| 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 |
| 3.13.av_he_abif |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 13 x^{2} )^{3}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$-7$ |
$[-7, 101, 1988, 27989, 370013, 4825292, 62754545, 815792645, 10604854484, 137860172621]$ |
$343$ |
$[343, 3176523, 9636401152, 22836204908811, 51009911926504363, 112420114045738942464, 247088272213595130613183, 542841978006048990217389147, 1192573227335183594875086966784, 2620027586828745701170376844269043]$ |
$None$ |
$0$ |
$78$ |
$18$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
1.13.ah 3 |
| 3.13.au_gq_abfi |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 6 x + 13 x^{2} )( 1 - 7 x + 13 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-6$ |
$[-6, 114, 2076, 28418, 371634, 4829868, 62761434, 815772482, 10604623308, 137858929314]$ |
$392$ |
$[392, 3457440, 10034898944, 23181512860800, 51232868046172232, 112526703776073646080, 247115398537287670388264, 542828560531927606535692800, 1192547229763648456436745832448, 2620003957632192333290694379351200]$ |
$None$ |
$0$ |
$96$ |
$12$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.13.ah 2 $\times$ 1.13.ag |
| 3.13.at_gc_abcl |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 13 x^{2} )( 1 - 7 x + 13 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$-5$ |
$[-5, 125, 2128, 28517, 371215, 4825292, 62739931, 815715557, 10604617744, 137859754325]$ |
$441$ |
$[441, 3695139, 10270374912, 23261199311259, 51175237809194541, 112420114045738942464, 247030727708668032881577, 542790679774383601869692475, 1192546604047795506691655814144, 2620019637063803102463380377310139]$ |
$None$ |
$0$ |
$78$ |
$18$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$ |
1.13.ah 2 $\times$ 1.13.af |
| 3.13.at_gd_abcs |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 13 x^{2} )( 1 - 6 x + 13 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-5$ |
$[-5, 127, 2164, 28847, 373255, 4834444, 62768323, 815752319, 10604392132, 137857686007]$ |
$448$ |
$[448, 3763200, 10449875968, 23532042240000, 51456798671174848, 112633394568133017600, 247142527839014863448512, 542815143389447140638720000, 1192521232758848936602628064256, 2619980328648743183307244126080000]$ |
$None$ |
$0$ |
$96$ |
$24$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.13.ah $\times$ 1.13.ag 2 |
| 3.13.as_fo_azo |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 13 x^{2} )( 1 - 7 x + 13 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-4$ |
$[-4, 134, 2150, 28418, 370196, 4821728, 62739428, 815772482, 10604908430, 137860295414]$ |
$490$ |
$[490, 3889620, 10369999360, 23181512860800, 51035082173203450, 112337097044228259840, 247028747081462727683890, 542828560531927606535692800, 1192579293990000853492740835840, 2620029920524230708253944980630100]$ |
$None$ |
$0$ |
$96$ |
$12$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.13.ah 2 $\times$ 1.13.ae |
| 3.13.as_fp_azv |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 13 x^{2} )( 1 - 11 x + 55 x^{2} - 143 x^{3} + 169 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-4$ |
$[-4, 136, 2183, 28684, 371571, 4826557, 62750054, 815780020, 10604876189, 137860208471]$ |
$497$ |
$[497, 3955623, 10532193392, 23398526640111, 51224412916463472, 112449530624823290304, 247070573660859256322357, 542833575266085419511276207, 1192575668211041284187628658544, 2620028268159512012487928792781568]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-17 +2 \sqrt{5}})\) |
$C_2$, $D_{4}$ |
1.13.ah $\times$ 2.13.al_cd |
| 3.13.as_fq_abac |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 13 x^{2} )( 1 - 6 x + 13 x^{2} )( 1 - 5 x + 13 x^{2} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-4$ |
