| 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 |
| 2.41.ay_is |
$2$ |
$\F_{41}$ |
$41$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 12 x + 41 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$18$ |
$[18, 1558, 68418, 2824798, 115865298, 4750252918, 194755685058, 7984936067518, 327382006596498, 13422659732208598]$ |
$900$ |
$[900, 2624400, 4715568900, 7982207078400, 13423713390562500, 22564196541890816400, 37929502028360121480900, 63759117458480055518822400, 107178954605339646251452752900, 180167788621537529528113580250000]$ |
$3$ |
$3$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-5}) \) |
$C_2$ |
1.41.am 2 |
| 2.41.ax_if |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 23 x + 213 x^{2} - 943 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$19$ |
$[19, 1579, 68623, 2825859, 115863654, 4750146163, 194754244879, 7984922497059, 327381904738843, 13422659112195054]$ |
$929$ |
$[929, 2657869, 4729562225, 7985197966709, 13423522599357184, 22563689430974477725, 37929221546754655472969, 63759009099352047982182629, 107178921258982243104814541225, 180167780299306908406769231785984]$ |
$1$ |
$1$ |
$2$ |
$2$ |
$1$ |
4.0.6725.1 |
$D_{4}$ |
simple |
| 2.41.ax_ig |
$2$ |
$\F_{41}$ |
$41$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 12 x + 41 x^{2} )( 1 - 11 x + 41 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$19$ |
$[19, 1581, 68692, 2827121, 115880099, 4750315938, 194755697099, 7984932910561, 327381965957092, 13422659378509101]$ |
$930$ |
$[930, 2661660, 4734384480, 7988770203840, 13425428245523250, 22564495898144928000, 37929504373404829279170, 63759092250397350790460160, 107178941300730830215779719520, 180167783873949608484309884041500]$ |
$0$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-43}) \) |
$C_2$, $C_2$ |
1.41.am $\times$ 1.41.al |
| 2.41.aw_hs |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 22 x + 200 x^{2} - 902 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$20$ |
$[20, 1598, 68768, 2826054, 115854640, 4750013774, 194753118244, 7984915998910, 327381883480484, 13422659145789518]$ |
$958$ |
$[958, 2688148, 4739456878, 7985745779152, 13422478261803358, 22563060575280725812, 37929002130195073152142, 63758957212136780899365888, 107178914299380148014018284302, 180167780750233967171674801087348]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
4.0.21312.1 |
$D_{4}$ |
simple |
| 2.41.aw_ht |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 22 x + 201 x^{2} - 902 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$20$ |
$[20, 1600, 68834, 2827188, 115868280, 4750141798, 194754106616, 7984922497764, 327381921496946, 13422659361415440]$ |
$959$ |
$[959, 2691913, 4744061756, 7988954416793, 13424058719930719, 22563668704226881168, 37929194619491139697439, 63759009104968249758154217, 107178926745281611659133934204, 180167783644507226540139088943833]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
4.0.45632.1 |
$D_{4}$ |
simple |
| 2.41.aw_hu |
$2$ |
$\F_{41}$ |
$41$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 12 x + 41 x^{2} )( 1 - 10 x + 41 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$20$ |
$[20, 1602, 68900, 2828318, 115881700, 4750263522, 194754969940, 7984927070398, 327381935106740, 13422659313990402]$ |
$960$ |
$[960, 2695680, 4748667840, 7992152064000, 13425613738584000, 22564246912784478720, 37929362755568712853440, 63759045617100820905984000, 107178931200881801984319898560, 180167783007937079057781079872000]$ |
$8$ |
$8$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.41.am $\times$ 1.41.ak |
| 2.41.aw_hv |
$2$ |
$\F_{41}$ |
$41$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 11 x + 41 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$20$ |
$[20, 1604, 68966, 2829444, 115894900, 4750378958, 194755709140, 7984929753604, 327381925317686, 13422659024809604]$ |
$961$ |
$[961, 2699449, 4753275136, 7995338725609, 13427143319553601, 22564795258370560000, 37929506718449682063121, 63759067042324612439597769, 107178927996123665741426718976, 180167779126361812543840365886009]$ |
$2$ |
$2$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-43}) \) |
$C_2$ |
1.41.al 2 |
