| 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 |
| 3.19.ay_jp_accu |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 19 x^{2} )^{3}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$-4$ |
$[-4, 284, 6692, 130460, 2480396, 47077628, 894044084, 16984338620, 322690627868, 6131074962524]$ |
$1728$ |
$[1728, 37933056, 314987206464, 2215710465196032, 15207499740585912768, 104197636641862317625344, 714347210949207045210372672, 4898986644046191229935846162432, 33600920046995882243396729236522176, 230466945107731775175860955872289509376]$ |
$None$ |
$0$ |
$78$ |
$18$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
1.19.ai 3 |
| 3.19.ax_iy_abyo |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 19 x^{2} )( 1 - 15 x + 93 x^{2} - 285 x^{3} + 361 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-3$ |
$[-3, 297, 6759, 130489, 2477832, 47050965, 893869533, 16983479969, 322687422891, 6131067137772]$ |
$1860$ |
$[1860, 39320400, 317987967780, 2216147602267200, 15191750840114904000, 104138603315246626635600, 714207732414274576514183460, 4898738969021850595453146067200, 33600586319992144320615459483739380, 230466650975323950893601257148864000000]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.1525.1 |
$C_2$, $D_{4}$ |
1.19.ai $\times$ 2.19.ap_dp |
| 3.19.ax_iz_abyw |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 19 x^{2} )( 1 - 8 x + 19 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$-3$ |
$[-3, 299, 6804, 131015, 2482107, 47077628, 894000993, 16983979535, 322688674476, 6131067134699]$ |
$1872$ |
$[1872, 39626496, 320172181056, 2225143142756352, 15218002140577574832, 104197636641862317625344, 714312776526346459209700368, 4898883065907900385724251963392, 33600716644231533527319457790760384, 230466650859719284717958045830818322176]$ |
$None$ |
$0$ |
$78$ |
$18$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$ |
1.19.ai 2 $\times$ 1.19.ah |
| 3.19.aw_ii_abuq |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 19 x^{2} )( 1 - 14 x + 85 x^{2} - 266 x^{3} + 361 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 310, 6832, 130690, 2477798, 47049652, 893886754, 16983761026, 322689525760, 6131077395110]$ |
$2004$ |
$[2004, 40793424, 321386586192, 2219586680383296, 15191554945740159204, 104135697665554925051136, 714221491319227172211121788, 4898820037894105276854804067584, 33600805286762206430487735279330096, 230467036548670214425066858694571685584]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.14912.2 |
$C_2$, $D_{4}$ |
1.19.ai $\times$ 2.19.ao_dh |
| 3.19.aw_ij_abuz |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 19 x^{2} )( 1 - 15 x + 93 x^{2} - 285 x^{3} + 361 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 312, 6871, 131044, 2479543, 47050965, 893826442, 16983120884, 322685469499, 6131059309947]$ |
$2015$ |
$[2015, 41075775, 323222337620, 2225582140798575, 15202242363811646000, 104138603315246626635600, 714173304714843127246216865, 4898635396120095342437697742575, 33600382919248007997626416968008420, 230466356727686993145479661120564000000]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.1525.1 |
$C_2$, $D_{4}$ |
1.19.ah $\times$ 2.19.ap_dp |
| 3.19.aw_ij_abuy |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 6 x + 19 x^{2} )( 1 - 8 x + 19 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-2$ |
$[-2, 312, 6874, 131132, 2480878, 47064888, 893937322, 16983825212, 322689058846, 6131073349752]$ |
$2016$ |
$[2016, 41094144, 323412790176, 2227131653160960, 15210458336024826336, 104169426322217022434304, 714261896432174674585328544, 4898838551408449119446724771840, 33600756667903450232209526361537504, 230466884483617720472188736317891759104]$ |
$None$ |
$0$ |
$48$ |
$12$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-10}) \) |
$C_2$, $C_2$ |
1.19.ai 2 $\times$ 1.19.ag |
| 3.19.aw_ik_abvg |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 19 x^{2} )( 1 - 7 x + 19 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$-2$ |