$[-4, 138, 2216, 28946, 372836, 4829868, 62746820, 815695394, 10604386568, 137858511018]$ |
$504$ |
$[504, 4021920, 10695089664, 23612933635200, 51398916541701624, 112526703776073646080, 247057847714898179985816, 542777263568205236101440000, 1192520607056636317090407802368, 2619996007938946139356712420637600]$ |
$None$ |
$0$ |
$96$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$, $C_2$ |
1.13.ah $\times$ 1.13.ag $\times$ 1.13.af |
| 3.13.as_fr_abai |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 6 x + 13 x^{2} )^{3}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$-4$ |
$[-4, 140, 2252, 29276, 374876, 4839020, 62775212, 815732156, 10604160956, 137856442700]$ |
$512$ |
$[512, 4096000, 10882013696, 23887872000000, 51681708060918272, 112740186517737472000, 247169660119103650167296, 542801726578599395328000000, 1192495236320772680785653842432, 2619956699878396329300777472000000]$ |
$None$ |
$0$ |
$44$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
1.13.ag 3 |
| 3.13.ar_fa_awr |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 13 x^{2} )( 1 - 7 x + 13 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-3$ |
$[-3, 141, 2148, 28229, 369417, 4822092, 62754717, 815826725, 10604871924, 137859308421]$ |
$539$ |
$[539, 4040883, 10360942592, 23029384182651, 50927936696817719, 112345575772777611264, 247088949485721000382571, 542864656551803925290156667, 1192575188601264731387374874624, 2620011162605555917374724132443243]$ |
$None$ |
$0$ |
$48$ |
$12$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-43}) \) |
$C_2$, $C_2$ |
1.13.ah 2 $\times$ 1.13.ad |
| 3.13.ar_fb_awy |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 13 x^{2} )( 1 - 10 x + 48 x^{2} - 130 x^{3} + 169 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-3$ |
$[-3, 143, 2178, 28439, 370317, 4824716, 62761437, 815853695, 10605003894, 137859688343]$ |
$546$ |
$[546, 4104828, 10506289248, 23199716148336, 51051603989492106, 112406642500855981824, 247115407244168646198834, 542882604488015191311055872, 1192590029730686634236253014496, 2620018383061626150738019492675068]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-24 -10 \sqrt{3}})\) |
$C_2$, $D_{4}$ |
1.13.ah $\times$ 2.13.ak_bw |
| 3.13.ar_fc_axf |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 13 x^{2} )( 1 - 10 x + 49 x^{2} - 130 x^{3} + 169 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-3$ |
$[-3, 145, 2208, 28645, 371117, 4826116, 62758497, 815826469, 10604911584, 137859378185]$ |
$553$ |
$[553, 4169067, 10652248768, 23367257826171, 51161662525287013, 112439219264720538624, 247103825522123129583457, 542864486380853702327156475, 1192579648654060719694371545536, 2620012488495518196392536516765347]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-25 -10 \sqrt{2}})\) |
$C_2$, $D_{4}$ |
1.13.ah $\times$ 2.13.ak_bx |
| 3.13.ar_fd_axm |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 13 x^{2} )( 1 - 6 x + 13 x^{2} )( 1 - 4 x + 13 x^{2} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-3$ |
$[-3, 147, 2238, 28847, 371817, 4826304, 62746317, 815752319, 10604677254, 137859052107]$ |
$560$ |
$[560, 4233600, 10798833920, 23532042240000, 51258148307970800, 112443608063027404800, 247055866870251819395120, 542815143389447140638720000, 1192553296286215309816730420480, 2620006291306630482093779865840000]$ |
$None$ |
$0$ |
$96$ |
$24$ |
$4$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$, $C_2$ |
1.13.ah $\times$ 1.13.ag $\times$ 1.13.ae |
| 3.13.ar_fe_axt |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 13 x^{2} )( 1 - 5 x + 13 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$-3$ |
$[-3, 149, 2268, 29045, 372417, 4825292, 62725317, 815638469, 10604381004, 137859336029]$ |
$567$ |
