| 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 |
| 2.13.ao_cx |
$2$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 13 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$0$ |
$[0, 124, 2058, 28180, 370440, 4825798, 62752536, 815772004, 10604736114, 137859612364]$ |
$49$ |
$[49, 21609, 4528384, 804913641, 137542331689, 23293210300416, 3937628638777729, 665450286236357769, 112457917496359649536, 19005118247840541139449]$ |
$0$ |
$0$ |
$24$ |
$12$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
1.13.ah 2 |
| 2.13.an_cq |
$2$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 13 x^{2} )( 1 - 6 x + 13 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$1$ |
$[1, 137, 2146, 28609, 372061, 4830374, 62759425, 815751841, 10604504938, 137858369057]$ |
$56$ |
$[56, 23520, 4715648, 817084800, 138143507096, 23315295467520, 3938060927158232, 665433838241625600, 112455465963248062592, 19004946846716043141600]$ |
$0$ |
$0$ |
$24$ |
$12$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.13.ah $\times$ 1.13.ag |
| 2.13.am_cj |
$2$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 7 x + 13 x^{2} )( 1 - 5 x + 13 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$2$ |
$[2, 148, 2198, 28708, 371642, 4825798, 62737922, 815694916, 10604499374, 137859194068]$ |
$63$ |
$[63, 25137, 4826304, 819893529, 137988113823, 23293210300416, 3936711602576151, 665387401595286825, 112455406959154934976, 19005060581950480989777]$ |
$2$ |
$2$ |
$24$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$ |
1.13.ah $\times$ 1.13.af |
| 2.13.am_ck |
$2$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 6 x + 13 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$2$ |
$[2, 150, 2234, 29038, 373682, 4834950, 62766314, 815731678, 10604273762, 137857125750]$ |
$64$ |
$[64, 25600, 4910656, 829440000, 138747310144, 23337401574400, 3938493262997056, 665417390653440000, 112453014483578818624, 19004775447137357440000]$ |
$1$ |
$1$ |
$16$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
1.13.ag 2 |
| 2.13.al_cc |
$2$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 7 x + 13 x^{2} )( 1 - 4 x + 13 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$3$ |
$[3, 157, 2220, 28609, 370623, 4822234, 62737419, 815751841, 10604790060, 137859735157]$ |
$70$ |
$[70, 26460, 4873120, 817084800, 137610200350, 23276009352960, 3936680039061070, 665433838241625600, 112458489573068467360, 19005135175967126514300]$ |
$1$ |
$1$ |
$24$ |
$12$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.13.ah $\times$ 1.13.ae |
| 2.13.al_cd |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 11 x + 55 x^{2} - 143 x^{3} + 169 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$3$ |
$[3, 159, 2253, 28875, 371998, 4827063, 62748045, 815759379, 10604757819, 137859648214]$ |
$71$ |
$[71, 26909, 4949339, 824733941, 138120708816, 23299305353501, 3937346592497291, 665439985622292389, 112458147667396136951, 19005123190067808033024]$ |
$1$ |
$1$ |
$2$ |
$2$ |
$1$ |
4.0.6725.1 |
$D_{4}$ |
simple |
| 2.13.al_ce |
$2$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 6 x + 13 x^{2} )( 1 - 5 x + 13 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$3$ |
$[3, 161, 2286, 29137, 373263, 4830374, 62744811, 815674753, 10604268198, 137857950761]$ |
$72$ |
$[72, 27360, 5025888, 832291200, 138591237672, 23315295467520, 3937143790280808, 665370955154880000, 112452955480771954272, 19004889181346053336800]$ |
$0$ |
$0$ |
$24$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$ |
1.13.ag $\times$ 1.13.af |
| 2.13.ak_bv |
$2$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 7 x + 13 x^{2} )( 1 - 3 x + 13 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$4$ |
$[4, 164, 2218, 28420, 369844, 4822598, 62752708, 815806084, 10604753554, 137858748164]$ |
$77$ |
$[77, 27489, 4868864, 811722681, 137321294957, 23277766127616, 3937639431868373, 665478087042808809, 112458102440893104896, 19004999110047710270049]$ |
$2$ |
$2$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-43}) \) |
$C_2$, $C_2$ |
1.13.ah $\times$ 1.13.ad |
| 2.13.ak_bw |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 10 x + 48 x^{2} - 130 x^{3} + 169 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$4$ |