$[-2, 314, 6916, 131570, 2483818, 47077628, 893957902, 16983620450, 322686721084, 6131059306874]$ |
$2028$ |
$[2028, 41395536, 325442505024, 2234615976919872, 15228511793596195068, 104197636641862317625344, 714278343763364234273921892, 4898779489959538094356471633152, 33600513242698480992621549580030656, 230466356612082474567763089151572224976]$ |
$None$ |
$0$ |
$78$ |
$18$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$ |
1.19.ai $\times$ 1.19.ah 2 |
| 3.19.av_hp_abpt |
$3$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 21 x + 197 x^{2} - 1085 x^{3} + 3743 x^{4} - 7581 x^{5} + 6859 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 315, 6755, 129563, 2470549, 47022783, 893837440, 16983737715, 322688804207, 6131067450095]$ |
$2113$ |
$[2113, 41176031, 317707854919, 2200473161067623, 15147133075884914623, 104076236471803961101919, 714182091169979124110840512, 4898813313984458420714154288647, 33600730152842051506494912587248477, 230466662715465323840912996794964557871]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.400967.1 |
$A_4\times C_2$ |
simple |
| 3.19.av_hr_abqk |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 8 x + 19 x^{2} )( 1 - 13 x + 76 x^{2} - 247 x^{3} + 361 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$3$ |
$0$ |
$-1$ |
$[-1, 319, 6830, 130231, 2474269, 47037016, 893881127, 16983918319, 322689959162, 6131073656879]$ |
$2136$ |
$[2136, 41745984, 321249880224, 2211793071581184, 15169914353306751816, 104107727714127645441024, 714216996331786782411647736, 4898865408824652135821938950144, 33600850415949491694689716684546272, 230466896028524319788515904268974996544]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.43928.1 |
$C_2$, $D_{4}$ |
1.19.ai $\times$ 2.19.an_cy |
| 3.19.av_hs_abqt |
$3$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 21 x + 200 x^{2} - 1111 x^{3} + 3800 x^{4} - 7581 x^{5} + 6859 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 321, 6866, 130517, 2475339, 47035320, 893829201, 16983522357, 322687945754, 6131065370381]$ |
$2147$ |
$[2147, 42023231, 322933919900, 2216626470540995, 15176460908586830417, 104103971144479889270000, 714175506811985743282547123, 4898751196179662358104856994955, 33600640764418611118689748855910900, 230466584539075875020520864015003678311]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.16537520.2 |
$S_4\times C_2$ |
simple |
| 3.19.av_hs_abqs |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 19 x^{2} )( 1 - 13 x + 77 x^{2} - 247 x^{3} + 361 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 321, 6869, 130601, 2476544, 47047149, 893918255, 16984068545, 322690782881, 6131078213676]$ |
$2148$ |
$[2148, 42040656, 323116768548, 2218091412091968, 15183864271616319168, 104130154148064123368016, 714246661983567890941051812, 4898908741055518045907668300032, 33600936188188438634402573882592852, 230467067318579954016144311646896664576]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.64389.1 |
$C_2$, $D_{4}$ |
1.19.ai $\times$ 2.19.an_cz |
| 3.19.av_ht_abrb |
$3$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 21 x + 201 x^{2} - 1119 x^{3} + 3819 x^{4} - 7581 x^{5} + 6859 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 323, 6905, 130883, 2477489, 47043539, 893847632, 16983548195, 322688249579, 6131069483003]$ |
$2159$ |
$[2159, 42318559, 324803818133, 2222862251232951, 15189649469380082429, 104122163780175055306951, 714190233713713525860397568, 4898758649264970152143724771751, 33600672401067828632157286080829391, 230466739132416360911415151701463483159]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.23035671.1 |
$A_4\times C_2$ |
simple |
| 3.19.av_ht_abra |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 19 x^{2} )( 1 - 8 x + 19 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-1$ |
$[-1, 323, 6908, 130967, 2478689, 47055164, 893932451, 16984034927, 322690454852, 6131076937523]$ |
$2160$ |
