Abelian variety search results

Results (12 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
4.2.ac_c_c_ah	$4$	$\F_{2}$	$2$			✓	✓			✓		$( 1 - x + 2 x^{2} )^{2}( 1 - 3 x^{2} + 4 x^{4} )$	$[0,0,0,0,1,1,1,1]$	$0$	$4$	$0$	$1$	$3$	$1$	$[1, 5, 19, 13, 11, 65, 155, 381, 523, 1025]$	$8$	$[8, 256, 14504, 65536, 523688, 17172736, 328632872, 6879707136, 70071739304, 1096996485376]$	$0$	$0$	$32$	$28$	$4$	\(\Q(\sqrt{-7}) \), \(\Q(i, \sqrt{7})\)	$C_2$, $C_2^2$	1.2.ab^2 $\times$ 2.2.a_ad
4.2.a_ag_a_r	$4$	$\F_{2}$	$2$			✓	✓			✓		$( 1 - 3 x^{2} + 4 x^{4} )^{2}$	$[0,0,0,0,1,1,1,1]$	$0$	$4$	$0$	$1$	$3$	$3$	$[3, -7, 9, 13, 33, 101, 129, 381, 513, 1253]$	$4$	$[4, 16, 5476, 65536, 1170724, 29986576, 265624804, 6879707136, 68197233316, 1370594684176]$	$0$	$0$	$32$	$28$	$2$	\(\Q(i, \sqrt{7})\)	$C_2^2$	2.2.a_ad^2
4.2.a_a_a_ab	$4$	$\F_{2}$	$2$			✓	✓			✓	✓	$( 1 - x + 2 x^{2} )( 1 + x + 2 x^{2} )( 1 - 3 x^{2} + 4 x^{4} )$	$[0,0,0,0,1,1,1,1]$	$0$	$4$	$0$	$1$	$3$	$3$	$[3, 5, 9, 13, 33, 65, 129, 381, 513, 1025]$	$16$	$[16, 256, 4144, 65536, 1047376, 17172736, 268460656, 6879707136, 68719003024, 1096996485376]$	$4$	$2$	$32$	$28$	$4$	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-7}) \), \(\Q(i, \sqrt{7})\)	$C_2$, $C_2$, $C_2^2$	1.2.ab $\times$ 1.2.b $\times$ 2.2.a_ad
4.2.c_c_ac_ah	$4$	$\F_{2}$	$2$			✓	✓			✓		$( 1 + x + 2 x^{2} )^{2}( 1 - 3 x^{2} + 4 x^{4} )$	$[0,0,0,0,1,1,1,1]$	$0$	$4$	$0$	$1$	$3$	$5$	$[5, 5, -1, 13, 55, 65, 103, 381, 503, 1025]$	$32$	$[32, 256, 1184, 65536, 2094752, 17172736, 219305888, 6879707136, 67392381344, 1096996485376]$	$0$	$0$	$32$	$28$	$4$	\(\Q(\sqrt{-7}) \), \(\Q(i, \sqrt{7})\)	$C_2$, $C_2^2$	1.2.b^2 $\times$ 2.2.a_ad
4.4.ag_s_abe_bx	$4$	$\F_{2^{2}}$	$2$			✓	✓			✓		$( 1 - 3 x + 4 x^{2} )^{2}( 1 + x^{2} + 16 x^{4} )$	$[0,0,0,0,1,1,1,1]$	$0$	$4$	$0$	$1$	$3$	$-1$	$[-1, 17, 83, 381, 1139, 4097, 16211, 63741, 260147, 1048577]$	$72$	$[72, 82944, 22177800, 6879707136, 1229000299272, 281675802240000, 71296422172839432, 17947489487642689536, 4686510494302609192200, 1208927259429932494070784]$	$None$	$0$	$32$	$28$	$4$	\(\Q(\sqrt{-7}) \), \(\Q(i, \sqrt{7})\)	$C_2$, $C_2^2$	1.4.ad^2 $\times$ 2.4.a_b
4.4.ae_m_au_br	$4$	$\F_{2^{2}}$	$2$			✓	✓			✓	?	$( 1 - 3 x + 4 x^{2} )( 1 - x + 4 x^{2} )( 1 + x^{2} + 16 x^{4} )$	$[0,0,0,0,1,1,1,1]$	$0$	$4$	$0$	$2$	$2$	$1$	$[1, 25, 85, 333, 1021, 4057, 16549, 64413, 260365, 1048105]$	$144$	$[144, 124416, 22777200, 5733089280, 1094968843344, 278956923840000, 72775020202930224, 18132788051674398720, 4690422709261896214800, 1208382456354006629684736]$	$None$	$0$	$28$	$28$	$4$	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-15}) \), \(\Q(i, \sqrt{7})\)	$C_2$, $C_2$, $C_2^2$	1.4.ad $\times$ 1.4.ab $\times$ 2.4.a_b