| 2.41.av_hf |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 21 x + 187 x^{2} - 861 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$21$ |
$[21, 1615, 68859, 2825611, 115842426, 4749901567, 194752569711, 7984915734451, 327381902340129, 13422659285930830]$ |
$987$ |
$[987, 2715237, 4745662803, 7984493803125, 13421063357891952, 22562527591813070925, 37928895301445060277267, 63758955100453314303853125, 107178920473686561823608718083, 180167782631303010314312004218112]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
4.0.16317.1 |
$D_{4}$ |
simple |
| 2.41.av_hg |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
|
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 21 x + 188 x^{2} - 861 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$21$ |
$[21, 1617, 68922, 2826625, 115853661, 4749997902, 194753261493, 7984920322369, 327381934393962, 13422659539712577]$ |
$988$ |
$[988, 2718976, 4750051072, 7987361780736, 13422365037551548, 22562985186608349184, 37929030028367375781052, 63758991734613322876145664, 107178930967532391731290738432, 180167786037728988982209161733376]$ |
$8$ |
$8$ |
$4$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}, \sqrt{17})\) |
$C_2^2$ |
simple |
| 2.41.av_hh |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 21 x + 189 x^{2} - 861 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$21$ |
$[21, 1619, 68985, 2827635, 115864686, 4750088555, 194753847729, 7984923400963, 327381948777429, 13422659617179374]$ |
$989$ |
$[989, 2722717, 4754440469, 7990218721333, 13423642423672784, 22563415794468383293, 37929144199923688788701, 63759016316936981557022373, 107178935676419235326651791301, 180167787077539419765035434258432]$ |
$3$ |
$3$ |
$2$ |
$2$ |
$1$ |
4.0.188773.1 |
$D_{4}$ |
simple |
| 2.41.av_hi |
$2$ |
$\F_{41}$ |
$41$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 12 x + 41 x^{2} )( 1 - 9 x + 41 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$21$ |
$[21, 1621, 69048, 2828641, 115875501, 4750173538, 194754329301, 7984925003521, 327381946348968, 13422659535300901]$ |
$990$ |
$[990, 2726460, 4758831000, 7993064629440, 13424895517794750, 22563819472715136000, 37929237987933420172110, 63759029113231317298287360, 107178934881384557380968471000, 180167785978512555597338603941500]$ |
$6$ |
$6$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-83}) \) |
$C_2$, $C_2$ |
1.41.am $\times$ 1.41.aj |
| 2.41.av_hj |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 21 x + 191 x^{2} - 861 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$21$ |
$[21, 1623, 69111, 2829643, 115886106, 4750252863, 194754707091, 7984925163283, 327381927962481, 13422659310827598]$ |
$991$ |
$[991, 2730205, 4763222671, 7995899509605, 13426124321479216, 22564196278680584005, 37929311564218773696631, 63759030388920630320850405, 107178928861980900446883344911, 180167782965483875237718100000000]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.55125.1 |
$C_4$ |
simple |
| 2.41.av_hk |
$2$ |
$\F_{41}$ |
$41$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 11 x + 41 x^{2} )( 1 - 10 x + 41 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$21$ |
$[21, 1625, 69174, 2830641, 115896501, 4750326542, 194754981981, 7984923913441, 327381894467334, 13422658960290905]$ |
$992$ |
$[992, 2733952, 4767615488, 7998723366400, 13427328836310752, 22564546269706854400, 37929365100604809915872, 63759020409046519698585600, 107178917896275891249947068928, 180167778260349305937542945110912]$ |
$0$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.41.al $\times$ 1.41.ak |
| 2.41.au_gt |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 20 x + 175 x^{2} - 820 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$22$ |
$[22, 1632, 68962, 2825636, 115839302, 4749905142, 194753078822, 7984922524228, 327381954578482, 13422659541937152]$ |
$1017$ |
$[1017, 2742849, 4752762372, 7984567838601, 13420701599035977, 22562544573642827664, 37928994452577705608217, 63759009316294399477055625, 107178937575579509291106372612, 180167786067588689632148122509729]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.352016.1 |
$D_{4}$ |
simple |