$[2160, 42336000, 324986800320, 2224327343616000, 15197021893253494800, 104147894363957144064000, 714258003970320600314383920, 4898899043741104798168571904000, 33600902031189184684759842632880960, 230467019347962033343598199542018400000]$ |
$None$ |
$0$ |
$48$ |
$12$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-51}) \) |
$C_2$, $C_2$ |
1.19.ai 2 $\times$ 1.19.af |
| 3.19.av_hu_abrk |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 6 x + 19 x^{2} )( 1 - 15 x + 93 x^{2} - 285 x^{3} + 361 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 325, 6941, 131161, 2478314, 47038225, 893762771, 16982966561, 322685853869, 6131065525000]$ |
$2170$ |
$[2170, 42597100, 326493818770, 2227571043516000, 15194706371629708000, 104110408978200046977100, 714122434555169417971874170, 4898590883871135970948766064000, 33600422942522406417640064137532770, 230466590351287267444322107107856000000]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-10}) \), 4.0.1525.1 |
$C_2$, $D_{4}$ |
1.19.ag $\times$ 2.19.ap_dp |
| 3.19.av_hu_abrj |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 19 x^{2} )( 1 - 14 x + 85 x^{2} - 266 x^{3} + 361 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 325, 6944, 131245, 2479509, 47049652, 893843663, 16983401941, 322687572368, 6131069567285]$ |
$2171$ |
$[2171, 42614559, 326676900368, 2229035859688131, 15202046334150949221, 104135697665554925051136, 714187062956560892633194247, 4898716463278329661754245127979, 33600601884692557405202172491767664, 230466742300540977010747122649460970159]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.14912.2 |
$C_2$, $D_{4}$ |
1.19.ah $\times$ 2.19.ao_dh |
| 3.19.av_hu_abri |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 19 x^{2} )( 1 - 13 x + 79 x^{2} - 247 x^{3} + 361 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 325, 6947, 131329, 2480704, 47061073, 893924261, 16983829969, 322689166253, 6131072007980]$ |
$2172$ |
$[2172, 42632016, 326860016364, 2230501108637760, 15209387845603707072, 104160975887241195393744, 714251459543936442395731788, 4898839924263639308275321647360, 33600767852147518767072188252531916, 230466834046347035470648946219800866816]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.21125.1 |
$C_2$, $C_4$ |
1.19.ai $\times$ 2.19.an_db |
| 3.19.av_hv_abrq |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 19 x^{2} )( 1 - 7 x + 19 x^{2} )( 1 - 6 x + 19 x^{2} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-1$ |
$[-1, 327, 6986, 131687, 2482589, 47064888, 893894231, 16983466127, 322687105454, 6131065521927]$ |
$2184$ |
$[2184, 42928704, 328736457504, 2236612952770560, 15220962779242083864, 104169426322217022434304, 714227466121818639047866536, 4898734976401246564800099287040, 33600553266128114882164373027120736, 230466590235682631678378057689348490304]$ |
$None$ |
$0$ |
$48$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-10}) \) |
$C_2$, $C_2$, $C_2$ |
1.19.ai $\times$ 1.19.ah $\times$ 1.19.ag |
| 3.19.av_hw_abrx |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 19 x^{2} )^{3}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$-1$ |
$[-1, 329, 7028, 132125, 2485529, 47077628, 893914811, 16983261365, 322684767692, 6131051479049]$ |
$2197$ |
$[2197, 43243551, 330799583296, 2244129138640467, 15239028704650761907, 104197636641862317625344, 714243912660180357557034673, 4898675916201058054681068232587, 33600309842396717185666417442720704, 230466062364821344245627328294959077151]$ |
$None$ |
$0$ |
$78$ |
$18$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
1.19.ah 3 |
| 3.19.au_ha_abme |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 8 x + 19 x^{2} )( 1 - 12 x + 67 x^{2} - 228 x^{3} + 361 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$0$ |
$[0, 326, 6804, 129746, 2472120, 47036804, 893914056, 16983947810, 322688674476, 6131064348326]$ |
$2268$ |
$[2268, 42484176, 320033297808, 2203578927160128, 15156742624074653868, 104107259223656017894656, 714243307349510827366234932, 4898873914811624006398955918592, 33600716644472285295107078137397232, 230466546120099380773172876630906922576]$ |
