LMFDB - Abelian variety search results

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Base field	Base char.	Dimension	$p$-rank	Initial coefficients

Simple	Geom. simple	Primitive	Princ. polarizable	Jacobian

Slopes	Points on variety	Points on curve	Simple factors

Newton elevation	# Jacobians	# Hyp. Jacobians	# twists	Max twist degree

Angle rank	Angle corank	End. degree	$p$-corank	(Geom.) Sq.free

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Dim 1 factors	Dim 2 factors	Dim 3 factors	Dim 4 factors	Dim 5 factors

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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
1.2.ac	$1$	$\F_{2}$	$2$	✓	✓	✓		✓	✓	✓	✓	$1 - 2 x + 2 x^{2}$	$[\frac{1}{2},\frac{1}{2}]$	$1$	$0$	$1$	$0$	$1$	$1$	$[1, 5, 13, 25, 41, 65, 113, 225, 481, 1025]$	$1$	$[1, 5, 13, 25, 41, 65, 113, 225, 481, 1025]$	$1$	$1$	$3$	$8$	$4$	$\Q(\sqrt{-1}) $	$C_2$	simple
1.2.ab	$1$	$\F_{2}$	$2$	✓	✓	✓	✓			✓	✓	$1 - x + 2 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$2$	$[2, 8, 14, 16, 22, 56, 142, 288, 518, 968]$	$2$	$[2, 8, 14, 16, 22, 56, 142, 288, 518, 968]$	$1$	$1$	$2$	$2$	$1$	$\Q(\sqrt{-7}) $	$C_2$	simple
1.2.a	$1$	$\F_{2}$	$2$	✓	✓	✓		✓	✓	✓	✓	$1 + 2 x^{2}$	$[\frac{1}{2},\frac{1}{2}]$	$1$	$0$	$1$	$0$	$1$	$3$	$[3, 9, 9, 9, 33, 81, 129, 225, 513, 1089]$	$3$	$[3, 9, 9, 9, 33, 81, 129, 225, 513, 1089]$	$1$	$1$	$3$	$8$	$2$	$\Q(\sqrt{-2}) $	$C_2$	simple
1.2.b	$1$	$\F_{2}$	$2$	✓	✓	✓	✓			✓	✓	$1 + x + 2 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$4$	$[4, 8, 4, 16, 44, 56, 116, 288, 508, 968]$	$4$	$[4, 8, 4, 16, 44, 56, 116, 288, 508, 968]$	$1$	$1$	$2$	$2$	$1$	$\Q(\sqrt{-7}) $	$C_2$	simple
1.2.c	$1$	$\F_{2}$	$2$	✓	✓	✓		✓	✓	✓	✓	$1 + 2 x + 2 x^{2}$	$[\frac{1}{2},\frac{1}{2}]$	$1$	$0$	$1$	$0$	$1$	$5$	$[5, 5, 5, 25, 25, 65, 145, 225, 545, 1025]$	$5$	$[5, 5, 5, 25, 25, 65, 145, 225, 545, 1025]$	$1$	$1$	$3$	$8$	$4$	$\Q(\sqrt{-1}) $	$C_2$	simple
1.3.ad	$1$	$\F_{3}$	$3$	✓	✓	✓		✓	✓	✓	✓	$1 - 3 x + 3 x^{2}$	$[\frac{1}{2},\frac{1}{2}]$	$1$	$0$	$1$	$0$	$1$	$1$	$[1, 7, 28, 91, 271, 784, 2269, 6643, 19684, 58807]$	$1$	$[1, 7, 28, 91, 271, 784, 2269, 6643, 19684, 58807]$	$1$	$1$	$3$	$3$	$6$	$\Q(\sqrt{-3}) $	$C_2$	simple
1.3.ac	$1$	$\F_{3}$	$3$	✓	✓	✓	✓			✓	✓	$1 - 2 x + 3 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$2$	$[2, 12, 38, 96, 242, 684, 2102, 6528, 19874, 59532]$	$2$	$[2, 12, 38, 96, 242, 684, 2102, 6528, 19874, 59532]$	$1$	$1$	$2$	$2$	$1$	$\Q(\sqrt{-2}) $	$C_2$	simple