$[567, 4298427, 10946057472, 23694103094571, 51341099522009787, 112420114045738942464, 246973196605307985010863, 542739386390369424398926875, 1192519981354751996352349595904, 2620011687322981914904984277550147]$ |
$None$ |
$0$ |
$78$ |
$18$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$ |
1.13.ah $\times$ 1.13.af 2 |
| 3.13.ar_fe_axs |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 6 x + 13 x^{2} )( 1 - 11 x + 55 x^{2} - 143 x^{3} + 169 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-3$ |
$[-3, 149, 2271, 29113, 373192, 4831133, 62756943, 815759857, 10604645013, 137858965164]$ |
$568$ |
$[568, 4305440, 10967735224, 23752337500800, 51448306585454208, 112556148246120910880, 247097698041534970160056, 542820157999655317229836800, 1192549670586296126218272874168, 2620004638956813938851726677811200]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-17 +2 \sqrt{5}})\) |
$C_2$, $D_{4}$ |
1.13.ag $\times$ 2.13.al_cd |
| 3.13.ar_ff_axy |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 13 x^{2} )( 1 - 6 x + 13 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-3$ |
$[-3, 151, 2304, 29375, 374457, 4834444, 62753709, 815675231, 10604155392, 137857267711]$ |
$576$ |
$[576, 4377600, 11137367808, 23969986560000, 51623572937967936, 112633394568133017600, 247084970698469424472128, 542763847693636448256000000, 1192494610632200094153107018496, 2619972379027192747539176403840000]$ |
$None$ |
$0$ |
$96$ |
$24$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$ |
1.13.ag 2 $\times$ 1.13.af |
| 3.13.aq_el_atn |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 7 x + 13 x^{2} )( 1 - 9 x + 39 x^{2} - 117 x^{3} + 169 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$3$ |
$0$ |
$-2$ |
$[-2, 144, 2101, 27868, 368563, 4822533, 62752156, 815728532, 10604296903, 137857882839]$ |
$581$ |
$[581, 4087335, 10141926704, 22738764255375, 50810670439501616, 112355835810658614720, 247078851740814348911033, 542799313739293649787795375, 1192510523761141254849914881328, 2619984069431691288457929961900800]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-18 +2 \sqrt{29}})\) |
$C_2$, $D_{4}$ |
1.13.ah $\times$ 2.13.aj_bn |
| 3.13.aq_em_atu |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 2 x + 13 x^{2} )( 1 - 7 x + 13 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$-2$ |
$[-2, 146, 2128, 28034, 369238, 4825292, 62767150, 815807810, 10604617744, 137858910146]$ |
$588$ |
$[588, 4148928, 10270374912, 22872426022656, 50903316619445388, 112420114045738942464, 247137906022586923887228, 542852069559639764582956032, 1192546604047795506691655814144, 2620003593342085758683201818392768]$ |
$None$ |
$0$ |
$78$ |
$18$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$ |
1.13.ah 2 $\times$ 1.13.ac |
| 3.13.aq_en_aub |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 13 x^{2} )( 1 - 9 x + 41 x^{2} - 117 x^{3} + 169 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 148, 2155, 28196, 369823, 4827073, 62775214, 815849444, 10604754715, 137859021943]$ |
$595$ |
$[595, 4210815, 10399333840, 23003113884975, 50983602291823600, 112461589614792922560, 247169665734669259945615, 542879775564162421878399375, 1192562007348115729035492404560, 2620005718030021365669969970483200]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-106 +18 \sqrt{21}})\) |
$C_2$, $D_{4}$ |
1.13.ah $\times$ 2.13.aj_bp |
| 3.13.aq_eo_aui |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 13 x^{2} )( 1 - 9 x + 42 x^{2} - 117 x^{3} + 169 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 150, 2182, 28354, 370318, 4827888, 62776726, 815859266, 10604766622, 137858657670]$ |
$602$ |
$[602, 4272996, 10528816256, 23130855418944, 51051550365090842, 112480550917882527744, 247175620057990922661986, 542886311873986997310261504, 1192563346506689112612359179904, 2619998795049031471509996087132516]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-110 +18 \sqrt{17}})\) |
