| 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 |
| 2.81.abk_ss |
$2$ |
$\F_{3^{4}}$ |
$3$ |
|
|
|
|
|
✓ |
✓ |
✓ |
$( 1 - 9 x )^{4}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$2$ |
$0$ |
$2$ |
$0$ |
$2$ |
$46$ |
$[46, 6238, 528526, 43020478, 3486548206, 282427410718, 22876773323086, 1853020016664958, 150094633747317166, 12157665445109791198]$ |
$4096$ |
$[4096, 40960000, 280883040256, 1851890728960000, 12156841915449020416, 79765842700025896960000, 523347195351541271899672576, 3433683501226751295288770560000, 22528399312340227300247719345524736, 147808829244781290288164388889600000000]$ |
$1$ |
$1$ |
$19$ |
$12$ |
$1$ |
\(\Q\) |
Trivial |
1.81.as 2 |
| 2.81.abj_sa |
$2$ |
$\F_{3^{4}}$ |
$3$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 9 x )^{2}( 1 - 17 x + 81 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$47$ |
$[47, 6273, 529202, 43030593, 3486678527, 282428924958, 22876789572047, 1853020179809793, 150094635290706962, 12157665458907527073]$ |
$4160$ |
$[4160, 41184000, 281241309440, 1852326013824000, 12157296301288424000, 79766270364517761024000, 523347567075494241117976640, 3433683803537410211490983424000, 22528399543994754656095934693423360, 147808829412529547052623058652140000000]$ |
$0$ |
$0$ |
$10$ |
$6$ |
$1$ |
\(\Q\), \(\Q(\sqrt{-35}) \) |
Trivial, $C_2$ |
1.81.as $\times$ 1.81.ar |
| 2.81.abi_ri |
$2$ |
$\F_{3^{4}}$ |
$3$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 9 x )^{2}( 1 - 16 x + 81 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$48$ |
$[48, 6306, 529776, 43037886, 3486751728, 282429493218, 22876792283568, 1853020170482046, 150094634844778416, 12157665451759669026]$ |
$4224$ |
$[4224, 41395200, 281545520256, 1852639857868800, 12157551528748543104, 79766430857322168960000, 523347629106371457147222144, 3433683786252907507046626099200, 22528399477063272521228548757444736, 147808829325628280218215120961342080000]$ |
$0$ |
$0$ |
$10$ |
$6$ |
$1$ |
\(\Q\), \(\Q(\sqrt{-17}) \) |
Trivial, $C_2$ |
1.81.as $\times$ 1.81.aq |
| 2.81.abi_rj |
$2$ |
$\F_{3^{4}}$ |
$3$ |
|
|
|
✓ |
|
|
✓ |
✓ |
$( 1 - 17 x + 81 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$48$ |
$[48, 6308, 529878, 43040708, 3486808848, 282430439198, 22876805821008, 1853020342954628, 150094636834096758, 12157665472705262948]$ |
$4225$ |
$[4225, 41409225, 281600035600, 1852761401001225, 12157750704111390625, 79766698031302547865600, 523347938799711239069860225, 3433684105848095743930383465225, 22528399775649284393996212438243600, 147808829580277804007459243690942015625]$ |
$5$ |
$5$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-35}) \) |
$C_2$ |
1.81.ar 2 |
| 2.81.abh_qr |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 33 x + 433 x^{2} - 2673 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$49$ |
$[49, 6339, 530353, 43045379, 3486832054, 282430242723, 22876798682689, 1853020224749699, 150094635360160033, 12157665457610533854]$ |
$4289$ |
$[4289, 41607589, 281851742225, 1852962395954949, 12157831611719411984, 79766642540390218694725, 523347775497815391710508689, 3433683886811970148283183192709, 22528399554419288579456186599040225, 147808829396761137425279399506119491584]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
4.0.29725.1 |
$D_{4}$ |
simple |
| 2.81.abh_qs |
$2$ |
$\F_{3^{4}}$ |
$3$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 17 x + 81 x^{2} )( 1 - 16 x + 81 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$49$ |
$[49, 6341, 530452, 43048001, 3486882049, 282431007458, 22876808532529, 1853020333626881, 150094636388168212, 12157665465557404901]$ |
$4290$ |
$[4290, 41621580, 281904634440, 1853075318814720, 12158005941111137250, 79766858524967437824000, 523348000830632514498085410, 3433684088563591517712280903680, 22528399708717801570887258860748360, 147808829493376537074427048595644759500]$ |
$0$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-17}) \) |
$C_2$, $C_2$ |
1.81.ar $\times$ 1.81.aq |
| 2.81.abg_py |
