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
2.2.ae_i	$2$	$\F_{2}$	$2$			✓			✓	✓		$( 1 - 2 x + 2 x^{2} )^{2}$	$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$	$2$	$0$	$2$	$0$	$2$	$-1$	$[-1, 5, 17, 33, 49, 65, 97, 193, 449, 1025]$	$1$	$[1, 25, 169, 625, 1681, 4225, 12769, 50625, 231361, 1050625]$	$0$	$0$	$11$	$24$	$4$	$\Q(\sqrt{-1})$	$C_2$	1.2.ac^2
2.2.ad_f	$2$	$\F_{2}$	$2$	✓		✓	✓			✓	✓	$1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$0$	$[0, 6, 9, 10, 30, 87, 168, 274, 513, 1086]$	$1$	$[1, 19, 76, 171, 961, 5776, 22051, 69939, 261364, 1113799]$	$1$	$1$	$4$	$12$	$6$	$\Q(\sqrt{-3}, \sqrt{5})$	$C_2^2$	simple
2.2.ad_g	$2$	$\F_{2}$	$2$			✓		✓		✓		$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$1$	$1$	$0$	$[0, 8, 18, 24, 30, 56, 126, 256, 486, 968]$	$2$	$[2, 40, 182, 400, 902, 3640, 16046, 64800, 249158, 992200]$	$0$	$0$	$6$	$8$	$4$	$\Q(\sqrt{-1})$, $\Q(\sqrt{-7})$	$C_2$, $C_2$	1.2.ac $\times$ 1.2.ab
2.2.ac_c	$2$	$\F_{2}$	$2$	✓		✓			✓	✓	✓	$1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4}$	$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$	$2$	$0$	$2$	$0$	$2$	$1$	$[1, 5, 1, 9, 41, 65, 113, 289, 577, 1025]$	$1$	$[1, 13, 25, 169, 1321, 4225, 14449, 74529, 297025, 1047553]$	$1$	$1$	$11$	$24$	$12$	$\Q(\zeta_{12})$	$C_2^2$	simple
2.2.ac_d	$2$	$\F_{2}$	$2$	✓	✓	✓	✓			✓	✓	$1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$1$	$[1, 7, 7, 15, 51, 91, 127, 255, 547, 987]$	$2$	$[2, 28, 62, 224, 1762, 6076, 16046, 65408, 280178, 1011388]$	$1$	$1$	$2$	$2$	$1$	4.0.1088.2	$D_{4}$	simple
2.2.ac_e	$2$	$\F_{2}$	$2$			✓			✓	✓	✓	$( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} )$	$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$	$2$	$0$	$2$	$0$	$2$	$1$	$[1, 9, 13, 17, 41, 81, 113, 193, 481, 1089]$	$3$	$[3, 45, 117, 225, 1353, 5265, 14577, 50625, 246753, 1116225]$	$1$	$1$	$11$	$24$	$8$	$\Q(\sqrt{-1})$, $\Q(\sqrt{-2})$	$C_2$, $C_2$	1.2.ac $\times$ 1.2.a
2.2.ac_f	$2$	$\F_{2}$	$2$			✓	✓			✓		$( 1 - x + 2 x^{2} )^{2}$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$1$	$[1, 11, 19, 15, 11, 47, 155, 319, 523, 911]$	$4$	$[4, 64, 196, 256, 484, 3136, 20164, 82944, 268324, 937024]$	$0$	$0$	$6$	$6$	$1$	$\Q(\sqrt{-7})$	$C_2$	1.2.ab^2
2.2.ab_ab	$2$	$\F_{2}$	$2$	✓		✓	✓					$1 - x - x^{2} - 2 x^{3} + 4 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$2$	$[2, 2, -1, 18, 22, 47, 142, 226, 503, 1082]$	$1$	$[1, 7, 16, 259, 751, 3136, 18103, 58275, 258064, 1109227]$	$0$	$0$	$6$	$12$	$3$	$\Q(\sqrt{-3}, \sqrt{-7})$	$C_2^2$	simple
