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
1.4.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
2.4.ai_y	$2$	$\F_{2^{2}}$	$2$						✓	✓		$( 1 - 2 x )^{4}$	$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$	$2$	$0$	$2$	$0$	$2$	$-3$	$[-3, 1, 33, 193, 897, 3841, 15873, 64513, 260097, 1044481]$	$1$	$[1, 81, 2401, 50625, 923521, 15752961, 260144641, 4228250625, 68184176641, 1095222947841]$	$0$	$0$	$19$	$12$	$1$	$\Q$	Trivial	1.4.ae^2
2.4.ah_u	$2$	$\F_{2^{2}}$	$2$			✓		✓		✓		$( 1 - 2 x )^{2}( 1 - 3 x + 4 x^{2} )$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$1$	$1$	$-2$	$[-2, 8, 58, 256, 1018, 4016, 16042, 64576, 260122, 1045328]$	$2$	$[2, 144, 3626, 64800, 1039802, 16447536, 262870442, 4232347200, 68190704666, 1096109357904]$	$0$	$0$	$10$	$6$	$1$	$\Q$, $\Q(\sqrt{-7})$	Trivial, $C_2$	1.4.ae $\times$ 1.4.ad
2.4.ag_q	$2$	$\F_{2^{2}}$	$2$			✓			✓	✓		$( 1 - 2 x )^{2}( 1 - 2 x + 4 x^{2} )$	$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$	$2$	$0$	$2$	$0$	$2$	$-1$	$[-1, 13, 65, 241, 929, 3841, 16001, 65281, 262145, 1047553]$	$3$	$[3, 189, 3969, 61425, 954273, 15752961, 262209153, 4278189825, 68718952449, 1098437884929]$	$0$	$0$	$19$	$30$	$6$	$\Q$, $\Q(\sqrt{-3})$	Trivial, $C_2$	1.4.ae $\times$ 1.4.ac
2.4.ag_r	$2$	$\F_{2^{2}}$	$2$				✓			✓		$( 1 - 3 x + 4 x^{2} )^{2}$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$-1$	$[-1, 15, 83, 319, 1139, 4191, 16211, 64639, 260147, 1046175]$	$4$	$[4, 256, 5476, 82944, 1170724, 17172736, 265624804, 4236447744, 68197233316, 1096996485376]$	$0$	$0$	$6$	$6$	$1$	$\Q(\sqrt{-7})$	$C_2$	1.4.ad^2
2.4.af_m	$2$	$\F_{2^{2}}$	$2$			✓		✓		✓		$( 1 - 2 x )^{2}( 1 - x + 4 x^{2} )$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$1$	$1$	$0$	$[0, 16, 60, 208, 900, 3976, 16380, 65248, 260340, 1044856]$	$4$	$[4, 216, 3724, 54000, 926404, 16288776, 268322044, 4276044000, 68247629044, 1095615396216]$	$0$	$0$	$10$	$6$	$1$	$\Q$, $\Q(\sqrt{-15})$	Trivial, $C_2$	1.4.ae $\times$ 1.4.ab
2.4.af_n	$2$	$\F_{2^{2}}$	$2$	✓	✓	✓	✓			✓	✓	$1 - 5 x + 13 x^{2} - 20 x^{3} + 16 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$0$	$[0, 18, 75, 258, 1000, 4143, 16800, 66498, 262875, 1047298]$	$5$	$[5, 275, 4820, 66275, 1022625, 16966400, 275308745, 4358310275, 68911390580, 1098171421875]$	$1$	$1$	$2$	$2$	$1$	4.0.1025.1	$D_{4}$	simple
2.4.af_o	$2$	$\F_{2^{2}}$	$2$			✓		✓		✓		$( 1 - 3 x + 4 x^{2} )( 1 - 2 x + 4 x^{2} )$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$1$	$1$	$0$	$[0, 20, 90, 304, 1050, 4016, 16170, 65344, 262170, 1048400]$	$6$	$[6, 336, 5994, 78624, 1074426, 16447536, 264956586, 4282334784, 68725531674, 1099326896976]$	$0$	$0$	$10$	$12$	$3$	$\Q(\sqrt{-7})$, $\Q(\sqrt{-3})$	$C_2$, $C_2$	1.4.ad $\times$ 1.4.ac
2.4.ae_i	$2$	$\F_{2^{2}}$	$2$			✓			✓	✓	✓	$( 1 - 2 x )^{2}( 1 + 4 x^{2} )$	$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$	$2$	$0$	$2$	$0$	$2$	$1$	$[1, 17, 49, 193, 961, 4097, 16129, 64513, 261121, 1048577]$	$5$	$[5, 225, 3185, 50625, 985025, 16769025, 264273665, 4228250625, 68451564545, 1099509530625]$	$1$	$1$	$19$	$20$	$4$	$\Q$, $\Q(\sqrt{-1})$	Trivial, $C_2$	1.4.ae $\times$ 1.4.a