$2$ |
$\F_{3^{4}}$ |
$3$ |
|
|
✓ |
|
✓ |
|
✓ |
✓ |
$( 1 - 9 x )^{2}( 1 - 14 x + 81 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$50$ |
$[50, 6366, 530642, 43045566, 3486780530, 282429103518, 22876782455570, 1853020045666686, 150094633757983922, 12157665446009349726]$ |
$4352$ |
$[4352, 41779200, 282004486400, 1852970355916800, 12157651951711430912, 79766320794946007040000, 523347404273394977385128192, 3433683554967536294019937075200, 22528399313941250143604756860985600, 147808829255717821926156950744494080000]$ |
$3$ |
$3$ |
$10$ |
$6$ |
$1$ |
\(\Q\), \(\Q(\sqrt{-2}) \) |
Trivial, $C_2$ |
1.81.as $\times$ 1.81.ao |
| 2.81.abg_pz |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 32 x + 415 x^{2} - 2592 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$50$ |
$[50, 6368, 530738, 43048004, 3486824690, 282429741734, 22876790245394, 1853020128981380, 150094634565798674, 12157665453430897568]$ |
$4353$ |
$[4353, 41793153, 282055751748, 1853075345635977, 12157805932625462433, 79766501046260613602832, 523347582479573769965280897, 3433683709351342094908635746313, 22528399435189910149350185590589892, 147808829345946517727908170670779841473]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.166032.2 |
$D_{4}$ |
simple |
| 2.81.abg_qa |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 32 x + 416 x^{2} - 2592 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$50$ |
$[50, 6370, 530834, 43050438, 3486868530, 282430366498, 22876797639186, 1853020203139454, 150094635197003186, 12157665457905185890]$ |
$4354$ |
$[4354, 41807108, 282107019586, 1853180164518928, 12157958798217988994, 79766677498438420393988, 523347751625829242736572354, 3433683846767748685695415222272, 22528399529930320847227930036689154, 147808829400343418280885631488839221508]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.147712.3 |
$D_{4}$ |
simple |
| 2.81.abg_qc |
$2$ |
$\F_{3^{4}}$ |
$3$ |
|
|
|
✓ |
|
|
✓ |
✓ |
$( 1 - 16 x + 81 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$50$ |
$[50, 6374, 531026, 43055294, 3486955250, 282431575718, 22876811244050, 1853020324299134, 150094635942239666, 12157665458409546854]$ |
$4356$ |
$[4356, 41835024, 282209562756, 1853389289816064, 12158261183469270276, 79767019018955247210000, 523348062861561142272444036, 3433684071279087378501042438144, 22528399641786318946630573420927236, 147808829406475270192486728160410157584]$ |
$16$ |
$16$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-17}) \) |
$C_2$ |
1.81.aq 2 |
| 2.81.abf_pg |
$2$ |
$\F_{3^{4}}$ |
$3$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 9 x )^{2}( 1 - 13 x + 81 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$51$ |
$[51, 6393, 530946, 43046673, 3486758331, 282428611038, 22876777221531, 1853020017948513, 150094633878696546, 12157665450587960073]$ |
$4416$ |
$[4416, 41952000, 282165601536, 1853017994112000, 12157574551206148416, 79766181704571328512000, 523347284535421141700840256, 3433683503605204513284828672000, 22528399332059567325095452566195456, 147808829311383034760430255547020000000]$ |
$0$ |
$0$ |
$10$ |
$6$ |
$1$ |
\(\Q\), \(\Q(\sqrt{-155}) \) |
Trivial, $C_2$ |
1.81.as $\times$ 1.81.an |
| 2.81.abf_ph |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 31 x + 397 x^{2} - 2511 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$51$ |
$[51, 6395, 531039, 43048931, 3486796926, 282429131507, 22876783119591, 1853020077184931, 150094634442404979, 12157665456112198430]$ |
$4417$ |
$[4417, 41965917, 282215244073, 1853115225667125, 12157709126150839552, 79766328700377920101725, 523347419464083218531937697, 3433683613371478111745983609125, 22528399416669178598900007161899033, 147808829378544876611347540560073101312]$ |
$12$ |
$12$ |
$2$ |
$2$ |
$1$ |
4.0.492597.2 |
$D_{4}$ |
simple |
| 2.81.abf_pi |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 31 x + 398 x^{2} - 2511 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$51$ |
