Abelian variety search results

Note: Search results may be incomplete due to uncomputed quantities: hyp_count (2212128 objects)

Results (10 matches)

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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.ac_h_abk	$3$	$\F_{13}$	$13$	✓	✓	✓	✓			✓	✓	$1 - 2 x + 7 x^{2} - 36 x^{3} + 91 x^{4} - 338 x^{5} + 2197 x^{6}$	$[0,0,0,1,1,1]$	$0$	$3$	$0$	$3$	$0$	$12$	$[12, 180, 2124, 28636, 370812, 4834260, 62783964, 815678396, 10604646252, 137859424500]$	$1920$	$[1920, 5130240, 10261226880, 23357777510400, 51119661365040000, 112629106255824046080, 247204130247878078017920, 542765951457429097650585600, 1192549809928560459965426782080, 2620013368718550172664055194880000]$	$None$	$332$	$2$	$2$	$1$	6.0.1079160000.1	$S_4\times C_2$	simple
3.13.ac_l_e	$3$	$\F_{13}$	$13$			✓	✓			✓	✓	$( 1 - 2 x + 13 x^{2} )( 1 - 2 x^{2} + 169 x^{4} )$	$[0,0,0,1,1,1]$	$0$	$3$	$0$	$2$	$1$	$12$	$[12, 188, 2268, 29084, 370092, 4828316, 62763132, 815657660, 10604381004, 137857231868]$	$2016$	$[2016, 5419008, 10949486688, 23726758035456, 51020221753753056, 112490563747313332224, 247122077872165768639584, 542752154939544014193426432, 1192519981134745626952238471136, 2619971697859409715728999937159168]$	$None$	$285$	$12$	$12$	$2$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-6}, \sqrt{7})\)	$C_2$, $C_2^2$	1.13.ac $\times$ 2.13.a_ac
3.13.ac_o_abm	$3$	$\F_{13}$	$13$	✓	✓	✓	✓			✓	✓	$1 - 2 x + 14 x^{2} - 38 x^{3} + 182 x^{4} - 338 x^{5} + 2197 x^{6}$	$[0,0,0,1,1,1]$	$0$	$3$	$0$	$3$	$0$	$12$	$[12, 194, 2160, 28802, 371892, 4831340, 62777748, 815639234, 10604135088, 137859005234]$	$2016$	$[2016, 5588352, 10427429376, 23493364747776, 51268494626417376, 112560974220851380224, 247179646487751552281952, 542739896801866860350994432, 1192492327369059762616107403776, 2620005400476308460638263349066112]$	$None$	$298$	$2$	$2$	$1$	6.0.845479287.1	$S_4\times C_2$	simple
3.13.a_e_ao	$3$	$\F_{13}$	$13$	✓	✓	✓	✓			✓	✓	$1 + 4 x^{2} - 14 x^{3} + 52 x^{4} + 2197 x^{6}$	$[0,0,0,1,1,1]$	$0$	$3$	$0$	$3$	$0$	$14$	$[14, 178, 2156, 28738, 371574, 4838284, 62752046, 815662018, 10604723612, 137857832738]$	$2240$	$[2240, 5080320, 10416143360, 23441104512000, 51224385327595200, 112723008800104120320, 247078427162569861853120, 542755055995963244775936000, 1192558509618738793283979914240, 2619983117251982629320922684857600]$	$None$	$271$	$2$	$2$	$1$	6.0.694674127.1	$S_4\times C_2$	simple
3.13.a_e_o	$3$	$\F_{13}$	$13$	✓	✓	✓	✓			✓	✓	$1 + 4 x^{2} + 14 x^{3} + 52 x^{4} + 2197 x^{6}$	$[0,0,0,1,1,1]$	$0$	$3$	$0$	$3$	$0$	$14$	$[14, 178, 2240, 28738, 371014, 4838284, 62744990, 815662018, 10604275136, 137857832738]$	$2268$	$[2268, 5080320, 10821952512, 23441104512000, 51147185085704988, 112723008800104120320, 247050645033681434763468, 542755055995963244775936000, 1192508076067643676992328373248, 2619983117251982629320922684857600]$	$None$	$271$	$2$	$2$	$1$	6.0.694674127.1	$S_4\times C_2$	simple