2.4.ae_j	$2$	$\F_{2^{2}}$	$2$	✓	✓	✓	✓			✓	✓	$1 - 4 x + 9 x^{2} - 16 x^{3} + 16 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$1$	$[1, 19, 61, 223, 1021, 4291, 16717, 65599, 262573, 1051939]$	$6$	$[6, 276, 3942, 57408, 1046166, 17589204, 273933078, 4298940672, 68831612838, 1103041860756]$	$2$	$2$	$2$	$2$	$1$	4.0.4752.1	$D_{4}$	simple
2.4.ae_l	$2$	$\F_{2^{2}}$	$2$			✓	✓			✓	✓	$( 1 - 3 x + 4 x^{2} )( 1 - x + 4 x^{2} )$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$1$	$[1, 23, 85, 271, 1021, 4151, 16549, 65311, 260365, 1045703]$	$8$	$[8, 384, 5624, 69120, 1043048, 17006976, 271133528, 4280186880, 68254163144, 1096502123904]$	$2$	$2$	$4$	$2$	$1$	$\Q(\sqrt{-7})$, $\Q(\sqrt{-15})$	$C_2$, $C_2$	1.4.ad $\times$ 1.4.ab
2.4.ae_m	$2$	$\F_{2^{2}}$	$2$						✓	✓	✓	$( 1 - 2 x + 4 x^{2} )^{2}$	$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$	$2$	$0$	$2$	$0$	$2$	$1$	$[1, 25, 97, 289, 961, 3841, 16129, 66049, 264193, 1050625]$	$9$	$[9, 441, 6561, 74529, 986049, 15752961, 264290049, 4328718849, 69257922561, 1101662259201]$	$1$	$1$	$19$	$30$	$3$	$\Q(\sqrt{-3})$	$C_2$	1.4.ac^2
2.4.ad_e	$2$	$\F_{2^{2}}$	$2$			✓		✓		✓		$( 1 - 2 x )^{2}( 1 + x + 4 x^{2} )$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$1$	$1$	$2$	$[2, 16, 38, 208, 1022, 3976, 15878, 65248, 261902, 1044856]$	$6$	$[6, 216, 2646, 54000, 1043646, 16288776, 260225286, 4276044000, 68655500046, 1095615396216]$	$0$	$0$	$10$	$6$	$1$	$\Q$, $\Q(\sqrt{-15})$	Trivial, $C_2$	1.4.ae $\times$ 1.4.b
2.4.ad_f	$2$	$\F_{2^{2}}$	$2$	✓			✓			✓	✓	$1 - 3 x + 5 x^{2} - 12 x^{3} + 16 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$2$	$[2, 18, 47, 226, 1082, 4191, 16298, 65986, 264143, 1049778]$	$7$	$[7, 259, 3136, 58275, 1109227, 17172736, 267001147, 4324529475, 69244764736, 1100771362579]$	$2$	$2$	$6$	$12$	$3$	$\Q(\sqrt{-3}, \sqrt{-7})$	$C_2^2$	simple
2.4.ad_g	$2$	$\F_{2^{2}}$	$2$	✓	✓	✓		✓		✓	✓	$1 - 3 x + 6 x^{2} - 12 x^{3} + 16 x^{4}$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$2$	$0$	$2$	$[2, 20, 56, 240, 1112, 4304, 16424, 65728, 263576, 1048880]$	$8$	$[8, 304, 3656, 61408, 1141688, 17643856, 269053352, 4307525568, 69095573912, 1099831434544]$	$2$	$2$	$2$	$2$	$1$	4.0.3757.1	$D_{4}$	simple
2.4.ad_h	$2$	$\F_{2^{2}}$	$2$	✓		✓	✓			✓	✓	$1 - 3 x + 7 x^{2} - 12 x^{3} + 16 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$2$	$[2, 22, 65, 250, 1112, 4327, 16382, 65074, 262145, 1048102]$	$9$	$[9, 351, 4212, 63531, 1141299, 17740944, 268402689, 4264772499, 68719584492, 1099012730751]$	$4$	$4$	$4$	$12$	$6$	$\Q(\sqrt{-3}, \sqrt{13})$	$C_2^2$	simple
2.4.ad_i	$2$	$\F_{2^{2}}$	$2$			✓		✓		✓	✓	$( 1 - 3 x + 4 x^{2} )( 1 + 4 x^{2} )$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$1$	$1$	$2$	$[2, 24, 74, 256, 1082, 4272, 16298, 64576, 261146, 1049424]$	$10$	$[10, 400, 4810, 64800, 1109050, 17508400, 267042730, 4232347200, 68458118170, 1100399410000]$	$1$	$1$	$10$	$12$	$2$	$\Q(\sqrt{-7})$, $\Q(\sqrt{-1})$	$C_2$, $C_2$	1.4.ad $\times$ 1.4.a