$[4, 166, 2248, 28630, 370744, 4825222, 62759428, 815833054, 10604885524, 137859128086]$ |
$78$ |
$[78, 27924, 4937166, 817726416, 137654749518, 23290419024756, 3938061065912142, 665500088766649344, 112459501937770802334, 19005051485687611153524]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.39744.5 |
$D_{4}$ |
simple |
| 2.13.ak_bx |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 10 x + 49 x^{2} - 130 x^{3} + 169 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$4$ |
$[4, 168, 2278, 28836, 371544, 4826622, 62756488, 815805828, 10604793214, 137858817928]$ |
$79$ |
$[79, 28361, 5005756, 823631801, 137951509639, 23297168861456, 3937876498186591, 665477878436414825, 112458523017372489244, 19005008727769158477321]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
4.0.27200.2 |
$D_{4}$ |
simple |
| 2.13.ak_by |
$2$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 6 x + 13 x^{2} )( 1 - 4 x + 13 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$4$ |
$[4, 170, 2308, 29038, 372244, 4826810, 62744308, 815731678, 10604558884, 137858491850]$ |
$80$ |
$[80, 28800, 5074640, 829440000, 138211672400, 23298078211200, 3937112223300560, 665417390653440000, 112456038027485859920, 19004963774689959120000]$ |
$5$ |
$5$ |
$16$ |
$12$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.13.ag $\times$ 1.13.ae |
| 2.13.ak_bz |
$2$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 5 x + 13 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$4$ |
$[4, 172, 2338, 29236, 372844, 4825798, 62723308, 815617828, 10604262634, 137858775772]$ |
$81$ |
$[81, 29241, 5143824, 835152201, 138435340761, 23293210300416, 3935794779943569, 665324522896775625, 112452896477996048016, 19005002916235392383721]$ |
$2$ |
$2$ |
$24$ |
$12$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
1.13.af 2 |
| 2.13.aj_bn |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
|
✓ |
|
✓ |
✓ |
$1 - 9 x + 39 x^{2} - 117 x^{3} + 169 x^{4}$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$2$ |
$0$ |
$5$ |
$[5, 167, 2171, 28059, 368990, 4823039, 62750147, 815707891, 10604178533, 137857322582]$ |
$83$ |
$[83, 27805, 4765943, 801479125, 137005100048, 23279891985805, 3937478512982279, 665397985659625125, 112452004640700347987, 19004802581974649094400]$ |
$1$ |
$1$ |
$2$ |
$2$ |
$1$ |
4.0.10933.1 |
$D_{4}$ |
simple |
| 2.13.aj_bo |
$2$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 7 x + 13 x^{2} )( 1 - 2 x + 13 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$5$ |
$[5, 169, 2198, 28225, 369665, 4825798, 62765141, 815787169, 10604499374, 137858349889]$ |
$84$ |
$[84, 28224, 4826304, 806190336, 137254909764, 23293210300416, 3938419609170564, 665462657105777664, 112455406959154934976, 19004944204233732354624]$ |
$4$ |
$4$ |
$24$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$ |
1.13.ah $\times$ 1.13.ac |
| 2.13.aj_bp |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 9 x + 41 x^{2} - 117 x^{3} + 169 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$5$ |
$[5, 171, 2225, 28387, 370250, 4827579, 62773205, 815828803, 10604636345, 137858461686]$ |
$85$ |
$[85, 28645, 4886905, 810796725, 137471390800, 23301803950765, 3938925735789745, 665496620891533125, 112456859467929137365, 19004959616264376217600]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
4.0.122157.1 |
$D_{4}$ |
simple |
| 2.13.aj_bq |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 9 x + 42 x^{2} - 117 x^{3} + 169 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$5$ |
$[5, 173, 2252, 28545, 370745, 4828394, 62774717, 815838625, 10604648252, 137858097413]$ |
$86$ |
$[86, 29068, 4947752, 815299264, 137654604926, 23305732692736, 3939020624607518, 665504633516606208, 112456985748631159016, 19004909398444914345388]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.119068.1 |
$D_{4}$ |
simple |
| 2.13.aj_br |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 9 x + 43 x^{2} - 117 x^{3} + 169 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$5$ |
$[5, 175, 2279, 28699, 371150, 4828255, 62770055, 815822419, 10604591957, 137857657750]$ |
$87$ |