1.3.ab	$1$	$\F_{3}$	$3$	✓	✓	✓	✓			✓	✓	$1 - x + 3 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$3$	$[3, 15, 36, 75, 213, 720, 2271, 6675, 19548, 58575]$	$3$	$[3, 15, 36, 75, 213, 720, 2271, 6675, 19548, 58575]$	$1$	$1$	$2$	$2$	$1$	$\Q(\sqrt{-11}) $	$C_2$	simple
1.3.a	$1$	$\F_{3}$	$3$	✓	✓	✓		✓	✓	✓	✓	$1 + 3 x^{2}$	$[\frac{1}{2},\frac{1}{2}]$	$1$	$0$	$1$	$0$	$1$	$4$	$[4, 16, 28, 64, 244, 784, 2188, 6400, 19684, 59536]$	$4$	$[4, 16, 28, 64, 244, 784, 2188, 6400, 19684, 59536]$	$2$	$2$	$3$	$6$	$2$	$\Q(\sqrt{-3}) $	$C_2$	simple
1.3.b	$1$	$\F_{3}$	$3$	✓	✓	✓	✓			✓	✓	$1 + x + 3 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$5$	$[5, 15, 20, 75, 275, 720, 2105, 6675, 19820, 58575]$	$5$	$[5, 15, 20, 75, 275, 720, 2105, 6675, 19820, 58575]$	$1$	$1$	$2$	$2$	$1$	$\Q(\sqrt{-11}) $	$C_2$	simple
1.3.c	$1$	$\F_{3}$	$3$	✓	✓	✓	✓			✓	✓	$1 + 2 x + 3 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$6$	$[6, 12, 18, 96, 246, 684, 2274, 6528, 19494, 59532]$	$6$	$[6, 12, 18, 96, 246, 684, 2274, 6528, 19494, 59532]$	$1$	$1$	$2$	$2$	$1$	$\Q(\sqrt{-2}) $	$C_2$	simple
1.3.d	$1$	$\F_{3}$	$3$	✓	✓	✓		✓	✓	✓	✓	$1 + 3 x + 3 x^{2}$	$[\frac{1}{2},\frac{1}{2}]$	$1$	$0$	$1$	$0$	$1$	$7$	$[7, 7, 28, 91, 217, 784, 2107, 6643, 19684, 58807]$	$7$	$[7, 7, 28, 91, 217, 784, 2107, 6643, 19684, 58807]$	$1$	$1$	$3$	$6$	$6$	$\Q(\sqrt{-3}) $	$C_2$	simple
1.4.ae	$1$	$\F_{2^{2}}$	$2$	✓	✓	✓		✓	✓	✓	✓	$( 1 - 2 x )^{2}$	$[\frac{1}{2},\frac{1}{2}]$	$1$	$0$	$1$	$0$	$1$	$1$	$[1, 9, 49, 225, 961, 3969, 16129, 65025, 261121, 1046529]$	$1$	$[1, 9, 49, 225, 961, 3969, 16129, 65025, 261121, 1046529]$	$1$	$1$	$5$	$6$	$1$	$\Q$	Trivial	simple
1.4.ad	$1$	$\F_{2^{2}}$	$2$	✓	✓	✓	✓			✓	✓	$1 - 3 x + 4 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$2$	$[2, 16, 74, 288, 1082, 4144, 16298, 65088, 261146, 1047376]$	$2$	$[2, 16, 74, 288, 1082, 4144, 16298, 65088, 261146, 1047376]$	$1$	$1$	$2$	$2$	$1$	$\Q(\sqrt{-7}) $	$C_2$	simple
1.4.ac	$1$	$\F_{2^{2}}$	$2$	✓	✓	✓		✓	✓	✓	✓	$1 - 2 x + 4 x^{2}$	$[\frac{1}{2},\frac{1}{2}]$	$1$	$0$	$1$	$0$	$1$	$3$	$[3, 21, 81, 273, 993, 3969, 16257, 65793, 263169, 1049601]$	$3$	$[3, 21, 81, 273, 993, 3969, 16257, 65793, 263169, 1049601]$	$2$	$2$	$5$	$12$	$3$	$\Q(\sqrt{-3}) $	$C_2$	simple
1.4.ab	$1$	$\F_{2^{2}}$	$2$	✓	✓	✓	✓			✓	✓	$1 - x + 4 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$4$	$[4, 24, 76, 240, 964, 4104, 16636, 65760, 261364, 1046904]$	$4$	$[4, 24, 76, 240, 964, 4104, 16636, 65760, 261364, 1046904]$	$2$	$2$	$2$	$2$	$1$	$\Q(\sqrt{-15}) $	$C_2$	simple
1.4.a	$1$	$\F_{2^{2}}$	$2$	✓	✓			✓	✓	✓	✓	$1 + 4 x^{2}$	$[\frac{1}{2},\frac{1}{2}]$	$1$	$0$	$1$	$0$	$1$	$5$	$[5, 25, 65, 225, 1025, 4225, 16385, 65025, 262145, 1050625]$	$5$	$[5, 25, 65, 225, 1025, 4225, 16385, 65025, 262145, 1050625]$	$1$	$1$	$5$	$12$	$2$	$\Q(\sqrt{-1}) $	$C_2$	simple