2.2.ab_a	$2$	$\F_{2}$	$2$	✓	✓	✓		✓		✓	✓	$1 - x - 2 x^{3} + 4 x^{4}$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$2$	$0$	$2$	$[2, 4, 2, 24, 42, 64, 170, 288, 506, 1104]$	$2$	$[2, 16, 26, 416, 1402, 3952, 22346, 74048, 258362, 1132816]$	$1$	$1$	$2$	$2$	$1$	4.0.2312.1	$D_{4}$	simple
2.2.ab_b	$2$	$\F_{2}$	$2$	✓	✓	✓	✓			✓	✓	$1 - x + x^{2} - 2 x^{3} + 4 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$2$	$[2, 6, 5, 26, 52, 63, 142, 274, 437, 966]$	$3$	$[3, 27, 36, 459, 1803, 3888, 18357, 70227, 225612, 989847]$	$1$	$1$	$2$	$2$	$1$	4.0.2873.1	$D_{4}$	simple
2.2.ab_c	$2$	$\F_{2}$	$2$			✓		✓		✓	✓	$( 1 - 2 x + 2 x^{2} )( 1 + x + 2 x^{2} )$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$1$	$1$	$2$	$[2, 8, 8, 24, 52, 56, 100, 256, 476, 968]$	$4$	$[4, 40, 52, 400, 1804, 3640, 13108, 64800, 244348, 992200]$	$1$	$1$	$6$	$8$	$4$	$\Q(\sqrt{-1})$, $\Q(\sqrt{-7})$	$C_2$, $C_2$	1.2.ac $\times$ 1.2.b
2.2.ab_d	$2$	$\F_{2}$	$2$	✓	✓	✓	✓			✓	✓	$1 - x + 3 x^{2} - 2 x^{3} + 4 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$2$	$[2, 10, 11, 18, 42, 55, 86, 258, 587, 1050]$	$5$	$[5, 55, 80, 275, 1375, 3520, 11555, 66275, 302480, 1073875]$	$1$	$1$	$2$	$2$	$1$	4.0.1025.1	$D_{4}$	simple
2.2.ab_e	$2$	$\F_{2}$	$2$			✓		✓		✓		$( 1 - x + 2 x^{2} )( 1 + 2 x^{2} )$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$1$	$1$	$2$	$[2, 12, 14, 8, 22, 72, 142, 256, 518, 1032]$	$6$	$[6, 72, 126, 144, 726, 4536, 18318, 64800, 265734, 1054152]$	$0$	$0$	$6$	$8$	$2$	$\Q(\sqrt{-7})$, $\Q(\sqrt{-2})$	$C_2$, $C_2$	1.2.ab $\times$ 1.2.a
2.2.a_ae	$2$	$\F_{2}$	$2$	✓		✓			✓	✓		$( 1 - 2 x^{2} )^{2}$	$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$	$2$	$0$	$2$	$0$	$2$	$3$	$[3, -3, 9, 1, 33, 33, 129, 193, 513, 897]$	$1$	$[1, 1, 49, 81, 961, 2401, 16129, 50625, 261121, 923521]$	$0$	$0$	$11$	$24$	$2$	$\Q(\sqrt{2})$	$C_2$	simple
2.2.a_ad	$2$	$\F_{2}$	$2$	✓		✓	✓			✓		$1 - 3 x^{2} + 4 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$3$	$[3, -1, 9, 15, 33, 83, 129, 319, 513, 1139]$	$2$	$[2, 4, 74, 256, 1082, 5476, 16298, 82944, 261146, 1170724]$	$0$	$0$	$6$	$12$	$2$	$\Q(i, \sqrt{7})$	$C_2^2$	simple
2.2.a_ac	$2$	$\F_{2}$	$2$	✓		✓			✓	✓		$1 - 2 x^{2} + 4 x^{4}$	$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$	$2$	$0$	$2$	$0$	$2$	$3$	$[3, 1, 9, 25, 33, 97, 129, 289, 513, 961]$	$3$	$[3, 9, 81, 441, 993, 6561, 16257, 74529, 263169, 986049]$	$0$	$0$	$11$	$24$	$6$	$\Q(\sqrt{-2}, \sqrt{-3})$	$C_2^2$	simple
2.2.a_ab	$2$	$\F_{2}$	$2$	✓		✓	✓			✓	✓	$1 - x^{2} + 4 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$3$	$[3, 3, 9, 31, 33, 87, 129, 223, 513, 903]$	$4$	$[4, 16, 76, 576, 964, 5776, 16636, 57600, 261364, 929296]$	$1$	$1$	$4$	$6$	$2$	$\Q(\sqrt{-3}, \sqrt{5})$	$C_2^2$	simple