$C_2$, $D_{4}$ |
1.13.ah $\times$ 2.13.aj_bq |
| 3.13.aq_ep_aup |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 13 x^{2} )( 1 - 9 x + 43 x^{2} - 117 x^{3} + 169 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 152, 2209, 28508, 370723, 4827749, 62772064, 815843060, 10604710327, 137858218007]$ |
$609$ |
$[609, 4335471, 10658834928, 23255678882079, 51107185572367344, 112477288427059953600, 247157259456221726495541, 542875527099808293462869007, 1192557015791458154074080282096, 2619990439286919822544018391652096]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-114 +18 \sqrt{13}})\) |
$C_2$, $D_{4}$ |
1.13.ah $\times$ 2.13.aj_br |
| 3.13.aq_eq_aux |
$3$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 16 x + 120 x^{2} - 543 x^{3} + 1560 x^{4} - 2704 x^{5} + 2197 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 154, 2233, 28594, 370358, 4821877, 62736574, 815703202, 10604283508, 137856949034]$ |
$615$ |
$[615, 4391715, 10769211495, 23323805483475, 51056734370604075, 112340505835142908155, 247017510590676700158255, 542782457877041823738771075, 1192509017310997013503638712320, 2619966322644293656283832526776075]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.9709203.1 |
$S_4\times C_2$ |
simple |
| 3.13.aq_eq_auw |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 13 x^{2} )( 1 - 6 x + 13 x^{2} )( 1 - 3 x + 13 x^{2} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 154, 2236, 28658, 371038, 4826668, 62761606, 815806562, 10604640748, 137858065114]$ |
$616$ |
$[616, 4398240, 10789402624, 23377613212800, 51150534515943016, 112452094830577582080, 247116075883767141604168, 542851238517134881136140800, 1192549190986974855482957436928, 2619987533557127401286211408631200]$ |
$None$ |
$0$ |
$48$ |
$12$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-43}) \) |
$C_2$, $C_2$, $C_2$ |
1.13.ah $\times$ 1.13.ag $\times$ 1.13.ad |
| 3.13.aq_er_ave |
$3$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 16 x + 121 x^{2} - 550 x^{3} + 1573 x^{4} - 2704 x^{5} + 2197 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 156, 2260, 28740, 370588, 4820016, 62722910, 815673180, 10604396206, 137858106216]$ |
$622$ |
$[622, 4454764, 10900314262, 23442910445104, 51088586067563662, 112297221797497705132, 246963725802684757947142, 542762482093583037879821056, 1192521690621180046710515155582, 2619988314736322028316787504697004]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.12178624.2 |
$S_4\times C_2$ |
simple |
| 3.13.aq_er_avd |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 13 x^{2} )( 1 - 9 x + 45 x^{2} - 117 x^{3} + 169 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 156, 2263, 28804, 371263, 4824657, 62745730, 815755460, 10604610859, 137858522871]$ |
$623$ |
$[623, 4461303, 10920532112, 23496688030431, 51181625711781488, 112405265180572883904, 247053563007046732215083, 542817232264809763704286767, 1192545829512406157608235611664, 2619996233207791499350984983687168]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-122 +18 \sqrt{5}})\) |
$C_2$, $D_{4}$ |
1.13.ah $\times$ 2.13.aj_bt |
| 3.13.aq_er_avc |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 6 x + 13 x^{2} )( 1 - 10 x + 48 x^{2} - 130 x^{3} + 169 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 156, 2266, 28868, 371938, 4829292, 62768326, 815833532, 10604772718, 137858445036]$ |
$624$ |
$[624, 4467840, 10940759856, 23550520780800, 51274742338460784, 112513219458313265280, 247142536546851714945072, 542869186009725389360332800, 1192564031792866668133252649712, 2619994753948078634931259038211200]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-24 -10 \sqrt{3}})\) |
$C_2$, $D_{4}$ |
1.13.ag $\times$ 2.13.ak_bw |
