Abelian variety search results

The results below are complete, since the LMFDB contains all isogeny classes of elliptic curves over fields of cardinality less than 500 or 512, 625, 729, 1024

Results (7 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
1.3.ad	$1$	$\F_{3}$	$3$	✓	✓	✓		✓	✓	✓	✓	$1 - 3 x + 3 x^{2}$	$[\frac{1}{2},\frac{1}{2}]$	$1$	$0$	$1$	$0$	$1$	$1$	$[1, 7, 28, 91, 271, 784, 2269, 6643, 19684, 58807]$	$1$	$[1, 7, 28, 91, 271, 784, 2269, 6643, 19684, 58807]$	$1$	$0$	$3$	$3$	$6$	\(\Q(\sqrt{-3}) \)	$C_2$	simple
1.3.ac	$1$	$\F_{3}$	$3$	✓	✓	✓	✓			✓	✓	$1 - 2 x + 3 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$2$	$[2, 12, 38, 96, 242, 684, 2102, 6528, 19874, 59532]$	$2$	$[2, 12, 38, 96, 242, 684, 2102, 6528, 19874, 59532]$	$1$	$0$	$2$	$2$	$1$	\(\Q(\sqrt{-2}) \)	$C_2$	simple
1.3.ab	$1$	$\F_{3}$	$3$	✓	✓	✓	✓			✓	✓	$1 - x + 3 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$3$	$[3, 15, 36, 75, 213, 720, 2271, 6675, 19548, 58575]$	$3$	$[3, 15, 36, 75, 213, 720, 2271, 6675, 19548, 58575]$	$1$	$0$	$2$	$2$	$1$	\(\Q(\sqrt{-11}) \)	$C_2$	simple
1.3.a	$1$	$\F_{3}$	$3$	✓	✓	✓		✓	✓	✓	✓	$1 + 3 x^{2}$	$[\frac{1}{2},\frac{1}{2}]$	$1$	$0$	$1$	$0$	$1$	$4$	$[4, 16, 28, 64, 244, 784, 2188, 6400, 19684, 59536]$	$4$	$[4, 16, 28, 64, 244, 784, 2188, 6400, 19684, 59536]$	$2$	$0$	$3$	$6$	$2$	\(\Q(\sqrt{-3}) \)	$C_2$	simple
1.3.b	$1$	$\F_{3}$	$3$	✓	✓	✓	✓			✓	✓	$1 + x + 3 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$5$	$[5, 15, 20, 75, 275, 720, 2105, 6675, 19820, 58575]$	$5$	$[5, 15, 20, 75, 275, 720, 2105, 6675, 19820, 58575]$	$1$	$0$	$2$	$2$	$1$	\(\Q(\sqrt{-11}) \)	$C_2$	simple
1.3.c	$1$	$\F_{3}$	$3$	✓	✓	✓	✓			✓	✓	$1 + 2 x + 3 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$6$	$[6, 12, 18, 96, 246, 684, 2274, 6528, 19494, 59532]$	$6$	$[6, 12, 18, 96, 246, 684, 2274, 6528, 19494, 59532]$	$1$	$0$	$2$	$2$	$1$	\(\Q(\sqrt{-2}) \)	$C_2$	simple
1.3.d	$1$	$\F_{3}$	$3$	✓	✓	✓		✓	✓	✓	✓	$1 + 3 x + 3 x^{2}$	$[\frac{1}{2},\frac{1}{2}]$	$1$	$0$	$1$	$0$	$1$	$7$	$[7, 7, 28, 91, 217, 784, 2107, 6643, 19684, 58807]$	$7$	$[7, 7, 28, 91, 217, 784, 2107, 6643, 19684, 58807]$	$1$	$0$	$3$	$6$	$6$	\(\Q(\sqrt{-3}) \)	$C_2$	simple

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