2.2.a_a	$2$	$\F_{2}$	$2$			✓			✓	✓	✓	$( 1 - 2 x + 2 x^{2} )( 1 + 2 x + 2 x^{2} )$	$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$	$2$	$0$	$2$	$0$	$2$	$3$	$[3, 5, 9, 33, 33, 65, 129, 193, 513, 1025]$	$5$	$[5, 25, 65, 625, 1025, 4225, 16385, 50625, 262145, 1050625]$	$1$	$1$	$11$	$24$	$4$	$\Q(\sqrt{-1})$, $\Q(\sqrt{-1})$	$C_2$, $C_2$	1.2.ac $\times$ 1.2.c
2.2.a_b	$2$	$\F_{2}$	$2$	✓		✓	✓			✓	✓	$1 + x^{2} + 4 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$3$	$[3, 7, 9, 31, 33, 43, 129, 223, 513, 1147]$	$6$	$[6, 36, 54, 576, 1086, 2916, 16134, 57600, 262926, 1179396]$	$1$	$1$	$4$	$12$	$2$	$\Q(\sqrt{3}, \sqrt{-5})$	$C_2^2$	simple
2.2.a_c	$2$	$\F_{2}$	$2$	✓		✓			✓	✓	✓	$1 + 2 x^{2} + 4 x^{4}$	$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$	$2$	$0$	$2$	$0$	$2$	$3$	$[3, 9, 9, 25, 33, 33, 129, 289, 513, 1089]$	$7$	$[7, 49, 49, 441, 1057, 2401, 16513, 74529, 261121, 1117249]$	$1$	$1$	$11$	$24$	$6$	$\Q(\sqrt{2}, \sqrt{-3})$	$C_2^2$	simple
2.2.a_d	$2$	$\F_{2}$	$2$			✓	✓			✓		$( 1 - x + 2 x^{2} )( 1 + x + 2 x^{2} )$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$3$	$[3, 11, 9, 15, 33, 47, 129, 319, 513, 911]$	$8$	$[8, 64, 56, 256, 968, 3136, 16472, 82944, 263144, 937024]$	$0$	$0$	$6$	$6$	$2$	$\Q(\sqrt{-7})$, $\Q(\sqrt{-7})$	$C_2$, $C_2$	1.2.ab $\times$ 1.2.b
2.2.a_e	$2$	$\F_{2}$	$2$			✓			✓	✓		$( 1 + 2 x^{2} )^{2}$	$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$	$2$	$0$	$2$	$0$	$2$	$3$	$[3, 13, 9, 1, 33, 97, 129, 193, 513, 1153]$	$9$	$[9, 81, 81, 81, 1089, 6561, 16641, 50625, 263169, 1185921]$	$0$	$0$	$11$	$24$	$2$	$\Q(\sqrt{-2})$	$C_2$	1.2.a^2
2.2.b_ab	$2$	$\F_{2}$	$2$	✓		✓	✓					$1 + x - x^{2} + 2 x^{3} + 4 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$4$	$[4, 2, 19, 18, 44, 47, 116, 226, 523, 1082]$	$7$	$[7, 7, 196, 259, 1477, 3136, 14749, 58275, 268324, 1109227]$	$0$	$0$	$6$	$12$	$3$	$\Q(\sqrt{-3}, \sqrt{-7})$	$C_2^2$	simple
2.2.b_a	$2$	$\F_{2}$	$2$	✓	✓	✓		✓		✓	✓	$1 + x + 2 x^{3} + 4 x^{4}$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$2$	$0$	$4$	$[4, 4, 16, 24, 24, 64, 88, 288, 520, 1104]$	$8$	$[8, 16, 152, 416, 808, 3952, 11768, 74048, 265544, 1132816]$	$1$	$1$	$2$	$2$	$1$	4.0.2312.1	$D_{4}$	simple
2.2.b_b	$2$	$\F_{2}$	$2$	✓	✓	✓	✓			✓	✓	$1 + x + x^{2} + 2 x^{3} + 4 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$4$	$[4, 6, 13, 26, 14, 63, 116, 274, 589, 966]$	$9$	$[9, 27, 108, 459, 549, 3888, 15003, 70227, 303588, 989847]$	$1$	$1$	$2$	$2$	$1$	4.0.2873.1	$D_{4}$	simple
2.2.b_c	$2$	$\F_{2}$	$2$			✓		✓		✓	✓	$( 1 - x + 2 x^{2} )( 1 + 2 x + 2 x^{2} )$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$1$	$1$	$4$	$[4, 8, 10, 24, 14, 56, 158, 256, 550, 968]$	$10$	$[10, 40, 70, 400, 550, 3640, 20590, 64800, 282310, 992200]$	$1$	$1$	$6$	$8$	$4$	$\Q(\sqrt{-7})$, $\Q(\sqrt{-1})$	$C_2$, $C_2$	1.2.ab $\times$ 1.2.c