$[51, 6397, 531132, 43051185, 3486835211, 282429639442, 22876788665243, 1853020128692129, 150094634865530892, 12157665459433474477]$ |
$4418$ |
$[4418, 41979836, 282264888992, 1853212286251456, 12157842620564660098, 79766472156290208383744, 523347546330792038254761202, 3433683708815352136166108047104, 22528399480178107852003180754079392, 147808829418923839671288258587540090876]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.646204.2 |
$D_{4}$ |
simple |
| 2.81.abf_pk |
$2$ |
$\F_{3^{4}}$ |
$3$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 17 x + 81 x^{2} )( 1 - 14 x + 81 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$51$ |
$[51, 6401, 531318, 43055681, 3486910851, 282430617758, 22876798704531, 1853020208811521, 150094635301373718, 12157665459807085601]$ |
$4420$ |
$[4420, 42007680, 282364186000, 1853405894545920, 12158106367827530500, 79766748462001176576000, 523347775997496339979781380, 3433683857278199941704279214080, 22528399545595777515915934575706000, 147808829423466078703027491480481872000]$ |
$14$ |
$14$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-2}) \) |
$C_2$, $C_2$ |
1.81.ar $\times$ 1.81.ao |
| 2.81.abf_pl |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 31 x + 401 x^{2} - 2511 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$51$ |
$[51, 6403, 531411, 43057923, 3486948206, 282431088163, 22876803200771, 1853020237569923, 150094635319743171, 12157665457028191198]$ |
$4421$ |
$[4421, 42021605, 282413838101, 1853502442275205, 12158236620690620416, 79766881318584619728005, 523347878857065106261369621, 3433683910568100629037696112005, 22528399548352933962212049119890661, 147808829389681210213442130821120000000]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.140125.1 |
$D_{4}$ |
simple |
| 2.81.abe_op |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 30 x + 379 x^{2} - 2430 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$52$ |
$[52, 6420, 531262, 43048484, 3486757252, 282428548446, 22876778566372, 1853020069124804, 150094634746167262, 12157665460641750900]$ |
$4481$ |
$[4481, 42125881, 282333399104, 1853095978864809, 12157570794021386801, 79766164027081734071296, 523347315301061296337714801, 3433683598435900758172770717129, 22528399462262267650518070295833664, 147808829433613660216210758339712522201]$ |
$12$ |
$12$ |
$2$ |
$2$ |
$1$ |
4.0.69184.1 |
$D_{4}$ |
simple |
| 2.81.abe_oq |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 30 x + 380 x^{2} - 2430 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$52$ |
$[52, 6422, 531352, 43050566, 3486790552, 282428960102, 22876782757972, 1853020106690558, 150094635076063252, 12157665463868084102]$ |
$4482$ |
$[4482, 42139764, 282381422562, 1853185626758736, 12157686905205490002, 79766280290773257636564, 523347411191392281383748882, 3433683668045998059745580160000, 22528399511777885815368791796115122, 147808829472838339954981605752171670804]$ |
$24$ |
$24$ |
$2$ |
$2$ |
$1$ |
4.0.1696576.1 |
$D_{4}$ |
simple |
| 2.81.abe_os |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 30 x + 382 x^{2} - 2430 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$52$ |
$[52, 6426, 531532, 43054718, 3486856252, 282429748506, 22876790208772, 1853020162606718, 150094635411500452, 12157665465668274906]$ |
$4484$ |
$[4484, 42167536, 282477476324, 1853364409286400, 12157915990403096804, 79766502959280916295536, 523347581641754796398026244, 3433683771659766410457365606400, 22528399562125209699595198299813764, 147808829494724457505524837170196424816]$ |
$36$ |
$36$ |
$2$ |
$2$ |
$1$ |
4.0.108400.1 |
$D_{4}$ |
simple |
| 2.81.abe_ot |
$2$ |
$\F_{3^{4}}$ |
$3$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 17 x + 81 x^{2} )( 1 - 13 x + 81 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$52$ |
$[52, 6428, 531622, 43056788, 3486888652, 282430125278, 22876793470492, 1853020181093348, 150094635422086342, 12157665464385695948]$ |
$4485$ |
