Abelian variety search results

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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.ac	$1$	$\F_{3}$	$3$	✓	✓	✓	✓			✓	✓	$1 - 2 x + 3 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$2$	$[2, 12, 38, 96, 242, 684, 2102, 6528, 19874, 59532]$	$2$	$[2, 12, 38, 96, 242, 684, 2102, 6528, 19874, 59532]$	$1$	$1$	$2$	$2$	$1$	\(\Q(\sqrt{-2}) \)	$C_2$	simple
2.3.ae_i	$2$	$\F_{3}$	$3$	✓		✓	✓			✓	✓	$1 - 4 x + 8 x^{2} - 12 x^{3} + 9 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$0$	$[0, 10, 24, 54, 200, 730, 2240, 6494, 19392, 59050]$	$2$	$[2, 68, 626, 4624, 49282, 532100, 4898098, 42614784, 381715394, 3486898628]$	$1$	$1$	$8$	$24$	$4$	\(\Q(\zeta_{8})\)	$C_2^2$	simple

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