Abelian variety search results

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

Results (13 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
3.2.ab_a_a	$3$	$\F_{2}$	$2$	✓	✓	✓				✓	✓	$1 - x - 4 x^{5} + 8 x^{6}$	$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$	$2$	$1$	$2$	$3$	$0$	$2$	$[2, 4, 8, 16, 12, 88, 156, 288, 548, 984]$	$4$	$[4, 56, 556, 4144, 16564, 381416, 2586476, 19037536, 143325124, 1029850136]$	$3$	$2$	$2$	$2$	$1$	6.0.839056.1	$S_4\times C_2$	simple
3.2.ab_b_ad	$3$	$\F_{2}$	$2$	✓	✓	✓	✓			✓	✓	$1 - x + x^{2} - 3 x^{3} + 2 x^{4} - 4 x^{5} + 8 x^{6}$	$[0,0,0,1,1,1]$	$0$	$3$	$0$	$3$	$0$	$2$	$[2, 6, 2, 14, 22, 78, 170, 222, 542, 1166]$	$4$	$[4, 80, 244, 3200, 25084, 326960, 2899124, 14566400, 142200028, 1231624400]$	$2$	$2$	$2$	$2$	$1$	6.0.503792.1	$S_4\times C_2$	simple
3.2.ab_b_b	$3$	$\F_{2}$	$2$			✓	✓			✓	✓	$( 1 - x + 2 x^{2} )( 1 - x^{2} + 4 x^{4} )$	$[0,0,0,1,1,1]$	$0$	$3$	$0$	$2$	$1$	$2$	$[2, 6, 14, 30, 22, 78, 142, 254, 518, 846]$	$8$	$[8, 128, 1064, 9216, 21208, 323456, 2362312, 16588800, 135386552, 899558528]$	$3$	$2$	$8$	$6$	$2$	$\Q(\sqrt{-7})$, $\Q(\sqrt{-3}, \sqrt{5})$	$C_2$, $C_2^2$	1.2.ab $\times$ 2.2.a_ab
3.2.ab_c_ac	$3$	$\F_{2}$	$2$	✓	✓	✓				✓	✓	$1 - x + 2 x^{2} - 2 x^{3} + 4 x^{4} - 4 x^{5} + 8 x^{6}$	$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$	$2$	$1$	$2$	$3$	$0$	$2$	$[2, 8, 8, 24, 32, 80, 184, 224, 440, 1008]$	$8$	$[8, 176, 488, 5984, 31768, 332816, 3193352, 14852288, 116449976, 1056031856]$	$3$	$2$	$2$	$2$	$1$	6.0.2296688.1	$S_4\times C_2$	simple
3.2.ab_d_ad	$3$	$\F_{2}$	$2$	✓	✓	✓	✓			✓	✓	$1 - x + 3 x^{2} - 3 x^{3} + 6 x^{4} - 4 x^{5} + 8 x^{6}$	$[0,0,0,1,1,1]$	$0$	$3$	$0$	$3$	$0$	$2$	$[2, 10, 8, 22, 42, 70, 156, 222, 386, 1050]$	$10$	$[10, 260, 430, 5200, 44050, 279500, 2611010, 14684800, 104258230, 1100633300]$	$2$	$2$	$2$	$2$	$1$	6.0.3307504.1	$S_4\times C_2$	simple
3.2.a_b_a	$3$	$\F_{2}$	$2$			✓		✓		✓	✓	$( 1 + 2 x^{2} )( 1 - x^{2} + 4 x^{4} )$	$[0,0,\frac{1}{2},\frac{1}{2},1,1]$	$1$	$2$	$1$	$1$	$2$	$3$	$[3, 7, 9, 23, 33, 103, 129, 191, 513, 967]$	$12$	$[12, 144, 684, 5184, 31812, 467856, 2146044, 12960000, 134079732, 1012003344]$	$3$	$2$	$12$	$24$	$2$	$\Q(\sqrt{-2})$, $\Q(\sqrt{-3}, \sqrt{5})$	$C_2$, $C_2^2$	1.2.a $\times$ 2.2.a_ab