1.4.b	$1$	$\F_{2^{2}}$	$2$	✓	✓	✓	✓			✓	✓	$1 + x + 4 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$6$	$[6, 24, 54, 240, 1086, 4104, 16134, 65760, 262926, 1046904]$	$6$	$[6, 24, 54, 240, 1086, 4104, 16134, 65760, 262926, 1046904]$	$2$	$2$	$2$	$2$	$1$	$\Q(\sqrt{-15}) $	$C_2$	simple
1.4.c	$1$	$\F_{2^{2}}$	$2$	✓	✓	✓		✓	✓	✓	✓	$1 + 2 x + 4 x^{2}$	$[\frac{1}{2},\frac{1}{2}]$	$1$	$0$	$1$	$0$	$1$	$7$	$[7, 21, 49, 273, 1057, 3969, 16513, 65793, 261121, 1049601]$	$7$	$[7, 21, 49, 273, 1057, 3969, 16513, 65793, 261121, 1049601]$	$2$	$2$	$5$	$12$	$3$	$\Q(\sqrt{-3}) $	$C_2$	simple
1.4.d	$1$	$\F_{2^{2}}$	$2$	✓	✓		✓			✓	✓	$1 + 3 x + 4 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$8$	$[8, 16, 56, 288, 968, 4144, 16472, 65088, 263144, 1047376]$	$8$	$[8, 16, 56, 288, 968, 4144, 16472, 65088, 263144, 1047376]$	$1$	$1$	$2$	$2$	$1$	$\Q(\sqrt{-7}) $	$C_2$	simple
1.4.e	$1$	$\F_{2^{2}}$	$2$	✓	✓			✓	✓	✓	✓	$( 1 + 2 x )^{2}$	$[\frac{1}{2},\frac{1}{2}]$	$1$	$0$	$1$	$0$	$1$	$9$	$[9, 9, 81, 225, 1089, 3969, 16641, 65025, 263169, 1046529]$	$9$	$[9, 9, 81, 225, 1089, 3969, 16641, 65025, 263169, 1046529]$	$1$	$1$	$5$	$6$	$1$	$\Q$	Trivial	simple
1.5.ae	$1$	$\F_{5}$	$5$	✓	✓	✓	✓			✓	✓	$1 - 4 x + 5 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$2$	$[2, 20, 122, 640, 3202, 15860, 78682, 391680, 1954562, 9766100]$	$2$	$[2, 20, 122, 640, 3202, 15860, 78682, 391680, 1954562, 9766100]$	$1$	$1$	$4$	$4$	$1$	$\Q(\sqrt{-1}) $	$C_2$	simple
1.5.ad	$1$	$\F_{5}$	$5$	✓	✓	✓	✓			✓	✓	$1 - 3 x + 5 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$3$	$[3, 27, 144, 675, 3183, 15552, 77619, 389475, 1952208, 9768627]$	$3$	$[3, 27, 144, 675, 3183, 15552, 77619, 389475, 1952208, 9768627]$	$1$	$1$	$2$	$2$	$1$	$\Q(\sqrt{-11}) $	$C_2$	simple
1.5.ac	$1$	$\F_{5}$	$5$	✓	✓	✓	✓			✓	✓	$1 - 2 x + 5 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$4$	$[4, 32, 148, 640, 3044, 15392, 78068, 391680, 1955524, 9765152]$	$4$	$[4, 32, 148, 640, 3044, 15392, 78068, 391680, 1955524, 9765152]$	$2$	$2$	$4$	$4$	$1$	$\Q(\sqrt{-1}) $	$C_2$	simple
1.5.ab	$1$	$\F_{5}$	$5$	✓	✓	✓	✓			✓	✓	$1 - x + 5 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$5$	$[5, 35, 140, 595, 3025, 15680, 78685, 390915, 1950620, 9761675]$	$5$	$[5, 35, 140, 595, 3025, 15680, 78685, 390915, 1950620, 9761675]$	$1$	$1$	$2$	$2$	$1$	$\Q(\sqrt{-19}) $	$C_2$	simple
1.5.a	$1$	$\F_{5}$	$5$	✓	✓	✓		✓	✓	✓	✓	$1 + 5 x^{2}$	$[\frac{1}{2},\frac{1}{2}]$	$1$	$0$	$1$	$0$	$1$	$6$	$[6, 36, 126, 576, 3126, 15876, 78126, 389376, 1953126, 9771876]$	$6$	$[6, 36, 126, 576, 3126, 15876, 78126, 389376, 1953126, 9771876]$	$2$	$2$	$1$	$1$	$2$	$\Q(\sqrt{-5}) $	$C_2$	simple