2.2.b_d	$2$	$\F_{2}$	$2$	✓	✓	✓	✓			✓	✓	$1 + x + 3 x^{2} + 2 x^{3} + 4 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$4$	$[4, 10, 7, 18, 24, 55, 172, 258, 439, 1050]$	$11$	$[11, 55, 44, 275, 781, 3520, 22649, 66275, 226556, 1073875]$	$1$	$1$	$2$	$2$	$1$	4.0.1025.1	$D_{4}$	simple
2.2.b_e	$2$	$\F_{2}$	$2$			✓		✓		✓		$( 1 + 2 x^{2} )( 1 + x + 2 x^{2} )$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$1$	$1$	$4$	$[4, 12, 4, 8, 44, 72, 116, 256, 508, 1032]$	$12$	$[12, 72, 36, 144, 1452, 4536, 14964, 64800, 260604, 1054152]$	$0$	$0$	$6$	$8$	$2$	$\Q(\sqrt{-2})$, $\Q(\sqrt{-7})$	$C_2$, $C_2$	1.2.a $\times$ 1.2.b
2.2.c_c	$2$	$\F_{2}$	$2$	✓		✓			✓	✓	✓	$1 + 2 x + 2 x^{2} + 4 x^{3} + 4 x^{4}$	$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$	$2$	$0$	$2$	$0$	$2$	$5$	$[5, 5, 17, 9, 25, 65, 145, 289, 449, 1025]$	$13$	$[13, 13, 169, 169, 793, 4225, 18577, 74529, 231361, 1047553]$	$1$	$1$	$11$	$24$	$12$	$\Q(\zeta_{12})$	$C_2^2$	simple
2.2.c_d	$2$	$\F_{2}$	$2$	✓	✓	✓	✓			✓	✓	$1 + 2 x + 3 x^{2} + 4 x^{3} + 4 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$5$	$[5, 7, 11, 15, 15, 91, 131, 255, 479, 987]$	$14$	$[14, 28, 98, 224, 574, 6076, 16562, 65408, 245294, 1011388]$	$1$	$1$	$2$	$2$	$1$	4.0.1088.2	$D_{4}$	simple
2.2.c_e	$2$	$\F_{2}$	$2$			✓			✓	✓	✓	$( 1 + 2 x^{2} )( 1 + 2 x + 2 x^{2} )$	$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$	$2$	$0$	$2$	$0$	$2$	$5$	$[5, 9, 5, 17, 25, 81, 145, 193, 545, 1089]$	$15$	$[15, 45, 45, 225, 825, 5265, 18705, 50625, 279585, 1116225]$	$1$	$1$	$11$	$24$	$8$	$\Q(\sqrt{-2})$, $\Q(\sqrt{-1})$	$C_2$, $C_2$	1.2.a $\times$ 1.2.c
2.2.c_f	$2$	$\F_{2}$	$2$			✓	✓			✓		$( 1 + x + 2 x^{2} )^{2}$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$5$	$[5, 11, -1, 15, 55, 47, 103, 319, 503, 911]$	$16$	$[16, 64, 16, 256, 1936, 3136, 13456, 82944, 258064, 937024]$	$0$	$0$	$6$	$6$	$1$	$\Q(\sqrt{-7})$	$C_2$	1.2.b^2
2.2.d_f	$2$	$\F_{2}$	$2$	✓		✓	✓			✓	✓	$1 + 3 x + 5 x^{2} + 6 x^{3} + 4 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$6$	$[6, 6, 9, 10, 36, 87, 90, 274, 513, 1086]$	$19$	$[19, 19, 76, 171, 1159, 5776, 11989, 69939, 261364, 1113799]$	$1$	$1$	$4$	$12$	$6$	$\Q(\sqrt{-3}, \sqrt{5})$	$C_2^2$	simple
2.2.d_g	$2$	$\F_{2}$	$2$			✓		✓		✓		$( 1 + x + 2 x^{2} )( 1 + 2 x + 2 x^{2} )$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$1$	$1$	$6$	$[6, 8, 0, 24, 36, 56, 132, 256, 540, 968]$	$20$	$[20, 40, 20, 400, 1100, 3640, 16820, 64800, 276860, 992200]$	$0$	$0$	$6$	$8$	$4$	$\Q(\sqrt{-7})$, $\Q(\sqrt{-1})$	$C_2$, $C_2$	1.2.b $\times$ 1.2.c