| 3.13.aq_es_avk |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 13 x^{2} )( 1 - 5 x + 13 x^{2} )( 1 - 4 x + 13 x^{2} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-2$ |
$[-2, 158, 2290, 28946, 371398, 4821728, 62724814, 815695394, 10604671690, 137859877118]$ |
$630$ |
$[630, 4524660, 11052236160, 23612933635200, 51200489634024150, 112337097044228259840, 246971216439371889206910, 542777263568205236101440000, 1192552670567179325263778029440, 2620021970752207141908792554997300]$ |
$None$ |
$0$ |
$96$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$, $C_2$ |
1.13.ah $\times$ 1.13.af $\times$ 1.13.ae |
| 3.13.aq_es_avj |
$3$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 16 x + 122 x^{2} - 555 x^{3} + 1586 x^{4} - 2704 x^{5} + 2197 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 158, 2293, 29010, 372068, 4826213, 62745212, 815752946, 10604702068, 137859244278]$ |
$631$ |
$[631, 4531211, 11072490799, 23666737082339, 51292846885738891, 112441506056786691707, 247051516374572851920007, 542815558600951600440704579, 1192556086446545013697266713152, 2620009943543046531274372722139691]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.11666459.1 |
$A_4\times C_2$ |
simple |
| 3.13.aq_es_avi |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 6 x + 13 x^{2} )( 1 - 10 x + 49 x^{2} - 130 x^{3} + 169 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 158, 2296, 29074, 372738, 4830692, 62765386, 815806306, 10604680408, 137858134878]$ |
$632$ |
$[632, 4537760, 11092755296, 23720595868800, 51385281922411832, 112545827109430561280, 247130953553319137008856, 542851068350390788895040000, 1192553650942543655591798074592, 2619988859435131899903417554224800]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-25 -10 \sqrt{2}})\) |
$C_2$, $D_{4}$ |
1.13.ag $\times$ 2.13.ak_bx |
| 3.13.aq_et_avp |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 13 x^{2} )( 1 - 11 x + 55 x^{2} - 143 x^{3} + 169 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 160, 2323, 29212, 372773, 4826557, 62735440, 815702932, 10604639449, 137859790175]$ |
$639$ |
$[639, 4601439, 11225100852, 23833986160959, 51390434008460304, 112449530624823290304, 247013033277756500911683, 542782277828473768235592975, 1192549044869162504826166878804, 2620020318392502099884099810974464]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-17 +2 \sqrt{5}})\) |
$C_2$, $D_{4}$ |
1.13.af $\times$ 2.13.al_cd |
| 3.13.aq_et_avo |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 13 x^{2} )( 1 - 6 x + 13 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$-2$ |
$[-2, 160, 2326, 29276, 373438, 4830880, 62753206, 815732156, 10604446078, 137857808800]$ |
$640$ |
$[640, 4608000, 11245402240, 23887872000000, 51482189428931200, 112550220068921856000, 247082989636358136952960, 542801726578599395328000000, 1192527299149168267745577554560, 2619982662302134663644776256000000]$ |
$None$ |
$0$ |
$44$ |
$12$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.13.ag 2 $\times$ 1.13.ae |
| 3.13.aq_eu_avu |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 6 x + 13 x^{2} )( 1 - 5 x + 13 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-2$ |
$[-2, 162, 2356, 29474, 374038, 4829868, 62732206, 815618306, 10604149828, 137858092722]$ |
$648$ |
$[648, 4678560, 11398713984, 24052383388800, 51565503209383368, 112526703776073646080, 247000310295547016257704, 542725971452014256712000000, 1192493984943955799137953449088, 2619988058269821139027985850544800]$ |
$None$ |
$0$ |
$96$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$ |
1.13.ag $\times$ 1.13.af 2 |
| 3.13.ap_dx_aqq |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 13 x^{2} )( 1 - 8 x + 32 x^{2} - 104 x^{3} + 169 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-1$ |