$None$ |
$0$ |
$24$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}, \sqrt{7})\) |
$C_2$, $C_2^2$ |
1.19.ai $\times$ 2.19.am_cp |
| 3.19.au_hb_abmm |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 8 x + 19 x^{2} )( 1 - 12 x + 68 x^{2} - 228 x^{3} + 361 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 328, 6840, 130052, 2473800, 47044264, 893951520, 16984182332, 322690050720, 6131070638248]$ |
$2280$ |
$[2280, 42772800, 321743401560, 2208774389068800, 15167037542527115400, 104123770282648644091200, 714273244101214451560506360, 4898941562752039626419286835200, 33600859949766909048650154004202280, 230466782558124112926234039163635720000]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.168192.4 |
$C_2$, $D_{4}$ |
1.19.ai $\times$ 2.19.am_cq |
| 3.19.au_hc_abmv |
$3$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 20 x + 184 x^{2} - 1009 x^{3} + 3496 x^{4} - 7220 x^{5} + 6859 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 330, 6873, 130274, 2474280, 47040057, 893902380, 16983892418, 322688697108, 6131064107970]$ |
$2291$ |
$[2291, 43045599, 323280189779, 2212521275751723, 15169969932654444941, 104114455928699482347759, 714233978579482263588954263, 4898857937767913334426448779603, 33600719001173394459048044353268288, 230466537085177535973231321004653443919]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.259972443.1 |
$S_4\times C_2$ |
simple |
| 3.19.au_hc_abmu |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 19 x^{2} )( 1 - 12 x + 69 x^{2} - 228 x^{3} + 361 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 330, 6876, 130354, 2475360, 47049948, 893971680, 16984290914, 322690673124, 6131072798730]$ |
$2292$ |
$[2292, 43062096, 323456281344, 2213905895826240, 15176598812023508772, 104136349707270831734784, 714289353037471174487571708, 4898972883250762927070690039040, 33600924759406787845689344658990336, 230466863770646445418458779605474404816]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.12625.1 |
$C_2$, $D_{4}$ |
1.19.ai $\times$ 2.19.am_cr |
| 3.19.au_hd_abne |
$3$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 20 x + 185 x^{2} - 1018 x^{3} + 3515 x^{4} - 7220 x^{5} + 6859 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 332, 6906, 130492, 2474650, 47034464, 893843580, 16983576412, 322687559892, 6131060858952]$ |
$2302$ |
$[2302, 43319036, 324819610138, 2216204827454448, 15172232911397882982, 104102077950241788590876, 714186997131103736264612818, 4898766787822136837690040653568, 33600600585545127292306417895977654, 230466414954687299937312043376295078876]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.250046912.2 |
$S_4\times C_2$ |
simple |
| 3.19.au_hd_abnd |
$3$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 20 x + 185 x^{2} - 1017 x^{3} + 3515 x^{4} - 7220 x^{5} + 6859 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 332, 6909, 130572, 2475725, 47044169, 893909450, 16983933572, 322689176943, 6131067243027]$ |
$2303$ |
$[2303, 43335551, 324995776532, 2217589046909663, 15178829278992650768, 104123556947097765600656, 714239628158665712607534317, 4898869808739068846335161955823, 33600768965198838361866174936341876, 230466654931819327895082317854517278976]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.266767367.1 |
$S_4\times C_2$ |
simple |
| 3.19.au_hd_abnc |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 4 x + 19 x^{2} )( 1 - 8 x + 19 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$0$ |
$[0, 332, 6912, 130652, 2476800, 47053868, 893975040, 16984284092, 322690687488, 6131072330252]$ |
$2304$ |
$[2304, 43352064, 325171977984, 2218973661757440, 15185426899925470464, 104145024617154922512384, 714292037240265820828705536, 4898970915433955343855475752960, 33600926255106087706740762038743296, 230466846160603507198152587478682927104]$ |
$None$ |
$1$ |
$48$ |
$12$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-15}) \) |
$C_2$, $C_2$ |
1.19.ai 2 $\times$ 1.19.ae |
| 3.19.au_he_abnn |