2.4.ad_j	$2$	$\F_{2^{2}}$	$2$	✓	✓	✓	✓			✓	✓	$1 - 3 x + 9 x^{2} - 12 x^{3} + 16 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$2$	$[2, 26, 83, 258, 1022, 4151, 16298, 64738, 261227, 1051106]$	$11$	$[11, 451, 5456, 65395, 1046771, 17000896, 267003671, 4242892995, 68479461776, 1102167168091]$	$2$	$2$	$2$	$2$	$1$	4.0.3625.1	$D_{4}$	simple
2.4.ad_k	$2$	$\F_{2^{2}}$	$2$			✓		✓		✓		$( 1 - 2 x + 4 x^{2} )( 1 - x + 4 x^{2} )$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$1$	$1$	$2$	$[2, 28, 92, 256, 932, 3976, 16508, 66016, 262388, 1047928]$	$12$	$[12, 504, 6156, 65520, 957252, 16288776, 270451452, 4326547680, 68782902516, 1098831485304]$	$0$	$0$	$10$	$12$	$3$	$\Q(\sqrt{-3})$, $\Q(\sqrt{-15})$	$C_2$, $C_2$	1.4.ac $\times$ 1.4.ab
2.4.ac_a	$2$	$\F_{2^{2}}$	$2$			✓			✓	✓		$( 1 - 2 x )^{2}( 1 + 2 x + 4 x^{2} )$	$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$	$2$	$0$	$2$	$0$	$2$	$3$	$[3, 13, 33, 241, 993, 3841, 16257, 65281, 260097, 1047553]$	$7$	$[7, 189, 2401, 61425, 1015777, 15752961, 266338177, 4278189825, 68184176641, 1098437884929]$	$0$	$0$	$19$	$30$	$3$	$\Q$, $\Q(\sqrt{-3})$	Trivial, $C_2$	1.4.ae $\times$ 1.4.c
2.4.ac_b	$2$	$\F_{2^{2}}$	$2$	✓	✓	✓	✓			✓	✓	$1 - 2 x + x^{2} - 8 x^{3} + 16 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$3$	$[3, 15, 39, 255, 1063, 3999, 16551, 66303, 262119, 1050655]$	$8$	$[8, 224, 2696, 65408, 1089288, 16380896, 271193672, 4345445888, 68712350792, 1101692811744]$	$3$	$3$	$2$	$2$	$1$	4.0.1088.2	$D_{4}$	simple
2.4.ac_d	$2$	$\F_{2^{2}}$	$2$	✓	✓	✓	✓			✓	✓	$1 - 2 x + 3 x^{2} - 8 x^{3} + 16 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$3$	$[3, 19, 51, 271, 1143, 4147, 16467, 66271, 261879, 1045699]$	$10$	$[10, 300, 3310, 69600, 1175050, 16980300, 269783230, 4343318400, 68650283770, 1096497907500]$	$4$	$4$	$2$	$2$	$1$	4.0.32832.1	$D_{4}$	simple
2.4.ac_e	$2$	$\F_{2^{2}}$	$2$	✓		✓			✓	✓	✓	$1 - 2 x + 4 x^{2} - 8 x^{3} + 16 x^{4}$	$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$	$2$	$0$	$2$	$0$	$2$	$3$	$[3, 21, 57, 273, 1153, 4161, 16257, 65793, 261633, 1044481]$	$11$	$[11, 341, 3641, 69905, 1185921, 17043521, 266354561, 4311810305, 68585520641, 1095222947841]$	$2$	$2$	$19$	$60$	$5$	$\Q(\zeta_{5})$	$C_4$	simple
2.4.ac_f	$2$	$\F_{2^{2}}$	$2$			✓	✓			✓	✓	$( 1 - 3 x + 4 x^{2} )( 1 + x + 4 x^{2} )$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$3$	$[3, 23, 63, 271, 1143, 4151, 16047, 65311, 261927, 1045703]$	$12$	$[12, 384, 3996, 69120, 1175052, 17006976, 262951932, 4280186880, 68662073196, 1096502123904]$	$4$	$4$	$4$	$2$	$1$	$\Q(\sqrt{-7})$, $\Q(\sqrt{-15})$	$C_2$, $C_2$	1.4.ad $\times$ 1.4.b
2.4.ac_h	$2$	$\F_{2^{2}}$	$2$	✓	✓	✓	✓			✓	✓	$1 - 2 x + 7 x^{2} - 8 x^{3} + 16 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$3$	$[3, 27, 75, 255, 1063, 4107, 15963, 64959, 263415, 1051627]$	$14$	$[14, 476, 4802, 64736, 1089774, 16816604, 261596594, 4257298304, 69053293022, 1102713976476]$	$4$	$4$	$2$	$2$	$1$	4.0.10304.1	$D_{4}$	simple