| 2.41.au_gu |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 20 x + 176 x^{2} - 820 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$22$ |
$[22, 1634, 69022, 2826534, 115848302, 4749973058, 194753505542, 7984925174974, 327381974247862, 13422659707241954]$ |
$1018$ |
$[1018, 2746564, 4756935850, 7987106988304, 13421744275906378, 22562867174484482500, 37929077557742789172058, 63759030482297998070267904, 107178944014979710786024358650, 180167788286418766789183391503684]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.555264.3 |
$D_{4}$ |
simple |
| 2.41.au_gv |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 20 x + 177 x^{2} - 820 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$22$ |
$[22, 1636, 69082, 2827428, 115857102, 4750035886, 194753844622, 7984926680388, 327381981833482, 13422659764981956]$ |
$1019$ |
$[1019, 2750281, 4761110384, 7989635062025, 13422763808553979, 22563165608669092096, 37929143594698973338859, 63759042502908302154118025, 107178946498374746323041553904, 180167789061443155593076886768041]$ |
$14$ |
$14$ |
$2$ |
$2$ |
$1$ |
4.0.37025.1 |
$D_{4}$ |
simple |
| 2.41.au_gw |
$2$ |
$\F_{41}$ |
$41$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 12 x + 41 x^{2} )( 1 - 8 x + 41 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$22$ |
$[22, 1638, 69142, 2828318, 115865702, 4750093638, 194754096902, 7984927070398, 327381978057142, 13422659728370598]$ |
$1020$ |
$[1020, 2754000, 4765285980, 7992152064000, 13423760198305500, 22563439933446594000, 37929192727070946323580, 63759045617100820905984000, 107178945262069042306587481020, 180167788570021362285822821250000]$ |
$20$ |
$20$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.41.am $\times$ 1.41.ai |
| 2.41.au_gx |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 20 x + 179 x^{2} - 820 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$22$ |
$[22, 1640, 69202, 2829204, 115874102, 4750146326, 194754263222, 7984926374884, 327381963636322, 13422659610423800]$ |
$1021$ |
$[1021, 2757721, 4769462644, 7994657998489, 13424733446508901, 22563690206075600656, 37929225118485592128901, 63759040063468174258696809, 107178940540952785470798453364, 180167786986861654353904538956201]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.363024.2 |
$D_{4}$ |
simple |
| 2.41.au_gy |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 20 x + 180 x^{2} - 820 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$22$ |
$[22, 1642, 69262, 2830086, 115882302, 4750193962, 194754344422, 7984924623678, 327381939284182, 13422659423960202]$ |
$1022$ |
$[1022, 2761444, 4773640382, 7997152869776, 13425683554533502, 22563916483823527204, 37929240932572054753982, 63759026080220113287680000, 107178932568501927486017183582, 180167784484024282754831215495204]$ |
$6$ |
$6$ |
$2$ |
$2$ |
$1$ |
4.0.194816.2 |
$D_{4}$ |
simple |
| 2.41.au_gz |
$2$ |
$\F_{41}$ |
$41$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 11 x + 41 x^{2} )( 1 - 9 x + 41 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$22$ |
$[22, 1644, 69322, 2830964, 115890302, 4750236558, 194754341342, 7984921846564, 327381905709562, 13422659181601404]$ |
$1023$ |
$[1023, 2765169, 4777819200, 7999636682169, 13426610523770103, 22564118823966720000, 37929240332961803300343, 63759003905183541132702249, 107178921576778189769127604800, 180167781230924704199688292061409]$ |
$9$ |
$9$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-83}) \) |
$C_2$, $C_2$ |
1.41.al $\times$ 1.41.aj |
| 2.41.au_ha |
$2$ |
$\F_{41}$ |
$41$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 10 x + 41 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$22$ |
$[22, 1646, 69382, 2831838, 115898102, 4750274126, 194754254822, 7984918073278, 327381863616982, 13422658895772206]$ |
$1024$ |
$[1024, 2768896, 4781999104, 8002109440000, 13427514355631104, 22564297283790585856, 37929223483288697979904, 63758973775802534461440000, 107178907796429068502685942784, 180167777394336803493908044988416]$ |
$10$ |
$10$ |
$16$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
1.41.ak 2 |
| 2.41.at_gg |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 19 x + 162 x^{2} - 779 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$23$ |