$[4485, 42181425, 282525506640, 1853453543938425, 12158028964429252125, 79766609370880765132800, 523347656259437456599909965, 3433683805915863638892410224425, 22528399563714094883713262410900560, 147808829479131291600475252525455890625]$ |
$48$ |
$48$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-155}) \) |
$C_2$, $C_2$ |
1.81.ar $\times$ 1.81.an |
| 2.81.abe_ov |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 30 x + 385 x^{2} - 2430 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$52$ |
$[52, 6432, 531802, 43060916, 3486952552, 282430844022, 22876799072872, 1853020199463908, 150094635141555802, 12157665457810735152]$ |
$4487$ |
$[4487, 42209209, 282621574172, 1853631300064761, 12158251775368239527, 79766812365732093948304, 523347784423933582361773847, 3433683839956882633574097395625, 22528399521607965820420932770913692, 147808829399195117831955119514368883529]$ |
$12$ |
$12$ |
$2$ |
$2$ |
$1$ |
4.0.486976.1 |
$D_{4}$ |
simple |
| 2.81.abe_ow |
$2$ |
$\F_{3^{4}}$ |
$3$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 16 x + 81 x^{2} )( 1 - 14 x + 81 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$52$ |
$[52, 6434, 531892, 43062974, 3486984052, 282431186018, 22876801416052, 1853020199483774, 150094634855445172, 12157665452659227554]$ |
$4488$ |
$[4488, 42223104, 282669611400, 1853719921557504, 12158361612293998728, 79766908955767535040000, 523347838028398318931175048, 3433683839993696966739140542464, 22528399478664295376291937646110600, 147808829336564811862189637126571677184]$ |
$32$ |
$32$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-17}) \), \(\Q(\sqrt{-2}) \) |
$C_2$, $C_2$ |
1.81.aq $\times$ 1.81.ao |
| 2.81.abd_nw |
$2$ |
$\F_{3^{4}}$ |
$3$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 9 x )^{2}( 1 - 11 x + 81 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$53$ |
$[53, 6441, 531326, 43045041, 3486683453, 282427735518, 22876773381053, 1853020057955361, 150094634799470366, 12157665458762840601]$ |
$4544$ |
$[4544, 42259200, 282366995456, 1852947763276800, 12157313476606637504, 79765934432794122240000, 523347196677639745627726784, 3433683577738698105284518195200, 22528399470262777315566881461185536, 147808829410770497330604832243834080000]$ |
$0$ |
$0$ |
$10$ |
$6$ |
$1$ |
\(\Q\), \(\Q(\sqrt{-203}) \) |
Trivial, $C_2$ |
1.81.as $\times$ 1.81.al |
| 2.81.abd_nx |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 29 x + 361 x^{2} - 2349 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$53$ |
$[53, 6443, 531413, 43046963, 3486712598, 282428079803, 22876776888893, 1853020093048163, 150094635187410413, 12157665463456559198]$ |
$4545$ |
$[4545, 42273045, 282413396745, 1853030515239045, 12157415098767450000, 79766031668791568059845, 523347276925733859867609945, 3433683642766367124221468155845, 22528399528490497335275231503415745, 147808829467835157825336903404659200000]$ |
$20$ |
$20$ |
$2$ |
$2$ |
$1$ |
4.0.26125.1 |
$D_{4}$ |
simple |
| 2.81.abd_ny |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 29 x + 362 x^{2} - 2349 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$53$ |
$[53, 6445, 531500, 43048881, 3486741453, 282428413282, 22876780120653, 1853020122702881, 150094635487090700, 12157665466911531805]$ |
$4546$ |
$[4546, 42286892, 282459800200, 1853113095980800, 12157515710003257106, 79766125852891924985600, 523347350858005750641704786, 3433683697717156530003068083200, 22528399573470900792358054980545800, 147808829509839558975231622091913144812]$ |
$12$ |
$12$ |
$2$ |
$2$ |
$1$ |
4.0.3516652.1 |
$D_{4}$ |
simple |
| 2.81.abd_oa |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 29 x + 364 x^{2} - 2349 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$53$ |
$[53, 6449, 531674, 43052705, 3486798293, 282429047870, 22876785760805, 1853020165951553, 150094635830675450, 12157665470350456049]$ |
$4548$ |
$[4548, 42314592, 282552613632, 1853277743837568, 12157713899722300548, 79766305078966740983808, 523347479886540892610608068, 3433683777857815302907439973888, 22528399625041128513427336385127168, 147808829551648849493807957103271412832]$ |