1.5.b	$1$	$\F_{5}$	$5$	✓	✓	✓	✓			✓	✓	$1 + x + 5 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$7$	$[7, 35, 112, 595, 3227, 15680, 77567, 390915, 1955632, 9761675]$	$7$	$[7, 35, 112, 595, 3227, 15680, 77567, 390915, 1955632, 9761675]$	$1$	$1$	$2$	$2$	$1$	$\Q(\sqrt{-19}) $	$C_2$	simple
1.5.c	$1$	$\F_{5}$	$5$	✓	✓	✓	✓			✓	✓	$1 + 2 x + 5 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$8$	$[8, 32, 104, 640, 3208, 15392, 78184, 391680, 1950728, 9765152]$	$8$	$[8, 32, 104, 640, 3208, 15392, 78184, 391680, 1950728, 9765152]$	$2$	$2$	$4$	$4$	$1$	$\Q(\sqrt{-1}) $	$C_2$	simple
1.5.d	$1$	$\F_{5}$	$5$	✓	✓	✓	✓			✓	✓	$1 + 3 x + 5 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$9$	$[9, 27, 108, 675, 3069, 15552, 78633, 389475, 1954044, 9768627]$	$9$	$[9, 27, 108, 675, 3069, 15552, 78633, 389475, 1954044, 9768627]$	$1$	$1$	$2$	$2$	$1$	$\Q(\sqrt{-11}) $	$C_2$	simple
1.5.e	$1$	$\F_{5}$	$5$	✓	✓	✓	✓			✓	✓	$1 + 4 x + 5 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$10$	$[10, 20, 130, 640, 3050, 15860, 77570, 391680, 1951690, 9766100]$	$10$	$[10, 20, 130, 640, 3050, 15860, 77570, 391680, 1951690, 9766100]$	$1$	$1$	$4$	$4$	$1$	$\Q(\sqrt{-1}) $	$C_2$	simple
1.7.af	$1$	$\F_{7}$	$7$	✓	✓	✓	✓			✓	✓	$1 - 5 x + 7 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$3$	$[3, 39, 324, 2379, 16833, 117936, 824799, 5769075, 40366188, 282508239]$	$3$	$[3, 39, 324, 2379, 16833, 117936, 824799, 5769075, 40366188, 282508239]$	$1$	$1$	$6$	$6$	$1$	$\Q(\sqrt{-3}) $	$C_2$	simple
1.7.ae	$1$	$\F_{7}$	$7$	✓	✓	✓	✓			✓	✓	$1 - 4 x + 7 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$4$	$[4, 48, 364, 2496, 17044, 117936, 823036, 5760768, 40341028, 282453168]$	$4$	$[4, 48, 364, 2496, 17044, 117936, 823036, 5760768, 40341028, 282453168]$	$2$	$2$	$6$	$6$	$1$	$\Q(\sqrt{-3}) $	$C_2$	simple
1.7.ad	$1$	$\F_{7}$	$7$	✓	✓	✓	✓			✓	✓	$1 - 3 x + 7 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$5$	$[5, 55, 380, 2475, 16775, 117040, 821945, 5764275, 40363220, 282507775]$	$5$	$[5, 55, 380, 2475, 16775, 117040, 821945, 5764275, 40363220, 282507775]$	$1$	$1$	$2$	$2$	$1$	$\Q(\sqrt{-19}) $	$C_2$	simple
1.7.ac	$1$	$\F_{7}$	$7$	✓	✓	✓	✓			✓	✓	$1 - 2 x + 7 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$6$	$[6, 60, 378, 2400, 16566, 117180, 824298, 5769600, 40357926, 282450300]$	$6$	$[6, 60, 378, 2400, 16566, 117180, 824298, 5769600, 40357926, 282450300]$	$2$	$2$	$2$	$2$	$1$	$\Q(\sqrt{-6}) $	$C_2$	simple