$[23, 1645, 68960, 2824401, 115827303, 4749867442, 194753332223, 7984925474721, 327381955721120, 13422659340089805]$ |
$1046$ |
$[1046, 2763532, 4752605600, 7981080416000, 13419311614315606, 22562365498830956800, 37929043803405427959926, 63759032875749307428224000, 107178937949658149141755018400, 180167783358260511027966124384012]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.558092.1 |
$D_{4}$ |
simple |
| 2.41.at_gh |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 19 x + 163 x^{2} - 779 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$23$ |
$[23, 1647, 69017, 2825195, 115834618, 4749919407, 194753678821, 7984928190259, 327381979946747, 13422659540145102]$ |
$1047$ |
$[1047, 2767221, 4756563927, 7983324663381, 13420159017819312, 22562612330832089469, 37929111304691614287543, 63759054559127439389730309, 107178945880691649347053549407, 180167786043534625378694696453376]$ |
$7$ |
$7$ |
$2$ |
$2$ |
$1$ |
4.0.1123949.1 |
$D_{4}$ |
simple |
| 2.41.at_gi |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
|
✓ |
|
✓ |
✓ |
$1 - 19 x + 164 x^{2} - 779 x^{3} + 1681 x^{4}$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$2$ |
$0$ |
$23$ |
$[23, 1649, 69074, 2825985, 115841743, 4749966830, 194753952535, 7984930020673, 327381995395970, 13422659664036449]$ |
$1048$ |
$[1048, 2770912, 4760523232, 7985557794688, 13420984426801048, 22562837588624171008, 37929164611481170118488, 63759069174851069175111168, 107178950938488724582675057888, 180167787706485985312147331307232]$ |
$6$ |
$6$ |
$2$ |
$2$ |
$1$ |
4.0.357192.2 |
$D_{4}$ |
simple |
| 2.41.at_gj |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 19 x + 165 x^{2} - 779 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$23$ |
$[23, 1651, 69131, 2826771, 115848678, 4750009723, 194754154163, 7984930992771, 327382002674471, 13422659722105326]$ |
$1049$ |
$[1049, 2774605, 4764483521, 7987779813845, 13421787842370304, 22563041329388594125, 37929203879206050681689, 63759076936981080358956005, 107178953321338722495950327441, 180167788485924748792019195392000]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.1518005.3 |
$D_{4}$ |
simple |
| 2.41.at_gk |
$2$ |
$\F_{41}$ |
$41$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 12 x + 41 x^{2} )( 1 - 7 x + 41 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$23$ |
$[23, 1653, 69188, 2827553, 115855423, 4750048098, 194754284503, 7984931133313, 327382002383828, 13422659724515973]$ |
$1050$ |
$[1050, 2778300, 4768444800, 7989990724800, 13422569265656250, 22563223610314060800, 37929229263299849875050, 63759078059195325925036800, 107178953226187440605312188800, 180167788518282043328992436437500]$ |
$10$ |
$10$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-115}) \) |
$C_2$, $C_2$ |
1.41.am $\times$ 1.41.ah |
| 2.41.at_gl |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 19 x + 167 x^{2} - 779 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$23$ |
$[23, 1655, 69245, 2828331, 115861978, 4750081967, 194754344353, 7984930469011, 327381995121515, 13422659681255630]$ |
$1051$ |
$[1051, 2781997, 4772407075, 7992190531525, 13423328697807856, 22563384488596700725, 37929240919197854613451, 63759072754788643729282725, 107178950848637129350740973675, 180167787937613187857793841837312]$ |
$6$ |
$6$ |
$2$ |
$2$ |
$1$ |
4.0.1233477.1 |
$D_{4}$ |
simple |
| 2.41.at_gm |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 19 x + 168 x^{2} - 779 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$23$ |
$[23, 1657, 69302, 2829105, 115868343, 4750111342, 194754334511, 7984929026529, 327381981480902, 13422659602134777]$ |
$1052$ |
$[1052, 2785696, 4776370352, 7994379238016, 13424066139994012, 22563524021440190464, 37929239002337100008348, 63759061236672872416684544, 107178946382946495300415435952, 180167786875600914652271574076576]$ |
$12$ |
$12$ |
$2$ |
$2$ |
$1$ |
4.0.238136.1 |
$D_{4}$ |
simple |
| 2.41.at_gn |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 19 x + 169 x^{2} - 779 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$23$ |
$[23, 1659, 69359, 2829875, 115874518, 4750136235, 194754255775, 7984926832483, 327381962051255, 13422659496787374]$ |