$3$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 20 x + 186 x^{2} - 1027 x^{3} + 3534 x^{4} - 7220 x^{5} + 6859 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 334, 6939, 130706, 2474910, 47027497, 893775582, 16983242738, 322686731772, 6131061506854]$ |
$2313$ |
$[2313, 43593111, 326361702501, 2219825250400059, 15173826937588402803, 104086663499372605732719, 714132669385827613910974653, 4898670542991701302102981877331, 33600514355521341904238517713510208, 230466439309229300600203159557237774591]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.6079419.1 |
$S_4\times C_2$ |
simple |
| 3.19.au_he_abnm |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
|
✓ |
|
✓ |
? |
$( 1 - 7 x + 19 x^{2} )( 1 - 13 x + 76 x^{2} - 247 x^{3} + 361 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$3$ |
$0$ |
$0$ |
$[0, 334, 6942, 130786, 2475980, 47037016, 893838036, 16983559234, 322688005770, 6131065829054]$ |
$2314$ |
$[2314, 43609644, 326537944096, 2221209072093024, 15180390796581150634, 104107727714127645441024, 714182568185797065579355534, 4898761833249609459996048430464, 33600647013606653678335013210974048, 230466601780574491068250050725585147244]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.43928.1 |
$C_2$, $D_{4}$ |
1.19.ah $\times$ 2.19.an_cy |
| 3.19.au_he_abnl |
$3$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 20 x + 186 x^{2} - 1025 x^{3} + 3534 x^{4} - 7220 x^{5} + 6859 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 334, 6945, 130866, 2477050, 47046529, 893900210, 16983869106, 322689174180, 6131068880854]$ |
$2315$ |
$[2315, 43626175, 326714220695, 2222593290056875, 15186955914913049825, 104128780606980430565575, 714232245004410826580645855, 4898851213779863508631378661875, 33600768677342458090150617525114560, 230466716497637998343589872592099304375]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.219205675.1 |
$A_4\times C_2$ |
simple |
| 3.19.au_he_abnk |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 19 x^{2} )( 1 - 12 x + 71 x^{2} - 228 x^{3} + 361 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 334, 6948, 130946, 2478120, 47056036, 893962104, 16984172354, 322690237020, 6131070663454]$ |
$2316$ |
$[2316, 43642704, 326890532304, 2223977904316224, 15193522294108601916, 104149822191606124786944, 714281699893464346275842916, 4898938684693632541973375710464, 33600879348756103457182981888520112, 230466783505671232678891067071140609744]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.134928.2 |
$C_2$, $D_{4}$ |
1.19.ai $\times$ 2.19.am_ct |
| 3.19.au_hf_abnv |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 5 x + 19 x^{2} )( 1 - 15 x + 93 x^{2} - 285 x^{3} + 361 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 336, 6975, 130996, 2476125, 47028501, 893757900, 16983176276, 322687249875, 6131069112771]$ |
$2325$ |
$[2325, 43884375, 328082823900, 2224766180709375, 15181283843650650000, 104088889218903269850000, 714118542853330737287177475, 4898651373145518367557186759375, 33600568304364381183437528899452300, 230466725215459460299545105412500000000]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-51}) \), 4.0.1525.1 |
$C_2$, $D_{4}$ |
1.19.af $\times$ 2.19.ap_dp |
| 3.19.au_hf_abnu |
$3$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 20 x + 187 x^{2} - 1034 x^{3} + 3553 x^{4} - 7220 x^{5} + 6859 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 336, 6978, 131076, 2477190, 47037828, 893816672, 16983446172, 322688092008, 6131070370716]$ |
$2326$ |
$[2326, 43900924, 328259176018, 2226150004654000, 15187816462768699726, 104109527334951837371356, 714165498612267566308100442, 4898729221414676263102315744000, 33600655993306235062901598345554638, 230466772501543237488095068324888336924]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.5870272.1 |
$S_4\times C_2$ |
simple |
| 3.19.au_hf_abnt |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 7 x + 19 x^{2} )( 1 - 13 x + 77 x^{2} - 247 x^{3} + 361 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 336, 6981, 131156, 2478255, 47047149, 893875164, 16983709460, 322688829489, 6131070385851]$ |