$[-1, 147, 2072, 27767, 369179, 4826304, 62751191, 815683199, 10604336456, 137859052107]$ |
$630$ |
$[630, 4154220, 10012857120, 22657863639600, 50895254892840750, 112443633371876002560, 247075057715527390608630, 542769149576876086635724800, 1192514971681397866466643104160, 2620006291359067191715284001015500]$ |
$None$ |
$0$ |
$24$ |
$24$ |
$4$ |
\(\Q(\sqrt{-3}) \), \(\Q(i, \sqrt{10})\) |
$C_2$, $C_2^2$ |
1.13.ah $\times$ 2.13.ai_bg |
| 3.13.ap_dy_aqx |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x + 13 x^{2} )( 1 - 7 x + 13 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-1$ |
$[-1, 149, 2096, 27893, 369659, 4828748, 62765639, 815746757, 10604540528, 137859744989]$ |
$637$ |
$[637, 4213755, 10125466624, 22758933199275, 50961221941086457, 112500615380537180160, 247131956265713730738709, 542811441823314176232085275, 1192537920497238107784957242368, 2620019459632019140624088299414275]$ |
$None$ |
$0$ |
$48$ |
$12$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-51}) \) |
$C_2$, $C_2$ |
1.13.ah 2 $\times$ 1.13.ab |
| 3.13.ap_dz_are |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 13 x^{2} )( 1 - 8 x + 34 x^{2} - 104 x^{3} + 169 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 151, 2120, 28015, 370059, 4830436, 62775383, 815785855, 10604614856, 137859742991]$ |
$644$ |
$[644, 4273584, 10238497472, 22856905042944, 51016152313775124, 112539965532274732032, 247170331084403268714116, 542837458761077365592211456, 1192546278982659896218419027392, 2620019421645100182730662587955504]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7 +4 \sqrt{2}})\) |
$C_2$, $D_{4}$ |
1.13.ah $\times$ 2.13.ai_bi |
| 3.13.ap_ea_arl |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 13 x^{2} )( 1 - 8 x + 35 x^{2} - 104 x^{3} + 169 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 153, 2144, 28133, 370379, 4831380, 62780759, 815805029, 10604599328, 137859312753]$ |
$651$ |
$[651, 4333707, 10351962432, 22951801980891, 51060059851663191, 112561965616195243008, 247191503987224050100203, 542850218228437080259907259, 1192544532792050915396807157312, 2620011244943064284872767660218787]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-29 +8 \sqrt{7}})\) |
$C_2$, $D_{4}$ |
1.13.ah $\times$ 2.13.ai_bj |
| 3.13.ap_eb_ars |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 13 x^{2} )( 1 - 8 x + 36 x^{2} - 104 x^{3} + 169 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 155, 2168, 28247, 370619, 4831592, 62782103, 815808767, 10604532104, 137858690675]$ |
$658$ |
$[658, 4394124, 10465874272, 23043647504304, 51092959908644458, 112566898734816363264, 247196797297426767647794, 542852706140314393827225600, 1192536973193493054737051483104, 2619999422337770858415665380625964]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-30 +8 \sqrt{6}})\) |
$C_2$, $D_{4}$ |
1.13.ah $\times$ 2.13.ai_bk |
| 3.13.ap_ec_asa |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 6 x + 13 x^{2} )( 1 - 9 x + 39 x^{2} - 117 x^{3} + 169 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$3$ |
$0$ |
$-1$ |
$[-1, 157, 2189, 28297, 370184, 4827109, 62759045, 815708369, 10604065727, 137856639532]$ |
$664$ |
$[664, 4448800, 10561329688, 23082598800000, 51032755706679424, 112462364596385658400, 247105977030290283831064, 542785897319708794766400000, 1192484527556516436306268638616, 2619960440627607501302888350720000]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-18 +2 \sqrt{29}})\) |
$C_2$, $D_{4}$ |
1.13.ag $\times$ 2.13.aj_bn |
| 3.13.ap_ec_arz |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 13 x^{2} )( 1 - 8 x + 37 x^{2} - 104 x^{3} + 169 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 157, 2192, 28357, 370779, 4831084, 62779751, 815801509, 10604449616, 137858083157]$ |
$665$ |