$1053$ |
$[1053, 2789397, 4780334637, 7996556848293, 13424781593403648, 22563642266055873333, 37929223668156425384013, 63759043717376867798801733, 107178940022030704517791309533, 180167785461558591280194101317632]$ |
$9$ |
$9$ |
$2$ |
$2$ |
$1$ |
4.0.641693.1 |
$D_{4}$ |
simple |
| 2.41.at_go |
$2$ |
$\F_{41}$ |
$41$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 11 x + 41 x^{2} )( 1 - 8 x + 41 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$23$ |
$[23, 1661, 69416, 2830641, 115880503, 4750156658, 194754108943, 7984923913441, 327381937417736, 13422659374671101]$ |
$1054$ |
$[1054, 2793100, 4784299936, 7998723366400, 13425475059245854, 22563739279662880000, 37929195072096531135454, 63759020409046519698585600, 107178931957461386093389910176, 180167783822433442599517794527500]$ |
$5$ |
$5$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.41.al $\times$ 1.41.ai |
| 2.41.at_gp |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 19 x + 171 x^{2} - 779 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$23$ |
$[23, 1663, 69473, 2831403, 115886298, 4750172623, 194753894813, 7984920295923, 327381908161403, 13422659245067598]$ |
$1055$ |
$[1055, 2796805, 4788266255, 8000878796405, 13426146538750000, 22563815119488249805, 37929153369600036433055, 63758991523444769269272005, 107178922379466635845639789655, 180167782082809772797913620000000]$ |
$7$ |
$7$ |
$10$ |
$10$ |
$1$ |
\(\Q(\zeta_{5})\) |
$C_4$ |
simple |
| 2.41.at_gq |
$2$ |
$\F_{41}$ |
$41$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 10 x + 41 x^{2} )( 1 - 9 x + 41 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$23$ |
$[23, 1665, 69530, 2832161, 115891903, 4750184142, 194753614183, 7984916006401, 327381874859210, 13422659117082705]$ |
$1056$ |
$[1056, 2800512, 4792233600, 8003023142400, 13426796033165856, 22563869842767052800, 37929098716111537778976, 63758957271951626794137600, 107178911476931020195175414400, 180167780364912187477387921418112]$ |
$0$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-83}) \) |
$C_2$, $C_2$ |
1.41.ak $\times$ 1.41.aj |
| 2.41.as_ft |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
|
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 18 x + 149 x^{2} - 738 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$24$ |
$[24, 1656, 68922, 2823076, 115818924, 4749877158, 194753758524, 7984926792196, 327381934393962, 13422659078648376]$ |
$1075$ |
$[1075, 2781025, 4749990700, 7977339621225, 13418341001726875, 22562411650086490000, 37929126827025765085675, 63759043395676530206174025, 107178930967531938606221248300, 180167779849021299747820853550625]$ |
$6$ |
$6$ |
$4$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}, \sqrt{14})\) |
$C_2^2$ |
simple |
| 2.41.as_fu |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 18 x + 150 x^{2} - 738 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$24$ |
$[24, 1658, 68976, 2823774, 115824864, 4749918554, 194754074280, 7984929703870, 327381960521160, 13422659274065018]$ |
$1076$ |
$[1076, 2784688, 4753734644, 7979311827712, 13419029081485556, 22562608280459359792, 37929188321937816103604, 63759066645192640858533888, 107178939521105083174709430644, 180167782472032291684741320352048]$ |
$6$ |
$6$ |
$2$ |
$2$ |
$1$ |
4.0.116272.1 |
$D_{4}$ |
simple |
| 2.41.as_fv |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 18 x + 151 x^{2} - 738 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$24$ |
$[24, 1660, 69030, 2824468, 115830624, 4749955918, 194754329808, 7984931931364, 327381980122998, 13422659411842540]$ |
$1077$ |
$[1077, 2788353, 4757479488, 7981272881433, 13419696318179757, 22562785758466003968, 37929238087133082166413, 63759084431578340749669737, 107178945938393199920974352448, 180167784321373025185937304447633]$ |
$12$ |
$12$ |
$2$ |
$2$ |
$1$ |
4.0.166032.2 |
$D_{4}$ |
simple |
| 2.41.as_fw |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 18 x + 152 x^{2} - 738 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$24$ |
$[24, 1662, 69084, 2825158, 115836204, 4749989262, 194754525864, 7984933498558, 327381993703944, 13422659500021902]$ |
$1078$ |