1.7.ab	$1$	$\F_{7}$	$7$	✓	✓	✓	✓			✓	✓	$1 - x + 7 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$7$	$[7, 63, 364, 2331, 16597, 117936, 825307, 5764563, 40341028, 282464343]$	$7$	$[7, 63, 364, 2331, 16597, 117936, 825307, 5764563, 40341028, 282464343]$	$2$	$2$	$6$	$6$	$1$	$\Q(\sqrt{-3}) $	$C_2$	simple
1.7.a	$1$	$\F_{7}$	$7$	✓	✓	✓		✓	✓	✓	✓	$1 + 7 x^{2}$	$[\frac{1}{2},\frac{1}{2}]$	$1$	$0$	$1$	$0$	$1$	$8$	$[8, 64, 344, 2304, 16808, 118336, 823544, 5760000, 40353608, 282508864]$	$8$	$[8, 64, 344, 2304, 16808, 118336, 823544, 5760000, 40353608, 282508864]$	$2$	$2$	$1$	$1$	$2$	$\Q(\sqrt{-7}) $	$C_2$	simple
1.7.b	$1$	$\F_{7}$	$7$	✓	✓	✓	✓			✓	✓	$1 + x + 7 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$9$	$[9, 63, 324, 2331, 17019, 117936, 821781, 5764563, 40366188, 282464343]$	$9$	$[9, 63, 324, 2331, 17019, 117936, 821781, 5764563, 40366188, 282464343]$	$2$	$2$	$6$	$6$	$1$	$\Q(\sqrt{-3}) $	$C_2$	simple
1.7.c	$1$	$\F_{7}$	$7$	✓	✓	✓	✓			✓	✓	$1 + 2 x + 7 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$10$	$[10, 60, 310, 2400, 17050, 117180, 822790, 5769600, 40349290, 282450300]$	$10$	$[10, 60, 310, 2400, 17050, 117180, 822790, 5769600, 40349290, 282450300]$	$2$	$2$	$2$	$2$	$1$	$\Q(\sqrt{-6}) $	$C_2$	simple
1.7.d	$1$	$\F_{7}$	$7$	✓	✓	✓	✓			✓	✓	$1 + 3 x + 7 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$11$	$[11, 55, 308, 2475, 16841, 117040, 825143, 5764275, 40343996, 282507775]$	$11$	$[11, 55, 308, 2475, 16841, 117040, 825143, 5764275, 40343996, 282507775]$	$1$	$1$	$2$	$2$	$1$	$\Q(\sqrt{-19}) $	$C_2$	simple
1.7.e	$1$	$\F_{7}$	$7$	✓	✓	✓	✓			✓	✓	$1 + 4 x + 7 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$12$	$[12, 48, 324, 2496, 16572, 117936, 824052, 5760768, 40366188, 282453168]$	$12$	$[12, 48, 324, 2496, 16572, 117936, 824052, 5760768, 40366188, 282453168]$	$2$	$2$	$6$	$6$	$1$	$\Q(\sqrt{-3}) $	$C_2$	simple
1.7.f	$1$	$\F_{7}$	$7$	✓	✓	✓	✓			✓	✓	$1 + 5 x + 7 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$13$	$[13, 39, 364, 2379, 16783, 117936, 822289, 5769075, 40341028, 282508239]$	$13$	$[13, 39, 364, 2379, 16783, 117936, 822289, 5769075, 40341028, 282508239]$	$1$	$1$	$6$	$6$	$1$	$\Q(\sqrt{-3}) $	$C_2$	simple
1.8.af	$1$	$\F_{2^{3}}$	$2$	✓	✓		✓			✓	✓	$1 - 5 x + 8 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$4$	$[4, 56, 508, 4144, 33044, 263144, 2099948, 16783200, 134225284, 1073731736]$	$4$	$[4, 56, 508, 4144, 33044, 263144, 2099948, 16783200, 134225284, 1073731736]$	$1$	$1$	$2$	$2$	$1$	$\Q(\sqrt{-7}) $	$C_2$	simple