$2327$ |
$[2327, 43917471, 328435563092, 2227534225771023, 15194350348796648432, 104130154148064123368016, 714212232407573853789209153, 4898805164564312063832579488367, 33600732785326379403813709957507268, 230466773070411431207638640727772037376]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.64389.1 |
$C_2$, $D_{4}$ |
1.19.ah $\times$ 2.19.an_cz |
| 3.19.au_hf_abns |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 8 x + 19 x^{2} )( 1 - 12 x + 72 x^{2} - 228 x^{3} + 361 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$0$ |
$[0, 336, 6984, 131236, 2479320, 47056464, 893933376, 16983966140, 322689462336, 6131069159376]$ |
$2328$ |
$[2328, 43934016, 328611985128, 2228918844085248, 15200885503259773368, 104150769671957219055936, 714258744291370348933277832, 4898879202706627226746289651712, 33600798682453766754881152854466392, 230466726967316229207924486107648160576]$ |
$None$ |
$1$ |
$48$ |
$24$ |
$4$ |
\(\Q(\sqrt{-3}) \), \(\Q(\zeta_{8})\) |
$C_2$, $C_2^2$ |
1.19.ai $\times$ 2.19.am_cu |
| 3.19.au_hg_aboc |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 6 x + 19 x^{2} )( 1 - 14 x + 85 x^{2} - 266 x^{3} + 361 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 338, 7014, 131362, 2478280, 47036912, 893779992, 16983247618, 322687956738, 6131075782338]$ |
$2338$ |
$[2338, 44192876, 329983346728, 2231027848838880, 15194510439144017058, 104107504115179801885376, 714136191816895424507455126, 4898671950292740343767797470080, 33600641908227777676324922952840184, 230466975924532106268181993570358344236]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-10}) \), 4.0.14912.2 |
$C_2$, $D_{4}$ |
1.19.ag $\times$ 2.19.ao_dh |
| 3.19.au_hg_abob |
$3$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 20 x + 188 x^{2} - 1041 x^{3} + 3572 x^{4} - 7220 x^{5} + 6859 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 338, 7017, 131442, 2479340, 47046041, 893834816, 16983465026, 322688280948, 6131073053058]$ |
$2339$ |
$[2339, 44209439, 330159844547, 2232412077758603, 15201013110132928469, 104127704874454389131471, 714179993778133831841286143, 4898734659071029270900612271507, 33600675667109747485510625502483008, 230466873330766656036988167377247531839]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.31028123.1 |
$A_4\times C_2$ |
simple |
| 3.19.au_hg_aboa |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 8 x + 19 x^{2} )( 1 - 7 x + 19 x^{2} )( 1 - 5 x + 19 x^{2} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$0$ |
$[0, 338, 7020, 131522, 2480400, 47055164, 893889360, 16983675842, 322688501460, 6131069109698]$ |
$2340$ |
$[2340, 44226000, 330336377280, 2233796704776000, 15207517057174427700, 104147894363957144064000, 714223573847596958936887980, 4898795467454926885432245024000, 33600698628533894437293854487896640, 230466725099854756884214303379569650000]$ |
$None$ |
$0$ |
$48$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-51}) \) |
$C_2$, $C_2$, $C_2$ |
1.19.ai $\times$ 1.19.ah $\times$ 1.19.af |
| 3.19.au_hh_aboi |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 8 x + 19 x^{2} )( 1 - 6 x + 19 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$0$ |
$[0, 340, 7056, 131804, 2481360, 47052148, 893830560, 16983311804, 322687489824, 6131071736980]$ |
$2352$ |
$[2352, 44518656, 332063749584, 2238611713228800, 15213417507053884272, 104141223640193463569664, 714176592104258611693993488, 4898690463247434737960406220800, 33600593289605422892280548166135216, 230466823859519612884937918141308482816]$ |
$None$ |
$1$ |
$36$ |
$12$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-10}) \) |
$C_2$, $C_2$ |
1.19.ai $\times$ 1.19.ag 2 |
| 3.19.au_hh_aboh |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 19 x^{2} )( 1 - 13 x + 79 x^{2} - 247 x^{3} + 361 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 340, 7059, 131884, 2482415, 47061073, 893881170, 16983470884, 322687212861, 6131064180155]$ |