$[1078, 2792020, 4761225238, 7983222786000, 13420342712719558, 22562944141231643380, 37929276269854713209158, 63759096945513747017856000, 107178950384549954029993308358, 180167785504974562533819980360500]$ |
$22$ |
$22$ |
$2$ |
$2$ |
$1$ |
4.0.38720.3 |
$D_{4}$ |
simple |
| 2.41.as_fx |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 18 x + 153 x^{2} - 738 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$24$ |
$[24, 1664, 69138, 2825844, 115841604, 4750018598, 194754663204, 7984934429284, 327382001764578, 13422659546485904]$ |
$1079$ |
$[1079, 2795689, 4764971900, 7985161545049, 13420968266033159, 22563083485887552400, 37929303017347036212359, 63759104377295843693028969, 107178953023456159915347203900, 180167786128645038389263878156409]$ |
$6$ |
$6$ |
$2$ |
$2$ |
$1$ |
4.0.3342400.2 |
$D_{4}$ |
simple |
| 2.41.as_fy |
$2$ |
$\F_{41}$ |
$41$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 12 x + 41 x^{2} )( 1 - 6 x + 41 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$24$ |
$[24, 1666, 69192, 2826526, 115846824, 4750043938, 194754742584, 7984934747326, 327382004801592, 13422659558959426]$ |
$1080$ |
$[1080, 2799360, 4768719480, 7987089162240, 13421572979067000, 22563203849571168000, 37929318476855600472120, 63759106916838493051944960, 107178954017719783117741454520, 180167786296072881445675492704000]$ |
$46$ |
$46$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-2}) \) |
$C_2$, $C_2$ |
1.41.am $\times$ 1.41.ag |
| 2.41.as_fz |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 18 x + 155 x^{2} - 738 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$24$ |
$[24, 1668, 69246, 2827204, 115851864, 4750065294, 194754764760, 7984934476420, 327382003307790, 13422659545009668]$ |
$1081$ |
$[1081, 2803033, 4772467984, 7989005641257, 13422156852785881, 22563305289426199552, 37929322795627223636329, 63759104753672447352926793, 107178953528675942319813923344, 180167786108830036107583218200473]$ |
$12$ |
$12$ |
$2$ |
$2$ |
$1$ |
4.0.194112.5 |
$D_{4}$ |
simple |
| 2.41.as_ga |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 18 x + 156 x^{2} - 738 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$24$ |
$[24, 1670, 69300, 2827878, 115856724, 4750082678, 194754730488, 7984933640254, 327381997772088, 13422659512046390]$ |
$1082$ |
$[1082, 2806708, 4776217418, 7990910985808, 13422719888173082, 22563387862602739348, 37929316120910038511978, 63759098076945360956347392, 107178951716386911480770805098, 180167785666375184195028472013908]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.2750272.1 |
$D_{4}$ |
simple |
| 2.41.as_gb |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 18 x + 157 x^{2} - 738 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$24$ |
$[24, 1672, 69354, 2828548, 115861404, 4750096102, 194754640524, 7984932262468, 327381988679514, 13422659467322152]$ |
$1083$ |
$[1083, 2810385, 4779967788, 7992805199625, 13423262086230483, 22563451626257373840, 37929298599953540648643, 63759087075421802837039625, 107178948739642122094446884268, 180167785066056966675074312504625]$ |
$22$ |
$22$ |
$2$ |
$2$ |
$1$ |
4.0.2295360.4 |
$D_{4}$ |
simple |
| 2.41.as_gc |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 18 x + 158 x^{2} - 738 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$24$ |
$[24, 1674, 69408, 2829214, 115865904, 4750105578, 194754495624, 7984930366654, 327381976511208, 13422659417932554]$ |
$1084$ |
$[1084, 2814064, 4783719100, 7994688286464, 13423783447978684, 22563496637553295600, 37929270380008636703164, 63759071937483269494861824, 107178944755958165574442479100, 180167784403117205421784853119984]$ |
$24$ |
$24$ |
$2$ |
$2$ |
$1$ |
4.0.111600.3 |
$D_{4}$ |
simple |
| 2.41.as_gd |
$2$ |
$\F_{41}$ |
$41$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 11 x + 41 x^{2} )( 1 - 7 x + 41 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$24$ |
$[24, 1676, 69462, 2829876, 115870224, 4750111118, 194754296544, 7984927976356, 327381961744422, 13422659370816476]$ |
$1085$ |
$[1085, 2817745, 4787471360, 7996560250105, 13424283974457125, 22563522953660416000, 37929231608327693590565, 63759052851128198269688745, 107178939921578795770045629440, 180167783770694125006066333338625]$ |