$[665, 4454835, 10580245760, 23132465785275, 51114869396254125, 112555049423952199680, 247187533981403309423465, 542847876568293294044814075, 1192527697090619236698821146880, 2619987876467511499388924222920875]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-106 -14 \sqrt{5}})\) |
$C_2$, $D_{4}$ |
1.13.ah $\times$ 2.13.ai_bl |
| 3.13.ap_ed_ash |
$3$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 15 x + 107 x^{2} - 475 x^{3} + 1391 x^{4} - 2535 x^{5} + 2197 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 159, 2213, 28403, 370269, 4826031, 62755188, 815710611, 10604103749, 137856712139]$ |
$671$ |
$[671, 4509791, 10676155523, 23168460479879, 51044453464796891, 112437272100305768759, 247090793820651893465408, 542787389009674883450894375, 1192488803215307020031633525831, 2619961820501932501511744178896831]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.279340175.1 |
$S_4\times C_2$ |
simple |
| 3.13.ap_ed_asg |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 13 x^{2} )( 1 - 6 x + 13 x^{2} )( 1 - 2 x + 13 x^{2} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-1$ |
$[-1, 159, 2216, 28463, 370859, 4829868, 62774039, 815787647, 10604386568, 137857666839]$ |
$672$ |
$[672, 4515840, 10695089664, 23218281676800, 51125806828172832, 112526703776073646080, 247165037795274499902624, 542838651836084540787916800, 1192520607056636317090407802368, 2619979964361922025454129187891200]$ |
$None$ |
$0$ |
$96$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$, $C_2$ |
1.13.ah $\times$ 1.13.ag $\times$ 1.13.ac |
| 3.13.ap_ed_asf |
$3$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 15 x + 107 x^{2} - 473 x^{3} + 1391 x^{4} - 2535 x^{5} + 2197 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 159, 2219, 28523, 371449, 4833699, 62792680, 815860995, 10604626025, 137858237039]$ |
$673$ |
$[673, 4521887, 10714034149, 23268151844951, 51207217894692733, 112616026553178240911, 247238464085360202766144, 542887462682608448742333191, 1192547535212590935925719001921, 2619990800980712195952923316943367]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.9678431.1 |
$A_4\times C_2$ |
simple |
| 3.13.ap_ee_aso |
$3$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 15 x + 108 x^{2} - 482 x^{3} + 1404 x^{4} - 2535 x^{5} + 2197 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 161, 2237, 28505, 370274, 4824257, 62748293, 815710097, 10604185655, 137857029056]$ |
$678$ |
$[678, 4571076, 10791466326, 23251344887424, 51045199500731808, 112395971660466168036, 247063647712058721521382, 542787046237881197925468672, 1192498013715060193302368871702, 2619967843446249868930769792664576]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.365587668.1 |
$S_4\times C_2$ |
simple |
| 3.13.ap_ee_asn |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 7 x + 13 x^{2} )( 1 - 8 x + 39 x^{2} - 104 x^{3} + 169 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$3$ |
$0$ |
$-1$ |
$[-1, 161, 2240, 28565, 370859, 4827956, 62765303, 815771525, 10604375936, 137857588841]$ |
$679$ |
$[679, 4577139, 10810418752, 23301120712779, 51125792364730699, 112482149567143652352, 247130633442863296681471, 542827922631607749748976091, 1192519411382458523679552016192, 2619978482014390258241850072620379]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-33 +8 \sqrt{3}})\) |
$C_2$, $D_{4}$ |
1.13.ah $\times$ 2.13.ai_bn |
| 3.13.ap_ee_asm |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 6 x + 13 x^{2} )( 1 - 9 x + 41 x^{2} - 117 x^{3} + 169 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 161, 2243, 28625, 371444, 4831649, 62782103, 815829281, 10604523539, 137857778636]$ |
$680$ |
$[680, 4583200, 10829381480, 23350945680000, 51206443416310400, 112568218669671623200, 247196800994063115498920, 542866357155795385896000000, 1192536010021171371049232913320, 2619982089030695746857167994880000]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-106 +18 \sqrt{21}})\) |