2.2.e_i	$2$	$\F_{2}$	$2$			✓			✓	✓		$( 1 + 2 x + 2 x^{2} )^{2}$	$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$	$2$	$0$	$2$	$0$	$2$	$7$	$[7, 5, 1, 33, 17, 65, 161, 193, 577, 1025]$	$25$	$[25, 25, 25, 625, 625, 4225, 21025, 50625, 297025, 1050625]$	$0$	$0$	$11$	$24$	$4$	$\Q(\sqrt{-1})$	$C_2$	1.2.c^2
2.3.ag_p	$2$	$\F_{3}$	$3$			✓			✓	✓		$( 1 - 3 x + 3 x^{2} )^{2}$	$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$	$2$	$0$	$2$	$0$	$2$	$-2$	$[-2, 4, 28, 100, 298, 838, 2350, 6724, 19684, 58564]$	$1$	$[1, 49, 784, 8281, 73441, 614656, 5148361, 44129449, 387459856, 3458263249]$	$0$	$0$	$9$	$24$	$6$	$\Q(\sqrt{-3})$	$C_2$	1.3.ad^2
2.3.af_m	$2$	$\F_{3}$	$3$			✓		✓		✓		$( 1 - 3 x + 3 x^{2} )( 1 - 2 x + 3 x^{2} )$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$1$	$1$	$-1$	$[-1, 9, 38, 105, 269, 738, 2183, 6609, 19874, 59289]$	$2$	$[2, 84, 1064, 8736, 65582, 536256, 4769438, 43365504, 391199816, 3500898324]$	$0$	$0$	$6$	$6$	$6$	$\Q(\sqrt{-3})$, $\Q(\sqrt{-2})$	$C_2$, $C_2$	1.3.ad $\times$ 1.3.ac
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
2.3.ae_j	$2$	$\F_{3}$	$3$			✓		✓		✓	✓	$( 1 - 3 x + 3 x^{2} )( 1 - x + 3 x^{2} )$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$1$	$1$	$0$	$[0, 12, 36, 84, 240, 774, 2352, 6756, 19548, 58332]$	$3$	$[3, 105, 1008, 6825, 57723, 564480, 5152899, 44342025, 384782832, 3444620025]$	$1$	$1$	$6$	$6$	$6$	$\Q(\sqrt{-3})$, $\Q(\sqrt{-11})$	$C_2$, $C_2$	1.3.ad $\times$ 1.3.ab
2.3.ae_k	$2$	$\F_{3}$	$3$			✓	✓			✓	✓	$( 1 - 2 x + 3 x^{2} )^{2}$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$0$	$[0, 14, 48, 110, 240, 638, 2016, 6494, 20064, 60014]$	$4$	$[4, 144, 1444, 9216, 58564, 467856, 4418404, 42614784, 394975876, 3544059024]$	$1$	$1$	$8$	$8$	$1$	$\Q(\sqrt{-2})$	$C_2$	1.3.ac^2
2.3.ad_f	$2$	$\F_{3}$	$3$	✓	✓	✓	✓			✓	✓	$1 - 3 x + 5 x^{2} - 9 x^{3} + 9 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$1$	$[1, 11, 19, 59, 256, 791, 2185, 6563, 20143, 59846]$	$3$	$[3, 81, 549, 4941, 62448, 578097, 4778049, 43050933, 396546543, 3534057216]$	$1$	$1$	$2$	$2$	$1$	4.0.2197.1	$C_4$	simple
2.3.ad_g	$2$	$\F_{3}$	$3$			✓			✓	✓	✓	$( 1 - 3 x + 3 x^{2} )( 1 + 3 x^{2} )$	$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$	$2$	$0$	$2$	$0$	$2$	$1$	$[1, 13, 28, 73, 271, 838, 2269, 6481, 19684, 59293]$	$4$	$[4, 112, 784, 5824, 66124, 614656, 4964572, 42515200, 387459856, 3501133552]$	$1$	$1$	$9$	$24$	$6$	$\Q(\sqrt{-3})$, $\Q(\sqrt{-3})$	$C_2$, $C_2$	1.3.ad $\times$ 1.3.a