3.13.a_h_ai	$3$	$\F_{13}$	$13$	✓	✓	✓	✓			✓	✓	$1 + 7 x^{2} - 8 x^{3} + 91 x^{4} + 2197 x^{6}$	$[0,0,0,1,1,1]$	$0$	$3$	$0$	$3$	$0$	$14$	$[14, 184, 2174, 28828, 371574, 4836664, 62750870, 815609020, 10604588990, 137857881464]$	$2288$	$[2288, 5271552, 10500027824, 23514327023616, 51224394544388208, 112685207276276084736, 247073800704613645581104, 542719793655255444001652736, 1192543370278797942597073612016, 2619984043275275045275488825864192]$	$None$	$298$	$2$	$2$	$1$	6.0.65351056.1	$S_4\times C_2$	simple
3.13.a_h_i	$3$	$\F_{13}$	$13$	✓	✓	✓	✓			✓	✓	$1 + 7 x^{2} + 8 x^{3} + 91 x^{4} + 2197 x^{6}$	$[0,0,0,1,1,1]$	$0$	$3$	$0$	$3$	$0$	$14$	$[14, 184, 2222, 28828, 371014, 4836664, 62746166, 815609020, 10604409758, 137857881464]$	$2304$	$[2304, 5271552, 10731896064, 23514327023616, 51147193960583424, 112685207276276084736, 247055279285576229610752, 542719793655255444001652736, 1192523214671300017481620121856, 2619984043275275045275488825864192]$	$None$	$298$	$2$	$2$	$1$	6.0.65351056.1	$S_4\times C_2$	simple
3.13.c_h_bk	$3$	$\F_{13}$	$13$	✓	✓	✓	✓			✓	✓	$1 + 2 x + 7 x^{2} + 36 x^{3} + 91 x^{4} + 338 x^{5} + 2197 x^{6}$	$[0,0,0,1,1,1]$	$0$	$3$	$0$	$3$	$0$	$16$	$[16, 180, 2272, 28636, 371776, 4834260, 62713072, 815678396, 10604352496, 137859424500]$	$2672$	$[2672, 5130240, 10976183216, 23357777510400, 51252557210997872, 112629106255824046080, 246925001749407969016496, 542765951457429097650585600, 1192516775478033772383505938032, 2620013368718550172664055194880000]$	$None$	$332$	$2$	$2$	$1$	6.0.1079160000.1	$S_4\times C_2$	simple
3.13.c_l_ae	$3$	$\F_{13}$	$13$			✓	✓			✓	✓	$( 1 + 2 x + 13 x^{2} )( 1 - 2 x^{2} + 169 x^{4} )$	$[0,0,0,1,1,1]$	$0$	$3$	$0$	$2$	$1$	$16$	$[16, 188, 2128, 29084, 372496, 4828316, 62733904, 815657660, 10604617744, 137857231868]$	$2688$	$[2688, 5419008, 10273592448, 23726758035456, 51351632897728128, 112490563747313332224, 247006996233281850910848, 542752154939544014193426432, 1192546603827784225707561415296, 2619971697859409715728999937159168]$	$None$	$285$	$12$	$12$	$2$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-6}, \sqrt{7})\)	$C_2$, $C_2^2$	1.13.c $\times$ 2.13.a_ac
3.13.c_o_bm	$3$	$\F_{13}$	$13$	✓	✓	✓	✓			✓	✓	$1 + 2 x + 14 x^{2} + 38 x^{3} + 182 x^{4} + 338 x^{5} + 2197 x^{6}$	$[0,0,0,1,1,1]$	$0$	$3$	$0$	$3$	$0$	$16$	$[16, 194, 2236, 28802, 370696, 4831340, 62719288, 815639234, 10604863660, 137859005234]$	$2772$	$[2772, 5588352, 10794700224, 23493364747776, 51103614794382612, 112560974220851380224, 246949467455521734508836, 542739896801866860350994432, 1192574259229832123086238715072, 2620005400476308460638263349066112]$	$None$	$298$	$2$	$2$	$1$	6.0.845479287.1	$S_4\times C_2$	simple

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