$2353$ |
$[2353, 44535231, 332240428156, 2239996752624735, 15219891549533193328, 104160975887241195393744, 714217029736680604402846747, 4898736349227410794777492367535, 33600564450304479730416402598190044, 230466539798476342317816488926176911616]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.21125.1 |
$C_2$, $C_4$ |
1.19.ah $\times$ 2.19.an_db |
| 3.19.au_hi_aboo |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 6 x + 19 x^{2} )( 1 - 7 x + 19 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$0$ |
$[0, 342, 7098, 132242, 2484300, 47064888, 893851140, 16983107042, 322685152062, 6131057694102]$ |
$2366$ |
$[2366, 44845164, 334147757216, 2246134615976160, 15231474476897364686, 104169426322217022434304, 714193037471142725233790234, 4898631403583906363123840058240, 33600349865584069726518097054195424, 230466295988123223093452979343516769004]$ |
$None$ |
$0$ |
$48$ |
$12$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-10}) \) |
$C_2$, $C_2$ |
1.19.ah 2 $\times$ 1.19.ag |
| 3.19.at_gi_abhp |
$3$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 19 x + 164 x^{2} - 873 x^{3} + 3116 x^{4} - 6859 x^{5} + 6859 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 329, 6730, 129141, 2471081, 47044376, 893944283, 16983821429, 322687825738, 6131068011429]$ |
$2389$ |
$[2389, 42741599, 316624308916, 2193364694800739, 15150388541614695559, 104124022040275104639344, 714267460433823299656227829, 4898837461410192661141676993099, 33600628267378854889680005230927228, 230466683815988249363050341595189098119]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.24948656.1 |
$S_4\times C_2$ |
simple |
| 3.19.at_gj_abhy |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 8 x + 19 x^{2} )( 1 - 11 x + 58 x^{2} - 209 x^{3} + 361 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 331, 6760, 129319, 2471471, 47043244, 893931949, 16983730639, 322686939160, 6131060694251]$ |
$2400$ |
$[2400, 43008000, 318008073600, 2196356628480000, 15152765954930532000, 104121511879594180608000, 714257602844153058601144800, 4898811272798154818786426880000, 33600535950375050704711208488540800, 230466408763532621365820320758835200000]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.8405.1 |
$C_2$, $D_{4}$ |
1.19.ai $\times$ 2.19.al_cg |
| 3.19.at_gk_abig |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 8 x + 19 x^{2} )( 1 - 11 x + 59 x^{2} - 209 x^{3} + 361 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 333, 6793, 129569, 2472736, 47049633, 893973991, 16984003505, 322688336083, 6131066532588]$ |
$2412$ |
$[2412, 43290576, 319563923868, 2200591754593344, 15160516464407867712, 104135656133289457259856, 714291199160673511385196444, 4898889980426686273861180559616, 33600681408412331651551233768764508, 230466628226397623580769067791798726656]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.291597.2 |
$C_2$, $D_{4}$ |
1.19.ai $\times$ 2.19.al_ch |
| 3.19.at_gl_abip |
$3$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 19 x + 167 x^{2} - 899 x^{3} + 3173 x^{4} - 6859 x^{5} + 6859 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 335, 6823, 129739, 2472921, 47046083, 893944864, 16983842179, 322687312327, 6131059613055]$ |
$2423$ |
$[2423, 43558271, 320952244601, 2203453724409495, 15161640658002721853, 104127795220684917412559, 714267923955527628808256192, 4898843446376108143553349663495, 33600574807529321720806082614588079, 230466368121500466907070014217084756391]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.1019852375.1 |
$S_4\times C_2$ |
simple |
| 3.19.at_gl_abio |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 8 x + 19 x^{2} )( 1 - 11 x + 60 x^{2} - 209 x^{3} + 361 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 335, 6826, 129815, 2473891, 47054552, 894003097, 16984187951, 322689184942, 6131068928735]$ |
$2424$ |
$[2424, 43573824, 321122182752, 2204761593194496, 15167592843844811304, 104146545138708290190336, 714314458069644937182935448, 4898943183634956033300123254784, 33600769798042763537090173630887456, 230466718297462034301299871267152107584]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.444312.2 |