$[87, 29493, 5008851, 819698949, 137804618832, 23305056711525, 3938728027833483, 665491412853217989, 112456388771410123359, 19004848787538456323328]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.92781.3 |
$D_{4}$ |
simple |
| 2.13.aj_bs |
$2$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 6 x + 13 x^{2} )( 1 - 3 x + 13 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$5$ |
$[5, 177, 2306, 28849, 371465, 4827174, 62759597, 815785921, 10604522378, 137857504857]$ |
$88$ |
$[88, 29920, 5070208, 823996800, 137921504248, 23299836651520, 3938071721433784, 665461638360921600, 112455650903749808512, 19004827709997678181600]$ |
$3$ |
$3$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-43}) \) |
$C_2$, $C_2$ |
1.13.ag $\times$ 1.13.ad |
| 2.13.aj_bt |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 9 x + 45 x^{2} - 117 x^{3} + 169 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$5$ |
$[5, 179, 2333, 28995, 371690, 4825163, 62743721, 815734819, 10604492489, 137857962614]$ |
$89$ |
$[89, 30349, 5131829, 828193861, 138005338064, 23290133646901, 3937075508657429, 665419951329961509, 112455333921596387681, 19004890815397948493824]$ |
$3$ |
$3$ |
$2$ |
$2$ |
$1$ |
4.0.20725.1 |
$D_{4}$ |
simple |
| 2.13.aj_bu |
$2$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 13 x^{2} )( 1 - 4 x + 13 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$5$ |
$[5, 181, 2360, 29137, 371825, 4822234, 62722805, 815674753, 10604553320, 137859316861]$ |
$90$ |
$[90, 30780, 5193720, 832291200, 138056202450, 23276009352960, 3935763223779330, 665370955154880000, 112455979023092576760, 19005077510025702543900]$ |
$0$ |
$0$ |
$24$ |
$12$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.13.af $\times$ 1.13.ae |
| 2.13.ai_bg |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
|
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 8 x + 32 x^{2} - 104 x^{3} + 169 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$6$ |
$[6, 170, 2142, 27958, 369606, 4826810, 62749182, 815662558, 10604218086, 137858491850]$ |
$90$ |
$[90, 28260, 4705290, 798627600, 137233172250, 23298083455140, 3937418050935690, 665361008507289600, 112452424073098948890, 19004963775070323766500]$ |
$3$ |
$3$ |
$4$ |
$8$ |
$4$ |
\(\Q(i, \sqrt{10})\) |
$C_2^2$ |
simple |
| 2.13.ai_bh |
$2$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 7 x + 13 x^{2} )( 1 - x + 13 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$6$ |
$[6, 172, 2166, 28084, 370086, 4829254, 62763630, 815726116, 10604422158, 137859184732]$ |
$91$ |
$[91, 28665, 4758208, 802190025, 137411044771, 23309890007040, 3938324793124267, 665412853037812425, 112454588112991214272, 19005059294898370518825]$ |
$6$ |
$6$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-51}) \) |
$C_2$, $C_2$ |
1.13.ah $\times$ 1.13.ab |
| 2.13.ai_bi |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 8 x + 34 x^{2} - 104 x^{3} + 169 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$6$ |
$[6, 174, 2190, 28206, 370486, 4830942, 62773374, 815765214, 10604496486, 137859182734]$ |
$92$ |
$[92, 29072, 4811324, 805643264, 137559158172, 23318043275408, 3938936338883708, 665444746257907712, 112455376305986338268, 19005059019349406723472]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.1088.2 |
$D_{4}$ |
simple |
| 2.13.ai_bj |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 8 x + 35 x^{2} - 104 x^{3} + 169 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$6$ |
$[6, 176, 2214, 28324, 370806, 4831886, 62778750, 815784388, 10604480958, 137858752496]$ |
$93$ |
$[93, 29481, 4864644, 808988121, 137677549773, 23322601646352, 3939273752827989, 665460387626023593, 112455211642756494948, 19004999707306338623241]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
4.0.308112.1 |
$D_{4}$ |
simple |
| 2.13.ai_bk |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 8 x + 36 x^{2} - 104 x^{3} + 169 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$6$ |
$[6, 178, 2238, 28438, 371046, 4832098, 62780094, 815788126, 10604413734, 137858130418]$ |
$94$ |
$[94, 29892, 4918174, 812225424, 137766260974, 23323623778116, 3939358107660622, 665463437466931200, 112454498783628485566, 19004913948662907285252]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.297216.1 |