1.8.ae	$1$	$\F_{2^{3}}$	$2$	✓	✓			✓	✓	✓	✓	$1 - 4 x + 8 x^{2}$	$[\frac{1}{2},\frac{1}{2}]$	$1$	$0$	$1$	$0$	$1$	$5$	$[5, 65, 545, 4225, 33025, 262145, 2095105, 16769025, 134201345, 1073741825]$	$5$	$[5, 65, 545, 4225, 33025, 262145, 2095105, 16769025, 134201345, 1073741825]$	$1$	$1$	$3$	$8$	$4$	$\Q(\sqrt{-1}) $	$C_2$	simple
1.8.ad	$1$	$\F_{2^{3}}$	$2$	✓	✓	✓	✓			✓	✓	$1 - 3 x + 8 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$6$	$[6, 72, 558, 4176, 32646, 261144, 2095134, 16779168, 134239734, 1073792232]$	$6$	$[6, 72, 558, 4176, 32646, 261144, 2095134, 16779168, 134239734, 1073792232]$	$3$	$3$	$2$	$2$	$1$	$\Q(\sqrt{-23}) $	$C_2$	simple
1.8.ab	$1$	$\F_{2^{3}}$	$2$	✓	✓	✓	✓			✓	✓	$1 - x + 8 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$8$	$[8, 80, 536, 4000, 32488, 262640, 2099896, 16776000, 134194568, 1073728400]$	$8$	$[8, 80, 536, 4000, 32488, 262640, 2099896, 16776000, 134194568, 1073728400]$	$3$	$3$	$2$	$2$	$1$	$\Q(\sqrt{-31}) $	$C_2$	simple
1.8.a	$1$	$\F_{2^{3}}$	$2$	✓	✓			✓	✓	✓	✓	$1 + 8 x^{2}$	$[\frac{1}{2},\frac{1}{2}]$	$1$	$0$	$1$	$0$	$1$	$9$	$[9, 81, 513, 3969, 32769, 263169, 2097153, 16769025, 134217729, 1073807361]$	$9$	$[9, 81, 513, 3969, 32769, 263169, 2097153, 16769025, 134217729, 1073807361]$	$1$	$1$	$3$	$8$	$2$	$\Q(\sqrt{-2}) $	$C_2$	simple
1.8.b	$1$	$\F_{2^{3}}$	$2$	✓	✓	✓	✓			✓	✓	$1 + x + 8 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$10$	$[10, 80, 490, 4000, 33050, 262640, 2094410, 16776000, 134240890, 1073728400]$	$10$	$[10, 80, 490, 4000, 33050, 262640, 2094410, 16776000, 134240890, 1073728400]$	$3$	$3$	$2$	$2$	$1$	$\Q(\sqrt{-31}) $	$C_2$	simple
1.8.d	$1$	$\F_{2^{3}}$	$2$	✓	✓	✓	✓			✓	✓	$1 + 3 x + 8 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$12$	$[12, 72, 468, 4176, 32892, 261144, 2099172, 16779168, 134195724, 1073792232]$	$12$	$[12, 72, 468, 4176, 32892, 261144, 2099172, 16779168, 134195724, 1073792232]$	$3$	$3$	$2$	$2$	$1$	$\Q(\sqrt{-23}) $	$C_2$	simple
1.8.e	$1$	$\F_{2^{3}}$	$2$	✓	✓			✓	✓	✓	✓	$1 + 4 x + 8 x^{2}$	$[\frac{1}{2},\frac{1}{2}]$	$1$	$0$	$1$	$0$	$1$	$13$	$[13, 65, 481, 4225, 32513, 262145, 2099201, 16769025, 134234113, 1073741825]$	$13$	$[13, 65, 481, 4225, 32513, 262145, 2099201, 16769025, 134234113, 1073741825]$	$1$	$1$	$3$	$8$	$4$	$\Q(\sqrt{-1}) $	$C_2$	simple
1.8.f	$1$	$\F_{2^{3}}$	$2$	✓	✓		✓			✓	✓	$1 + 5 x + 8 x^{2}$	$[0,1]$	$0$	$1$	$0$	$1$	$0$	$14$	$[14, 56, 518, 4144, 32494, 263144, 2094358, 16783200, 134210174, 1073731736]$	$14$	$[14, 56, 518, 4144, 32494, 263144, 2094358, 16783200, 134210174, 1073731736]$	$1$	$1$	$2$	$2$	$1$	$\Q(\sqrt{-7}) $	$C_2$	simple

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

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