$C_2$, $D_{4}$ |
1.13.ag $\times$ 2.13.aj_bp |
| 3.13.ap_ef_asv |
$3$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 15 x + 109 x^{2} - 489 x^{3} + 1417 x^{4} - 2535 x^{5} + 2197 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 163, 2261, 28603, 370199, 4821799, 62738696, 815711123, 10604342747, 137857710463]$ |
$685$ |
$[685, 4632655, 10907274865, 23331278233575, 51035015651132425, 112338752869076393455, 247025864572125233807680, 542787728252166194461755975, 1192515679248513143466178585885, 2619980793491707865286568425897775]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.296888383.1 |
$S_4\times C_2$ |
simple |
| 3.13.ap_ef_asu |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 13 x^{2} )( 1 - 8 x + 40 x^{2} - 104 x^{3} + 169 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 163, 2264, 28663, 370779, 4825360, 62753879, 815757439, 10604448968, 137857967003]$ |
$686$ |
$[686, 4638732, 10926245792, 23381009108016, 51114847857411366, 112421676386927432448, 247085646745369705463918, 542818548136892226822733824, 1192527624141034433696590886432, 2619985668964138696373481391519212]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-34 +8 \sqrt{2}})\) |
$C_2$, $D_{4}$ |
1.13.ah $\times$ 2.13.ai_bo |
| 3.13.ap_ef_ast |
$3$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 15 x + 109 x^{2} - 487 x^{3} + 1417 x^{4} - 2535 x^{5} + 2197 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 163, 2267, 28723, 371359, 4828915, 62768852, 815800099, 10604513195, 137857868003]$ |
$687$ |
$[687, 4644807, 10945226979, 23430789293991, 51194738741758707, 112504491215063671023, 247144610265913121230848, 542846936277244377955333959, 1192534846672217710084252249239, 2619983787442601875420928888080287]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.319611111.1 |
$S_4\times C_2$ |
simple |
| 3.13.ap_ef_ass |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 6 x + 13 x^{2} )( 1 - 9 x + 42 x^{2} - 117 x^{3} + 169 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 163, 2270, 28783, 371939, 4832464, 62783615, 815839103, 10604535446, 137857414363]$ |
$688$ |
$[688, 4650880, 10964218432, 23480618803200, 51274688479675888, 112587197950684487680, 247202755971073843853488, 542872893304061401979289600, 1192537349150551687055542497088, 2619975166112142019158876065814400]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-110 +18 \sqrt{17}})\) |
$C_2$, $D_{4}$ |
1.13.ag $\times$ 2.13.aj_bq |
| 3.13.ap_eg_atc |
$3$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 15 x + 110 x^{2} - 496 x^{3} + 1430 x^{4} - 2535 x^{5} + 2197 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 165, 2285, 28697, 370044, 4818669, 62726733, 815717937, 10604604599, 137858847500]$ |
$692$ |
$[692, 4694528, 11023593908, 23408287410176, 51013925488225472, 112265907265155318272, 246978771567299420628692, 542792262946231369189203968, 1192545125878570895730884198324, 2620002402814583034388045374291968]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.5611187.1 |
$S_4\times C_2$ |
simple |
| 3.13.ap_eg_atb |
$3$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 13 x^{2} )( 1 - 5 x + 13 x^{2} )( 1 - 3 x + 13 x^{2} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-1$ |
$[-1, 165, 2288, 28757, 370619, 4822092, 62740103, 815749637, 10604635184, 137858890125]$ |
$693$ |
$[693, 4700619, 11042583552, 23457973758219, 51092996893356033, 112345575772777611264, 247031404823063675979549, 542813356177029969244688475, 1192548565270092874353721795584, 2620003212890448180857709012026739]$ |
$None$ |
$0$ |
$48$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-43}) \) |
$C_2$, $C_2$, $C_2$ |
1.13.ah $\times$ 1.13.af $\times$ 1.13.ad |