$24$ |
$24$ |
$2$ |
$2$ |
$1$ |
4.0.1141272.2 |
$D_{4}$ |
simple |
| 2.81.abd_ob |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 29 x + 365 x^{2} - 2349 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$53$ |
$[53, 6451, 531761, 43054611, 3486826278, 282429349003, 22876788171633, 1853020179672131, 150094635879065981, 12157665470455972126]$ |
$4549$ |
$[4549, 42328445, 282599023621, 1853359810970005, 12157811478216868304, 79766390127723975786125, 523347535038533206964973149, 3433683803282321725484769281445, 22528399632304287547545486385634221, 147808829552931678657905977319664128000]$ |
$12$ |
$12$ |
$2$ |
$2$ |
$1$ |
4.0.4411045.2 |
$D_{4}$ |
simple |
| 2.81.abd_od |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 29 x + 367 x^{2} - 2349 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$53$ |
$[53, 6455, 531935, 43058411, 3486881378, 282429919007, 22876792180883, 1853020191621971, 150094635740211545, 12157665467739893630]$ |
$4551$ |
$[4551, 42356157, 282691850175, 1853523431686725, 12158003602504751856, 79766551113635315013525, 523347626757290126395110711, 3433683825425614248529597335525, 22528399611462981457366098972523575, 147808829519910504928186174392518522112]$ |
$24$ |
$24$ |
$2$ |
$2$ |
$1$ |
4.0.3244437.1 |
$D_{4}$ |
simple |
| 2.81.abd_oe |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 29 x + 368 x^{2} - 2349 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$53$ |
$[53, 6457, 532022, 43060305, 3486908493, 282430187902, 22876793781741, 1853020189977569, 150094635557415062, 12157665465037360777]$ |
$4552$ |
$[4552, 42370016, 282738266752, 1853604985288576, 12158098148309661512, 79766627057572417624064, 523347663379783912639315208, 3433683822378503778807242817024, 22528399584026209958825841702654592, 147808829487054014599978118831406654176]$ |
$24$ |
$24$ |
$2$ |
$2$ |
$1$ |
4.0.608056.1 |
$D_{4}$ |
simple |
| 2.81.abd_og |
$2$ |
$\F_{3^{4}}$ |
$3$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 16 x + 81 x^{2} )( 1 - 13 x + 81 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$53$ |
$[53, 6461, 532196, 43064081, 3486961853, 282430693538, 22876796182013, 1853020171765601, 150094634976157796, 12157665457237837901]$ |
$4554$ |
$[4554, 42397740, 282831106536, 1853767579023360, 12158284207270731354, 79766769864367266912000, 523347718290325243344640314, 3433683788631360922475376599040, 22528399496782612690260060577140456, 147808829392230024726910141358664283500]$ |
$16$ |
$16$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-17}) \), \(\Q(\sqrt{-155}) \) |
$C_2$, $C_2$ |
1.81.aq $\times$ 1.81.an |
| 2.81.abd_oh |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 29 x + 371 x^{2} - 2349 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$53$ |
$[53, 6463, 532283, 43065963, 3486988098, 282430930303, 22876796983863, 1853020155324083, 150094634582107913, 12157665452257411198]$ |
$4555$ |
$[4555, 42411605, 282877529755, 1853848619174005, 12158375720438750000, 79766836734008238973805, 523347736634102091930211355, 3433683758164898343319027264005, 22528399437637839403187723911958755, 147808829331679663039543606140020000000]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.290125.1 |
$D_{4}$ |
simple |
| 2.81.abc_ne |
$2$ |
$\F_{3^{4}}$ |
$3$ |
|
|
✓ |
|
✓ |
|
✓ |
✓ |
$( 1 - 9 x )^{2}( 1 - 10 x + 81 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$54$ |
$[54, 6462, 531414, 43042878, 3486643254, 282427491582, 22876774935894, 1853020102770558, 150094635166483254, 12157665458525626302]$ |
$4608$ |
$[4608, 42393600, 282413634048, 1852854681600000, 12157173316107883008, 79765865538321986150400, 523347232247399729580691968, 3433683660782159055362457600000, 22528399525349442604848641883345408, 147808829407886525242912359911869440000]$ |
$4$ |
$4$ |
$10$ |
$6$ |
$1$ |
\(\Q\), \(\Q(\sqrt{-14}) \) |
Trivial, $C_2$ |
1.81.as $\times$ 1.81.ak |
