.an_dh |
| 3.23.aw_is_acay |
$3$ |
$\F_{23}$ |
$23$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 7 x + 23 x^{2} )( 1 - 15 x + 98 x^{2} - 345 x^{3} + 529 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$2$ |
$[2, 498, 12308, 280674, 6435142, 147997356, 3404561722, 78309931970, 1801150295324, 41426510508018]$ |
$4556$ |
$[4556, 139541168, 1821759462848, 21979728282373056, 266585443173655141756, 3243306556454999711166464, 39468526900289286522868864564, 480244304486641330202298302967552, 5843203369432517605014798526304526656, 71094347580176791451799651413789902718768]$ |
$None$ |
$0$ |
$8$ |
$12$ |
$6$ |
\(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-3}, \sqrt{17})\) |
$C_2$, $C_2^2$ |
1.23.ah $\times$ 2.23.ap_du |
| 3.23.aw_is_acax |
$3$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 22 x + 226 x^{2} - 1375 x^{3} + 5198 x^{4} - 11638 x^{5} + 12167 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$2$ |
$[2, 498, 12311, 280762, 6436432, 148009833, 3404649250, 78310390226, 1801152072260, 41426515736358]$ |
$4557$ |
$[4557, 139567239, 1822286102553, 21986705596018779, 266638895595308819247, 3243579938145113146735743, 39469541552566786342430931693, 480247114772583627424736085624627, 5843209134077744319625892429755651392, 71094356552824358812240542221662732488879]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.651528243.1 |
$S_4\times C_2$ |
simple |
| 3.23.aw_is_acaw |
$3$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 22 x + 226 x^{2} - 1374 x^{3} + 5198 x^{4} - 11638 x^{5} + 12167 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$2$ |
$[2, 498, 12314, 280850, 6437722, 148022304, 3404736470, 78310840482, 1801153709606, 41426519134658]$ |
$4558$ |
$[4558, 139593308, 1822812807016, 21993683946249056, 266692352831520365038, 3243853199287119272656832, 39470552648261328279518346578, 480249876007481667892450720029056, 5843214445873942394508029117026639384, 71094362384835330131654903250949767568988]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.1108002176.1 |
$S_4\times C_2$ |
simple |