4.4.ac_g_ak_bl	$4$	$\F_{2^{2}}$	$2$			✓	✓			✓	✓	$( 1 - 3 x + 4 x^{2} )( 1 + x + 4 x^{2} )( 1 + x^{2} + 16 x^{4} )$	$[0,0,0,0,1,1,1,1]$	$0$	$4$	$0$	$2$	$2$	$3$	$[3, 25, 63, 333, 1143, 4057, 16047, 64413, 261927, 1048105]$	$216$	$[216, 124416, 16183800, 5733089280, 1233543738456, 278956923840000, 70578995909718456, 18132788051674398720, 4718454267823393138200, 1208382456354006629684736]$	$None$	$2$	$28$	$28$	$4$	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-15}) \), \(\Q(i, \sqrt{7})\)	$C_2$, $C_2$, $C_2^2$	1.4.ad $\times$ 1.4.b $\times$ 2.4.a_b
4.4.a_a_a_bf	$4$	$\F_{2^{2}}$	$2$			✓	✓			✓	?	$( 1 - 3 x + 4 x^{2} )( 1 + 3 x + 4 x^{2} )( 1 + x^{2} + 16 x^{4} )$	$[0,0,0,0,1,1,1,1]$	$0$	$4$	$0$	$1$	$3$	$5$	$[5, 17, 65, 381, 1025, 4097, 16385, 63741, 262145, 1048577]$	$288$	$[288, 82944, 16783200, 6879707136, 1099512282528, 281675802240000, 72057593939809248, 17947489487642689536, 4722366482782680160800, 1208927259429932494070784]$	$None$	$0$	$32$	$28$	$4$	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-7}) \), \(\Q(i, \sqrt{7})\)	$C_2$, $C_2$, $C_2^2$	1.4.ad $\times$ 1.4.d $\times$ 2.4.a_b
4.4.a_c_a_bh	$4$	$\F_{2^{2}}$	$2$				✓			✓	✓	$( 1 + x^{2} + 16 x^{4} )^{2}$	$[0,0,0,0,1,1,1,1]$	$0$	$4$	$0$	$1$	$3$	$5$	$[5, 21, 65, 381, 1025, 3909, 16385, 63741, 262145, 1053381]$	$324$	$[324, 104976, 16402500, 6879707136, 1102033849284, 269042006250000, 72044066599626564, 17947489487642689536, 4722431589850455202500, 1214478604967710027312656]$	$None$	$4$	$32$	$28$	$2$	\(\Q(i, \sqrt{7})\)	$C_2^2$	2.4.a_b^2
4.4.c_g_k_bl	$4$	$\F_{2^{2}}$	$2$			✓	✓			✓	✓	$( 1 - x + 4 x^{2} )( 1 + 3 x + 4 x^{2} )( 1 + x^{2} + 16 x^{4} )$	$[0,0,0,0,1,1,1,1]$	$0$	$4$	$0$	$2$	$2$	$7$	$[7, 25, 67, 333, 907, 4057, 16723, 64413, 262363, 1048105]$	$576$	$[576, 124416, 17236800, 5733089280, 979602440256, 278956923840000, 73551977713993536, 18132788051674398720, 4726308629678464987200, 1208382456354006629684736]$	$None$	$2$	$28$	$28$	$4$	\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-7}) \), \(\Q(i, \sqrt{7})\)	$C_2$, $C_2$, $C_2^2$	1.4.ab $\times$ 1.4.d $\times$ 2.4.a_b
4.4.e_m_u_br	$4$	$\F_{2^{2}}$	$2$			✓	✓			✓	?	$( 1 + x + 4 x^{2} )( 1 + 3 x + 4 x^{2} )( 1 + x^{2} + 16 x^{4} )$	$[0,0,0,0,1,1,1,1]$	$0$	$4$	$0$	$2$	$2$	$9$	$[9, 25, 45, 333, 1029, 4057, 16221, 64413, 263925, 1048105]$	$864$	$[864, 124416, 12247200, 5733089280, 1103577022944, 278956923840000, 71332508321565984, 18132788051674398720, 4754554654684042504800, 1208382456354006629684736]$	$None$	$0$	$28$	$28$	$4$	\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-7}) \), \(\Q(i, \sqrt{7})\)	$C_2$, $C_2$, $C_2^2$	1.4.b $\times$ 1.4.d $\times$ 2.4.a_b
4.4.g_s_be_bx	$4$	$\F_{2^{2}}$	$2$			✓	✓			✓	?	$( 1 + 3 x + 4 x^{2} )^{2}( 1 + x^{2} + 16 x^{4} )$	$[0,0,0,0,1,1,1,1]$	$0$	$4$	$0$	$1$	$3$	$11$	$[11, 17, 47, 381, 911, 4097, 16559, 63741, 264143, 1048577]$	$1152$	$[1152, 82944, 12700800, 6879707136, 983667180672, 281675802240000, 72826892095750272, 17947489487642689536, 4758496801579827331200, 1208927259429932494070784]$	$None$	$0$	$32$	$28$	$4$	\(\Q(\sqrt{-7}) \), \(\Q(i, \sqrt{7})\)	$C_2$, $C_2^2$	1.4.d^2 $\times$ 2.4.a_b

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