3.2.a_c_ab	$3$	$\F_{2}$	$2$	✓	✓	✓	✓			✓	✓	$1 + 2 x^{2} - x^{3} + 4 x^{4} + 8 x^{6}$	$[0,0,0,1,1,1]$	$0$	$3$	$0$	$3$	$0$	$3$	$[3, 9, 6, 25, 43, 78, 129, 177, 510, 1069]$	$14$	$[14, 224, 392, 5824, 45794, 326144, 2103374, 12218752, 133422296, 1121769824]$	$3$	$2$	$2$	$2$	$1$	6.0.6660007.1	$S_4\times C_2$	simple
3.2.a_c_b	$3$	$\F_{2}$	$2$	✓	✓	✓	✓			✓	✓	$1 + 2 x^{2} + x^{3} + 4 x^{4} + 8 x^{6}$	$[0,0,0,1,1,1]$	$0$	$3$	$0$	$3$	$0$	$3$	$[3, 9, 12, 25, 23, 78, 129, 177, 516, 1069]$	$16$	$[16, 224, 832, 5824, 24496, 326144, 2098672, 12218752, 135024448, 1121769824]$	$3$	$2$	$2$	$2$	$1$	6.0.6660007.1	$S_4\times C_2$	simple
3.2.b_a_a	$3$	$\F_{2}$	$2$	✓	✓	✓				✓	✓	$1 + x + 4 x^{5} + 8 x^{6}$	$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$	$2$	$1$	$2$	$3$	$0$	$4$	$[4, 4, 10, 16, 54, 88, 102, 288, 478, 984]$	$14$	$[14, 56, 686, 4144, 62174, 381416, 1694518, 19037536, 125011838, 1029850136]$	$2$	$2$	$2$	$2$	$1$	6.0.839056.1	$S_4\times C_2$	simple
3.2.b_b_ab	$3$	$\F_{2}$	$2$			✓	✓			✓	✓	$( 1 + x + 2 x^{2} )( 1 - x^{2} + 4 x^{4} )$	$[0,0,0,1,1,1]$	$0$	$3$	$0$	$2$	$1$	$4$	$[4, 6, 4, 30, 44, 78, 116, 254, 508, 846]$	$16$	$[16, 128, 304, 9216, 42416, 323456, 1929776, 16588800, 132772912, 899558528]$	$2$	$2$	$8$	$6$	$2$	$\Q(\sqrt{-7})$, $\Q(\sqrt{-3}, \sqrt{5})$	$C_2$, $C_2^2$	1.2.b $\times$ 2.2.a_ab
3.2.b_b_d	$3$	$\F_{2}$	$2$	✓	✓	✓	✓			✓	✓	$1 + x + x^{2} + 3 x^{3} + 2 x^{4} + 4 x^{5} + 8 x^{6}$	$[0,0,0,1,1,1]$	$0$	$3$	$0$	$3$	$0$	$4$	$[4, 6, 16, 14, 44, 78, 88, 222, 484, 1166]$	$20$	$[20, 80, 1340, 3200, 49100, 326960, 1530220, 14566400, 126969020, 1231624400]$	$3$	$2$	$2$	$2$	$1$	6.0.503792.1	$S_4\times C_2$	simple
3.2.b_c_c	$3$	$\F_{2}$	$2$	✓	✓	✓				✓	✓	$1 + x + 2 x^{2} + 2 x^{3} + 4 x^{4} + 4 x^{5} + 8 x^{6}$	$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$	$2$	$1$	$2$	$3$	$0$	$4$	$[4, 8, 10, 24, 34, 80, 74, 224, 586, 1008]$	$22$	$[22, 176, 682, 5984, 33242, 332816, 1351834, 14852288, 154874698, 1056031856]$	$3$	$2$	$2$	$2$	$1$	6.0.2296688.1	$S_4\times C_2$	simple
3.2.b_d_d	$3$	$\F_{2}$	$2$	✓	✓	✓	✓			✓	✓	$1 + x + 3 x^{2} + 3 x^{3} + 6 x^{4} + 4 x^{5} + 8 x^{6}$	$[0,0,0,1,1,1]$	$0$	$3$	$0$	$3$	$0$	$4$	$[4, 10, 10, 22, 24, 70, 102, 222, 640, 1050]$	$26$	$[26, 260, 650, 5200, 24986, 279500, 1714102, 14684800, 171253550, 1100633300]$	$3$	$2$	$2$	$2$	$1$	6.0.3307504.1	$S_4\times C_2$	simple

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