$C_2$, $D_{4}$ |
1.19.ai $\times$ 2.19.al_ci |
| 3.19.at_gm_abiy |
$3$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 19 x + 168 x^{2} - 908 x^{3} + 3192 x^{4} - 6859 x^{5} + 6859 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 337, 6853, 129905, 2473006, 47041429, 893909479, 16983673361, 322686474223, 6131054596072]$ |
$2434$ |
$[2434, 43826604, 322342878562, 2206251230291424, 15162154935567467104, 104117492955728411647596, 714239649612035379029994634, 4898794751619228901262751767424, 33600487538140748486538170016611482, 230466179533460642744183180523165225984]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.901877544.2 |
$S_4\times C_2$ |
simple |
| 3.19.at_gm_abix |
$3$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 19 x + 168 x^{2} - 907 x^{3} + 3192 x^{4} - 6859 x^{5} + 6859 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 337, 6856, 129981, 2473971, 47049724, 893964737, 16983986037, 322688080168, 6131062280737]$ |
$2435$ |
$[2435, 43842175, 322512866960, 2207558600943475, 15168074679636163925, 104135855319576414380800, 714283804952438575761072935, 4898884941936538191233964870475, 33600654760813922151790111827198320, 230466468399488372259595646920031629375]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.87681712.1 |
$S_4\times C_2$ |
simple |
| 3.19.at_gm_abiw |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 19 x^{2} )( 1 - 11 x + 61 x^{2} - 209 x^{3} + 361 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 337, 6859, 130057, 2474936, 47058013, 894019729, 16984292737, 322689595231, 6131068910252]$ |
$2436$ |
$[2436, 43857744, 322682891076, 2208866330448960, 15173995421836431936, 104154205726857117044304, 714327748772286456022580484, 4898973409093389327294189891840, 33600812520529022479570598009802804, 230466717602688594871101405033691951104]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.508805.3 |
$C_2$, $D_{4}$ |
1.19.ai $\times$ 2.19.al_cj |
| 3.19.at_gn_abjg |
$3$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 19 x + 169 x^{2} - 916 x^{3} + 3211 x^{4} - 6859 x^{5} + 6859 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 339, 6886, 130143, 2473951, 47043804, 893920553, 16983784047, 322687238374, 6131058052179]$ |
$2446$ |
$[2446, 44111164, 323905904632, 2210291327897200, 15167946936127908586, 104122751034325259899456, 714248499638842488393130774, 4898826678652943052707865779200, 33600567107033308284948099087027688, 230466309448248158680494926305760367004]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.98662336.1 |
$S_4\times C_2$ |
simple |
| 3.19.at_gn_abjf |
$3$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
? |
$1 - 19 x + 169 x^{2} - 915 x^{3} + 3211 x^{4} - 6859 x^{5} + 6859 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 339, 6889, 130219, 2474911, 47051919, 893972584, 16984058291, 322688501221, 6131063264679]$ |
$2447$ |
$[2447, 44126751, 324075979313, 2211598561887975, 15173835238231082897, 104140713875799751722351, 714290075843090750535714368, 4898905783445233421736123234375, 33600698603961132777063425755505747, 230466505385783031164561422254171934191]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.57050895.1 |
$S_4\times C_2$ |
simple |
| 3.19.at_gn_abje |
$3$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - 3 x + 19 x^{2} )( 1 - 8 x + 19 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$1$ |
$[1, 339, 6892, 130295, 2475871, 47060028, 894024349, 16984326575, 322689674068, 6131067446499]$ |
$2448$ |
$[2448, 44142336, 324246089664, 2212906155651072, 15179724544816029168, 104158664771708691615744, 714331440525333065383418832, 4898983169663591808577313636352, 33600820729727952506101551665933376, 230466662580284102470625501650401758976]$ |
$None$ |
$0$ |
$48$ |
$12$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-67}) \) |
$C_2$, $C_2$ |
1.19.ai 2 $\times$ 1.19.ad |