$D_{4}$ |
simple |
| 2.13.ai_bl |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 8 x + 37 x^{2} - 104 x^{3} + 169 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$6$ |
$[6, 180, 2262, 28548, 371206, 4831590, 62777742, 815780868, 10604331246, 137857522900]$ |
$95$ |
$[95, 30305, 4971920, 815356025, 137825337375, 23321168625920, 3939210486334295, 665457517069810025, 112453624060644805520, 19004830197396067022625]$ |
$10$ |
$10$ |
$2$ |
$2$ |
$1$ |
4.0.16025.1 |
$D_{4}$ |
simple |
| 2.13.ai_bm |
$2$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 6 x + 13 x^{2} )( 1 - 2 x + 13 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$6$ |
$[6, 182, 2286, 28654, 371286, 4830374, 62772030, 815767006, 10604268198, 137857106582]$ |
$96$ |
$[96, 30720, 5025888, 818380800, 137854828896, 23315295467520, 3938851984386912, 665446208805273600, 112452955480771954272, 19004772804678878361600]$ |
$12$ |
$12$ |
$24$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$ |
1.13.ag $\times$ 1.13.ac |
| 2.13.ai_bn |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
|
✓ |
|
✓ |
✓ |
$1 - 8 x + 39 x^{2} - 104 x^{3} + 169 x^{4}$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$2$ |
$0$ |
$6$ |
$[6, 184, 2310, 28756, 371286, 4828462, 62763294, 815750884, 10604257566, 137857028584]$ |
$97$ |
$[97, 31137, 5080084, 821300649, 137854789897, 23306063929488, 3938303712459073, 665433056262766857, 112452842730439348468, 19004762052047773538097]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.129168.1 |
$D_{4}$ |
simple |
| 2.13.ai_bo |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 8 x + 40 x^{2} - 104 x^{3} + 169 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$6$ |
$[6, 186, 2334, 28854, 371206, 4825866, 62751870, 815736798, 10604330598, 137857406746]$ |
$98$ |
$[98, 31556, 5134514, 824116496, 137825279298, 23293534014212, 3937586798998034, 665421564409806848, 112453617181605262178, 19004814184640001576516]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.65792.3 |
$D_{4}$ |
simple |
| 2.13.ai_bp |
$2$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 5 x + 13 x^{2} )( 1 - 3 x + 13 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$6$ |
$[6, 188, 2358, 28948, 371046, 4822598, 62738094, 815728996, 10604516814, 137858329868]$ |
$99$ |
$[99, 31977, 5189184, 826829289, 137766360699, 23277766127616, 3936722393153187, 665415199774578825, 112455591899559644736, 19004941444519141523577]$ |
$4$ |
$4$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-43}) \) |
$C_2$, $C_2$ |
1.13.af $\times$ 1.13.ad |
| 2.13.ai_bq |
$2$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 4 x + 13 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$6$ |
$[6, 190, 2382, 29038, 370806, 4818670, 62722302, 815731678, 10604844006, 137859857950]$ |
$100$ |
$[100, 32400, 5244100, 829440000, 137678102500, 23258821107600, 3935731667868100, 665417390653440000, 112459061652687456100, 19005152104108790010000]$ |
$5$ |
$5$ |
$16$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
1.13.ae 2 |
| 2.13.ah_z |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 7 x + 25 x^{2} - 91 x^{3} + 169 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$7$ |
$[7, 171, 2107, 27939, 370482, 4828251, 62737591, 815649603, 10604473075, 137859097846]$ |
$97$ |
$[97, 28421, 4631653, 798090101, 137557633792, 23305037451917, 3936690876993517, 665350440947283653, 112455128083212236881, 19005047316761795260416]$ |
$1$ |
$1$ |
$2$ |
$2$ |
$1$ |
4.0.148877.1 |
$C_4$ |
simple |
| 2.13.ah_ba |
$2$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
|
✓ |
|
✓ |
✓ |
$( 1 - 7 x + 13 x^{2} )( 1 + 13 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$7$ |
$[7, 173, 2128, 28033, 370867, 4830698, 62750527, 815694241, 10604617744, 137859794693]$ |
$98$ |
$[98, 28812, 4677344, 800743104, 137700691898, 23316859190016, 3937502572968986, 665386850963116800, 112456662227757292256, 19005143383543652756652]$ |
$2$ |
$2$ |
$6$ |
$6$ |
$2$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-13}) \) |
$C_2$, $C_2$ |
1.13.ah $\times$ 1.13.a |
| 2.13.ah_bb |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 7 x + 27 x^{2} - 91 x^{3} + 169 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$7$ |