2.3.ad_h	$2$	$\F_{3}$	$3$	✓	✓	✓	✓			✓	✓	$1 - 3 x + 7 x^{2} - 9 x^{3} + 9 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$1$	$[1, 15, 37, 83, 256, 795, 2227, 6323, 19171, 58950]$	$5$	$[5, 145, 1055, 6525, 62000, 581305, 4870955, 41505525, 377427305, 3480928000]$	$1$	$1$	$2$	$2$	$1$	4.0.1525.1	$D_{4}$	simple
2.3.ad_i	$2$	$\F_{3}$	$3$			✓	✓			✓		$( 1 - 2 x + 3 x^{2} )( 1 - x + 3 x^{2} )$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$1$	$[1, 17, 46, 89, 211, 674, 2185, 6641, 19738, 59057]$	$6$	$[6, 180, 1368, 7200, 51546, 492480, 4773642, 43574400, 388496952, 3487086900]$	$0$	$0$	$4$	$2$	$1$	$\Q(\sqrt{-2})$, $\Q(\sqrt{-11})$	$C_2$, $C_2$	1.3.ac $\times$ 1.3.ab
2.3.ac_b	$2$	$\F_{3}$	$3$	✓		✓	✓			✓	✓	$1 - 2 x + x^{2} - 6 x^{3} + 9 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$2$	$[2, 8, 8, 68, 242, 638, 2102, 6596, 19304, 58568]$	$3$	$[3, 57, 324, 5529, 58323, 467856, 4600011, 43264425, 380016036, 3458495577]$	$1$	$1$	$8$	$24$	$3$	$\Q(\sqrt{-2}, \sqrt{-3})$	$C_2^2$	simple
2.3.ac_c	$2$	$\F_{3}$	$3$	✓		✓	✓			✓	✓	$1 - 2 x + 2 x^{2} - 6 x^{3} + 9 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$2$	$[2, 10, 14, 78, 282, 730, 2214, 6878, 19922, 59050]$	$4$	$[4, 80, 436, 6400, 69044, 531920, 4840196, 45158400, 392133604, 3486722000]$	$2$	$2$	$4$	$8$	$4$	$\Q(i, \sqrt{5})$	$C_2^2$	simple
2.3.ac_d	$2$	$\F_{3}$	$3$			✓		✓		✓	✓	$( 1 - 3 x + 3 x^{2} )( 1 + x + 3 x^{2} )$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$1$	$1$	$2$	$[2, 12, 20, 84, 302, 774, 2186, 6756, 19820, 58332]$	$5$	$[5, 105, 560, 6825, 74525, 564480, 4776245, 44342025, 390136880, 3444620025]$	$2$	$2$	$6$	$6$	$6$	$\Q(\sqrt{-3})$, $\Q(\sqrt{-11})$	$C_2$, $C_2$	1.3.ad $\times$ 1.3.b
2.3.ac_e	$2$	$\F_{3}$	$3$	✓	✓	✓	✓			✓	✓	$1 - 2 x + 4 x^{2} - 6 x^{3} + 9 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$2$	$[2, 14, 26, 86, 302, 782, 2102, 6494, 19682, 58334]$	$6$	$[6, 132, 702, 6864, 74526, 571428, 4598502, 42611712, 387350262, 3444740772]$	$2$	$2$	$2$	$2$	$1$	4.0.7488.1	$D_{4}$	simple
2.3.ac_f	$2$	$\F_{3}$	$3$	✓	✓	✓	✓			✓	✓	$1 - 2 x + 5 x^{2} - 6 x^{3} + 9 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$2$	$[2, 16, 32, 84, 282, 766, 2046, 6308, 19760, 59296]$	$7$	$[7, 161, 868, 6601, 69167, 558992, 4481687, 41408073, 388913476, 3501441041]$	$1$	$1$	$2$	$2$	$1$	4.0.4672.2	$D_{4}$	simple
2.3.ac_g	$2$	$\F_{3}$	$3$			✓		✓		✓	✓	$( 1 - 2 x + 3 x^{2} )( 1 + 3 x^{2} )$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$1$	$1$	$2$	$[2, 18, 38, 78, 242, 738, 2102, 6366, 19874, 60018]$	$8$	$[8, 192, 1064, 6144, 59048, 536256, 4599176, 41779200, 391199816, 3544297152]$	$2$	$2$	$6$	$6$	$2$	$\Q(\sqrt{-2})$, $\Q(\sqrt{-3})$	$C_2$, $C_2$	1.3.ac $\times$ 1.3.a

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