| 2.81.abc_nf |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 28 x + 343 x^{2} - 2268 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$54$ |
$[54, 6464, 531498, 43044644, 3486668454, 282427772678, 22876777758294, 1853020132993604, 150094635534352938, 12157665463102486304]$ |
$4609$ |
$[4609, 42407409, 282458416900, 1852930711993449, 12157261182123833809, 79765944927862858592400, 523347296814835850353056049, 3433683716786073755345243799369, 22528399580564708934075595577656900, 147808829463530458027810961147215513809]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.3632400.1 |
$D_{4}$ |
simple |
| 2.81.abc_ng |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 28 x + 344 x^{2} - 2268 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$54$ |
$[54, 6466, 531582, 43046406, 3486693374, 282428043778, 22876780337654, 1853020158679166, 150094635832300182, 12157665466736335426]$ |
$4610$ |
$[4610, 42421220, 282503201810, 1853006571051280, 12157348072029135250, 79766021494260220470500, 523347355822296617516069890, 3433683764381938628509465067520, 22528399625284992067353363690641090, 147808829507709580004996979704132310500]$ |
$16$ |
$16$ |
$2$ |
$2$ |
$1$ |
4.0.6334720.3 |
$D_{4}$ |
simple |
| 2.81.abc_ni |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 28 x + 346 x^{2} - 2268 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$54$ |
$[54, 6470, 531750, 43049918, 3486742374, 282428556038, 22876784771958, 1853020196672894, 150094636226406678, 12157665471381896390]$ |
$4612$ |
$[4612, 42448848, 282592777828, 1853157775193088, 12157518923527741732, 79766166171188136124368, 523347457264906158554681668, 3433683834785082646683598405632, 22528399684438263088015271397877828, 147808829564188756106345874444728134608]$ |
$56$ |
$56$ |
$2$ |
$2$ |
$1$ |
4.0.145728.1 |
$D_{4}$ |
simple |
| 2.81.abc_nj |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 28 x + 347 x^{2} - 2268 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$54$ |
$[54, 6472, 531834, 43051668, 3486766454, 282428797222, 22876786629254, 1853020209098468, 150094636326540474, 12157665472496086552]$ |
$4613$ |
$[4613, 42462665, 282637568948, 1853233120293625, 12157602885131125933, 79766234288500633222160, 523347499753862005633322653, 3433683857809921318469987843625, 22528399699467808718570297652884468, 147808829577734707361487637876061401625]$ |
$32$ |
$32$ |
$2$ |
$2$ |
$1$ |
4.0.9805840.2 |
$D_{4}$ |
simple |
| 2.81.abc_nl |
$2$ |
$\F_{3^{4}}$ |
$3$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 17 x + 81 x^{2} )( 1 - 11 x + 81 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$54$ |
$[54, 6476, 532002, 43055156, 3486813774, 282429249758, 22876789630014, 1853020221100196, 150094636342860162, 12157665472560576476]$ |
$4615$ |
$[4615, 42490305, 282727157440, 1853383296595545, 12157767880071565375, 79766362097777811456000, 523347568401593656749553135, 3433683880049363757802715577705, 22528399701917306295297609517831360, 147808829578518754283444671557294512625]$ |
$56$ |
$56$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-203}) \) |
$C_2$, $C_2$ |
1.81.ar $\times$ 1.81.al |
| 2.81.abc_nm |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 28 x + 350 x^{2} - 2268 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$54$ |
$[54, 6478, 532086, 43056894, 3486837014, 282429461134, 22876790775830, 1853020220793470, 150094636262984310, 12157665471611031118]$ |
$4616$ |
$[4616, 42504128, 282771954824, 1853458127813632, 12157848913418949256, 79766421796524634715072, 523347594614176631679881224, 3433683879480993415489966030848, 22528399689928369358706582110789384, 147808829566974499476487216073818893248]$ |
$28$ |
$28$ |
$2$ |
$2$ |
$1$ |
4.0.130048.1 |
$D_{4}$ |
simple |
| 2.81.abc_nn |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
|
✓ |
|
✓ |
✓ |
$1 - 28 x + 351 x^{2} - 2268 x^{3} + 6561 x^{4}$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$2$ |
$0$ |
$54$ |