$12$ |
$12$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-115}) \) |
$C_2$, $C_2$ |
1.41.al $\times$ 1.41.ah |
| 2.41.as_ge |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 18 x + 160 x^{2} - 738 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$24$ |
$[24, 1678, 69516, 2830534, 115874364, 4750112734, 194754044040, 7984925115070, 327381944852520, 13422659332756318]$ |
$1086$ |
$[1086, 2821428, 4791224574, 7998421094352, 13424763666724206, 22563530631755478612, 37929182432164588426254, 63759030003971981067138048, 107178934391474931616704695694, 180167783259825574516798829600148]$ |
$16$ |
$16$ |
$2$ |
$2$ |
$1$ |
4.0.781632.1 |
$D_{4}$ |
simple |
| 2.41.as_gf |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 18 x + 161 x^{2} - 738 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$24$ |
$[24, 1680, 69570, 2831188, 115878324, 4750110438, 194753738868, 7984921806244, 327381926304978, 13422659310378240]$ |
$1087$ |
$[1087, 2825113, 4794978748, 8000270823033, 13425222525857407, 22563519729022173328, 37929122998774759264543, 63759003583246978501382697, 107178928319344659924873508348, 180167782959452249414726279823433]$ |
$9$ |
$9$ |
$2$ |
$2$ |
$1$ |
4.0.4672.2 |
$D_{4}$ |
simple |
| 2.41.as_gg |
$2$ |
$\F_{41}$ |
$41$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 10 x + 41 x^{2} )( 1 - 8 x + 41 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$24$ |
$[24, 1682, 69624, 2831838, 115882104, 4750104242, 194753381784, 7984918073278, 327381906567384, 13422659310152402]$ |
$1088$ |
$[1088, 2828800, 4798733888, 8002109440000, 13425660552953408, 22563490302651251200, 37929053455415256638528, 63758973775802534461440000, 107178921857613238311108542528, 180167782956420913420611757120000]$ |
$10$ |
$10$ |
$16$ |
$12$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.41.ak $\times$ 1.41.ai |
| 2.41.as_gh |
$2$ |
$\F_{41}$ |
$41$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 9 x + 41 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$24$ |
$[24, 1684, 69678, 2832484, 115885704, 4750094158, 194752973544, 7984913939524, 327381886101438, 13422659338393204]$ |
$1089$ |
$[1089, 2832489, 4802490000, 8003936949129, 13426077749128209, 22563442409840640000, 37928973949344795906369, 63758940768104991107368329, 107178915157433098275355290000, 180167783335487620439204765476809]$ |
$15$ |
$15$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-83}) \) |
$C_2$ |
1.41.aj 2 |
| 2.41.ar_fg |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 17 x + 136 x^{2} - 697 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$25$ |
$[25, 1665, 68854, 2821793, 115814705, 4749919758, 194754129161, 7984925607169, 327381901673926, 13422658911744465]$ |
$1104$ |
$[1104, 2795328, 4745327616, 7973717845248, 13417852287134544, 22562613999085436928, 37929199009791142678224, 63759033933322076439892992, 107178920255583877233036063744, 180167777608726990502351849740608]$ |
$7$ |
$7$ |
$2$ |
$2$ |
$1$ |
4.0.42632.1 |
$D_{4}$ |
simple |
| 2.41.ar_fh |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 17 x + 137 x^{2} - 697 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$25$ |
$[25, 1667, 68905, 2822403, 115819550, 4749954707, 194754440465, 7984928647363, 327381927068305, 13422659084793902]$ |
$1105$ |
$[1105, 2798965, 4748857945, 7975440845125, 13418413507642000, 22562780008557322885, 37929259637816171101945, 63759058209058089612925125, 107178928569244685541462002305, 180167779931510589413014183936000]$ |
$10$ |
$10$ |
$2$ |
$2$ |
$1$ |
4.0.2689965.2 |
$D_{4}$ |
simple |
| 2.41.ar_fi |
$2$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 17 x + 138 x^{2} - 697 x^{3} + 1681 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$25$ |
$[25, 1669, 68956, 2823009, 115824225, 4749986098, 194754702265, 7984931155329, 327381947429596, 13422659211124629]$ |
$1106$ |
$[1106, 2802604, 4752389096, 7977152658944, 13418955038131426, 22562929116813030400, 37929310624670311619906, 63759078234991576274991104, 107178935235163539673658858216, 180167781627204873407109820735084]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.4241900.1 |
$D_{4}$ |
simple |