$[7, 175, 2149, 28123, 371182, 4832575, 62760229, 815721043, 10604658967, 137859961750]$ |
$99$ |
$[99, 29205, 4723191, 803283525, 137817648144, 23325927456645, 3938111380279791, 665408712724467525, 112457099369691216459, 19005166413893781792000]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.6525.1 |
$D_{4}$ |
simple |
| 2.13.ah_bc |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 7 x + 28 x^{2} - 91 x^{3} + 169 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$7$ |
$[7, 177, 2170, 28209, 371427, 4833894, 62766991, 815733441, 10604623330, 137859767257]$ |
$100$ |
$[100, 29600, 4769200, 805712000, 137908520500, 23332299929600, 3938535727702900, 665418825721664000, 112456721449576759600, 19005139601246920068000]$ |
$6$ |
$6$ |
$2$ |
$2$ |
$1$ |
4.0.154652.1 |
$D_{4}$ |
simple |
| 2.13.ah_bd |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 7 x + 29 x^{2} - 91 x^{3} + 169 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$7$ |
$[7, 179, 2191, 28291, 371602, 4834667, 62771107, 815734819, 10604535907, 137859356534]$ |
$101$ |
$[101, 29997, 4815377, 808029189, 137973330176, 23336034433173, 3938794045074017, 665419950171347877, 112455794370804724637, 19005082979348421660672]$ |
$9$ |
$9$ |
$2$ |
$2$ |
$1$ |
4.0.72557.1 |
$D_{4}$ |
simple |
| 2.13.ah_be |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 7 x + 30 x^{2} - 91 x^{3} + 169 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$7$ |
$[7, 181, 2212, 28369, 371707, 4834906, 62772871, 815728513, 10604420260, 137858852221]$ |
$102$ |
$[102, 30396, 4861728, 810235776, 138012101742, 23337188957952, 3938904764517342, 665414807044689408, 112454567999145347616, 19005013455302895068316]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.640332.1 |
$D_{4}$ |
simple |
| 2.13.ah_bf |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 7 x + 31 x^{2} - 91 x^{3} + 169 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$7$ |
$[7, 183, 2233, 28443, 371742, 4834623, 62772577, 815717811, 10604298439, 137858354518]$ |
$103$ |
$[103, 30797, 4908259, 812332469, 138024863248, 23335821681341, 3938886321816451, 665406078106775525, 112453276162713512311, 19004944842626077700352]$ |
$3$ |
$3$ |
$2$ |
$2$ |
$1$ |
4.0.589541.1 |
$D_{4}$ |
simple |
| 2.13.ah_bg |
$2$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 6 x + 13 x^{2} )( 1 - x + 13 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$7$ |
$[7, 185, 2254, 28513, 371707, 4833830, 62770519, 815705953, 10604190982, 137857941425]$ |
$104$ |
$[104, 31200, 4954976, 814320000, 138011646344, 23331990988800, 3938757157931336, 665396405968320000, 112452136652458719584, 19004887894305550380000]$ |
$6$ |
$6$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-51}) \) |
$C_2$, $C_2$ |
1.13.ag $\times$ 1.13.ab |
| 2.13.ah_bh |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 7 x + 33 x^{2} - 91 x^{3} + 169 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$7$ |
$[7, 187, 2275, 28579, 371602, 4832539, 62766991, 815696131, 10604116915, 137857668982]$ |
$105$ |
$[105, 31605, 5001885, 816199125, 137972486400, 23325755495805, 3938535720666645, 665388394150885125, 112451351223301255305, 19004850335877097574400]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.411453.3 |
$D_{4}$ |
simple |
| 2.13.ah_bi |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 7 x + 34 x^{2} - 91 x^{3} + 169 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$7$ |
$[7, 189, 2296, 28641, 371427, 4830762, 62762287, 815691489, 10604093752, 137857571509]$ |
$106$ |
$[106, 32012, 5048992, 817970624, 137907422626, 23317174070528, 3938240466496162, 665384607166844672, 112451105596046887072, 19004836898524828256172]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.304028.1 |
$D_{4}$ |
simple |
| 2.13.ah_bj |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 7 x + 35 x^{2} - 91 x^{3} + 169 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$7$ |
$[7, 191, 2317, 28699, 371182, 4828511, 62756701, 815695123, 10604137495, 137857661846]$ |
$107$ |
$[107, 32421, 5096303, 819635301, 137816498192, 23306305857237, 3937889862548567, 665387570615358213, 112451569460223669251, 19004849352214592169216]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.198237.1 |