$[54, 6480, 532170, 43058628, 3486859974, 282429662598, 22876791686838, 1853020216359684, 150094636127033418, 12157665470073084240]$ |
$4617$ |
$[4617, 42517953, 282816754308, 1853532787754313, 12157928970691398057, 79766478695865098248848, 523347615455109181447945833, 3433683871265097726749572691337, 22528399669522869732220049926149828, 147808829548276655830696851322697565633]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.88592.1 |
$D_{4}$ |
simple |
| 2.81.abc_no |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 28 x + 352 x^{2} - 2268 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$54$ |
$[54, 6482, 532254, 43060358, 3486882654, 282429854162, 22876792364214, 1853020207857278, 150094635936961494, 12157665467995846802]$ |
$4618$ |
$[4618, 42531780, 282861555898, 1853607276426000, 12158008051894180858, 79766532799190357642820, 523347630951294933864337738, 3433683855509967289081276416000, 22528399640994093547434361655434378, 147808829523022297969440837011284114500]$ |
$48$ |
$48$ |
$2$ |
$2$ |
$1$ |
4.0.5863680.3 |
$D_{4}$ |
simple |
| 2.81.abc_np |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 28 x + 353 x^{2} - 2268 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$54$ |
$[54, 6484, 532338, 43062084, 3486905054, 282430035838, 22876792809134, 1853020195344644, 150094635694716498, 12157665465428043604]$ |
$4619$ |
$[4619, 42545609, 282906359600, 1853681593837129, 12158086157032608859, 79766584109891602745600, 523347641129637534134885659, 3433683832323803761238477838729, 22528399604634419165263146081383600, 147808829491803805712342190185133579209]$ |
$32$ |
$32$ |
$2$ |
$2$ |
$1$ |
4.0.280225.1 |
$D_{4}$ |
simple |
| 2.81.abc_nr |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 28 x + 355 x^{2} - 2268 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$54$ |
$[54, 6488, 532506, 43065524, 3486949014, 282430369574, 22876793006310, 1853020158522020, 150094635061468890, 12157665459013709768]$ |
$4621$ |
$[4621, 42573273, 282995973364, 1853829714911577, 12158239439137856581, 79766678366986982306832, 523347645640407947554716949, 3433683764090739377272547490153, 22528399509587350399441439059372084, 147808829413820480777577630855396809673]$ |
$24$ |
$24$ |
$2$ |
$2$ |
$1$ |
4.0.1911312.2 |
$D_{4}$ |
simple |
| 2.81.abc_ns |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 28 x + 356 x^{2} - 2268 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$54$ |
$[54, 6490, 532590, 43067238, 3486970574, 282430521658, 22876792760918, 1853020134328574, 150094634674331958, 12157665455262700090]$ |
$4622$ |
$[4622, 42587108, 283040783438, 1853903518591888, 12158314616115510382, 79766721320163670059428, 523347640026643140373205998, 3433683719259797146373768712192, 22528399451480173884864760885901678, 147808829368216959981224260956276399908]$ |
$16$ |
$16$ |
$2$ |
$2$ |
$1$ |
4.0.915712.1 |
$D_{4}$ |
simple |
| 2.81.abc_nu |
$2$ |
$\F_{3^{4}}$ |
$3$ |
|
|
|
✓ |
|
|
✓ |
✓ |
$( 1 - 14 x + 81 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$54$ |
$[54, 6494, 532758, 43070654, 3487012854, 282430796318, 22876791588054, 1853020074668414, 150094633768650678, 12157665446908908254]$ |
$4624$ |
$[4624, 42614784, 283130410000, 1854050612281344, 12158462041948282384, 79766798892731688960000, 523347613195332085134594064, 3433683608708322133851330576384, 22528399315542272987075574060010000, 147808829266654353564958718144685686784]$ |
$46$ |
$46$ |
$8$ |
$8$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$C_2$ |
1.81.ao 2 |
| 2.81.abb_mm |
$2$ |
$\F_{3^{4}}$ |
$3$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 - 9 x )^{2}( 1 - 9 x + 81 x^{2} )$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$2$ |
$0$ |
$2$ |
$0$ |
$2$ |
$55$ |
$[55, 6481, 531442, 43040161, 3486607255, 282427410718, 22876778106055, 1853020145805121, 150094635296999122, 12157665455570144401]$ |
$4672$ |
$[4672, 42515200, 282428473600, 1852737759308800, 12157047799607605312, 79765842700025896960000, 523347304770484649831904832, 3433683740526069407785296179200, 22528399544939174111650877280774400, 147808829371954765040867006688602080000]$ |