$D_{4}$ |
simple |
| 2.13.ah_bk |
$2$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 5 x + 13 x^{2} )( 1 - 2 x + 13 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$7$ |
$[7, 193, 2338, 28753, 370867, 4825798, 62750527, 815710081, 10604262634, 137857931593]$ |
$108$ |
$[108, 32832, 5143824, 821193984, 137699760348, 23293210300416, 3937502388759516, 665399771295667200, 112452896477996048016, 19004886538871760447552]$ |
$7$ |
$7$ |
$24$ |
$12$ |
$3$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$ |
1.13.af $\times$ 1.13.ac |
| 2.13.ah_bl |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 7 x + 37 x^{2} - 91 x^{3} + 169 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$7$ |
$[7, 195, 2359, 28803, 370482, 4822635, 62744059, 815739363, 10604482147, 137858351350]$ |
$109$ |
$[109, 33245, 5191561, 822647525, 137557260544, 23277947169605, 3937096540195081, 665423657339063525, 112455224289323433109, 19004944405616091648000]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.35525.3 |
$D_{4}$ |
simple |
| 2.13.ah_bm |
$2$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 13 x^{2} )( 1 - 3 x + 13 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$7$ |
$[7, 197, 2380, 28849, 370027, 4819034, 62737591, 815785921, 10604807500, 137858870957]$ |
$110$ |
$[110, 33660, 5239520, 823996800, 137389054550, 23260576584960, 3936690829551590, 665461638360921600, 112458674518542740960, 19005016038068177934300]$ |
$0$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-43}) \) |
$C_2$, $C_2$ |
1.13.ae $\times$ 1.13.ad |
| 2.13.ag_s |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
|
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 6 x + 18 x^{2} - 78 x^{3} + 169 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$8$ |
$[8, 170, 2072, 28014, 371288, 4826810, 62727176, 815694814, 10604669096, 137858491850]$ |
$104$ |
$[104, 28288, 4557800, 800210944, 137856264104, 23298088028800, 3936037434568616, 665387319878221824, 112457206783202925800, 19004963775156489689728]$ |
$8$ |
$8$ |
$4$ |
$8$ |
$4$ |
\(\Q(i, \sqrt{17})\) |
$C_2^2$ |
simple |
| 2.13.ag_t |
$2$ |
$\F_{13}$ |
$13$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 7 x + 13 x^{2} )( 1 + x + 13 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$8$ |
$[8, 172, 2090, 28084, 371648, 4829254, 62737424, 815726116, 10604813330, 137859184732]$ |
$105$ |
$[105, 28665, 4596480, 802190025, 137990339025, 23309890007040, 3936680352813705, 665412853037812425, 112458736342523370240, 19005059294898370518825]$ |
$8$ |
$8$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-51}) \) |
$C_2$, $C_2$ |
1.13.ah $\times$ 1.13.b |
| 2.13.ag_u |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 6 x + 20 x^{2} - 78 x^{3} + 169 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$8$ |
$[8, 174, 2108, 28150, 371948, 4831278, 62745320, 815742814, 10604873864, 137859492414]$ |
$106$ |
$[106, 29044, 4635274, 804054096, 138102032266, 23319664860436, 3937175737938346, 665426473200497664, 112459378287178054426, 19005101711592935851924]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.878400.4 |
$D_{4}$ |
simple |
| 2.13.ag_v |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 6 x + 21 x^{2} - 78 x^{3} + 169 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$8$ |
$[8, 176, 2126, 28212, 372188, 4832894, 62751116, 815747428, 10604868518, 137859530336]$ |
$107$ |
$[107, 29425, 4674188, 805803625, 138191347547, 23327470051600, 3937539395235203, 665430236259215625, 112459321594157760812, 19005106939521087834625]$ |
$6$ |
$6$ |
$2$ |
$2$ |
$1$ |
4.0.1056832.1 |
$D_{4}$ |
simple |
| 2.13.ag_w |
$2$ |
$\F_{13}$ |
$13$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 6 x + 22 x^{2} - 78 x^{3} + 169 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$8$ |
$[8, 178, 2144, 28270, 372368, 4834114, 62755064, 815742430, 10604813816, 137859397138]$ |
$108$ |
$[108, 29808, 4713228, 807439104, 138258290988, 23333363095536, 3937787128076364, 665426158870376448, 112458741497626342572, 19005088576997958498288]$ |
$18$ |
$18$ |
$2$ |
$2$ |
$1$ |
4.0.8112.1 |
$D_{4}$ |
simple |