$0$ |
$0$ |
$19$ |
$30$ |
$6$ |
\(\Q\), \(\Q(\sqrt{-3}) \) |
Trivial, $C_2$ |
1.81.as $\times$ 1.81.aj |
| 2.81.abb_mn |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 27 x + 325 x^{2} - 2187 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$55$ |
$[55, 6483, 531523, 43041779, 3486628990, 282427642299, 22876780479139, 1853020173659075, 150094635656016799, 12157665459924665118]$ |
$4673$ |
$[4673, 42528973, 282471639473, 1852807413525237, 12157123583429758208, 79765908105094472487037, 523347359059024270581661337, 3433683792140010132980315011173, 22528399598825801686274794000126457, 147808829424895571165077143069102542848]$ |
$12$ |
$12$ |
$2$ |
$2$ |
$1$ |
4.0.5768917.1 |
$D_{4}$ |
simple |
| 2.81.abb_mo |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 27 x + 326 x^{2} - 2187 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$55$ |
$[55, 6485, 531604, 43043393, 3486650455, 282427864658, 22876782639031, 1853020197735809, 150094635959406916, 12157665463547162165]$ |
$4674$ |
$[4674, 42542748, 282514807296, 1852876896297408, 12157198425962650194, 79765970905609058562048, 523347408470413649616061314, 3433683836754685544345851721472, 22528399644363030889184488038726144, 147808829468936678401529321762760778908]$ |
$28$ |
$28$ |
$2$ |
$2$ |
$1$ |
4.0.10380892.1 |
$D_{4}$ |
simple |
| 2.81.abb_mq |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 27 x + 328 x^{2} - 2187 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$55$ |
$[55, 6489, 531766, 43046609, 3486692575, 282428281758, 22876786323775, 1853020234775009, 150094636406349526, 12157665468769929129]$ |
$4676$ |
$[4676, 42570304, 282601148816, 1853015347540224, 12157345287178245476, 79766088706538539110400, 523347492765511920526165796, 3433683905389072304141132104704, 22528399711446719288002649309272976, 147808829532433331943284638217361822784]$ |
$32$ |
$32$ |
$2$ |
$2$ |
$1$ |
4.0.257725.1 |
$D_{4}$ |
simple |
| 2.81.abb_mr |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 27 x + 329 x^{2} - 2187 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$55$ |
$[55, 6491, 531847, 43048211, 3486713230, 282428476523, 22876787850895, 1853020247846051, 150094636553409967, 12157665470456223326]$ |
$4677$ |
$[4677, 42584085, 282644322525, 1853084316026565, 12157417305869843712, 79766143713734644225125, 523347527701105963467405837, 3433683929609977238870415647685, 22528399733519702660071807859806725, 147808829552934732664897829305004544000]$ |
$36$ |
$36$ |
$2$ |
$2$ |
$1$ |
4.0.18177085.2 |
$D_{4}$ |
simple |
| 2.81.abb_mt |
$2$ |
$\F_{3^{4}}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 27 x + 331 x^{2} - 2187 x^{3} + 6561 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$55$ |
$[55, 6495, 532009, 43051403, 3486753730, 282428838543, 22876790280301, 1853020263362099, 150094636703435251, 12157665472191003390]$ |
$4679$ |
$[4679, 42611653, 282730675871, 1853221738768533, 12157558519443173744, 79766245958542830005053, 523347583278096840455213759, 3433683958361527126079973163077, 22528399756037693056694733707909759, 147808829574025608338568292471545879808]$ |
$24$ |
$24$ |
$2$ |
$2$ |
$1$ |
4.0.19250077.2 |
$D_{4}$ |
simple |
| 2.81.abb_mu |
$2$ |
$\F_{3^{4}}$ |
$3$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 17 x + 81 x^{2} )( 1 - 10 x + 81 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$55$ |
$[55, 6497, 532090, 43052993, 3486773575, 282429005822, 22876791184855, 1853020265915393, 150094636709873050, 12157665472323362177]$ |
$4680$ |
$[4680, 42625440, 282773855520, 1853290193040000, 12157627714334037000, 79766293202936297717760, 523347603971378905253288520, 3433683963092832019248575040000, 22528399757003972151023316279682080, 147808829575634782192479178981954596000]$ |
$84$ |
$84$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-14}) \) |
$C_2$, $C_2$ |
1.81.ar $\times$ 1.81.ak |