2.4.ac_i	$2$	$\F_{2^{2}}$	$2$			✓			✓	✓		$( 1 - 2 x + 4 x^{2} )( 1 + 4 x^{2} )$	$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$	$2$	$0$	$2$	$0$	$2$	$3$	$[3, 29, 81, 241, 993, 4097, 16257, 65281, 263169, 1051649]$	$15$	$[15, 525, 5265, 61425, 1017825, 16769025, 266370945, 4278189825, 68988437505, 1102737050625]$	$0$	$0$	$19$	$60$	$12$	$\Q(\sqrt{-3})$, $\Q(\sqrt{-1})$	$C_2$, $C_2$	1.4.ac $\times$ 1.4.a
2.4.ac_j	$2$	$\F_{2^{2}}$	$2$				✓			✓	✓	$( 1 - x + 4 x^{2} )^{2}$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$3$	$[3, 31, 87, 223, 903, 4111, 16887, 65983, 260583, 1045231]$	$16$	$[16, 576, 5776, 57600, 929296, 16842816, 276756496, 4324377600, 68311140496, 1096007985216]$	$1$	$1$	$6$	$6$	$1$	$\Q(\sqrt{-15})$	$C_2$	1.4.ab^2
2.4.ab_ae	$2$	$\F_{2^{2}}$	$2$			✓		✓		✓		$( 1 - 2 x )^{2}( 1 + 3 x + 4 x^{2} )$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$1$	$1$	$4$	$[4, 8, 40, 256, 904, 4016, 16216, 64576, 262120, 1045328]$	$8$	$[8, 144, 2744, 64800, 930248, 16447536, 265676888, 4232347200, 68712424424, 1096109357904]$	$0$	$0$	$10$	$6$	$1$	$\Q$, $\Q(\sqrt{-7})$	Trivial, $C_2$	1.4.ae $\times$ 1.4.d
2.4.ab_ad	$2$	$\F_{2^{2}}$	$2$	✓		✓	✓			✓	✓	$1 - x - 3 x^{2} - 4 x^{3} + 16 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$4$	$[4, 10, 43, 274, 964, 4111, 16636, 65314, 263707, 1050250]$	$9$	$[9, 171, 2916, 69939, 988749, 16842816, 272594709, 4280336739, 69130081476, 1101267647451]$	$1$	$1$	$6$	$12$	$3$	$\Q(\sqrt{-3}, \sqrt{5})$	$C_2^2$	simple
2.4.ab_ac	$2$	$\F_{2^{2}}$	$2$	✓	✓	✓		✓		✓	✓	$1 - x - 2 x^{2} - 4 x^{3} + 16 x^{4}$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$2$	$0$	$4$	$[4, 12, 46, 288, 1014, 4152, 16846, 65568, 263494, 1050952]$	$10$	$[10, 200, 3070, 74000, 1038550, 17007800, 276074830, 4296884000, 69074008390, 1102005405000]$	$2$	$2$	$2$	$2$	$1$	4.0.8405.1	$D_{4}$	simple
2.4.ab_ab	$2$	$\F_{2^{2}}$	$2$	✓	✓	✓	✓			✓	✓	$1 - x - x^{2} - 4 x^{3} + 16 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$4$	$[4, 14, 49, 298, 1054, 4151, 16888, 65554, 262417, 1050014]$	$11$	$[11, 231, 3212, 76923, 1079441, 16997904, 276773123, 4296072627, 68791272308, 1101020105031]$	$2$	$2$	$2$	$2$	$1$	4.0.45177.1	$D_{4}$	simple
2.4.ab_a	$2$	$\F_{2^{2}}$	$2$	✓	✓	✓		✓		✓	✓	$1 - x - 4 x^{3} + 16 x^{4}$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$2$	$0$	$4$	$[4, 16, 52, 304, 1084, 4120, 16804, 65440, 261196, 1048936]$	$12$	$[12, 264, 3348, 78672, 1110972, 16867224, 275376036, 4288725408, 68471444556, 1099886721384]$	$2$	$2$	$2$	$2$	$1$	4.0.13068.1	$D_{4}$	simple
2.4.ab_b	$2$	$\F_{2^{2}}$	$2$	✓	✓	✓	✓			✓	✓	$1 - x + x^{2} - 4 x^{3} + 16 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$4$	$[4, 18, 55, 306, 1104, 4071, 16636, 65346, 260335, 1048378]$	$13$	$[13, 299, 3484, 79235, 1132573, 16667456, 272590513, 4282572515, 68246337484, 1099301402979]$	$2$	$2$	$2$	$2$	$1$	4.0.54665.1	$D_{4}$	simple
2.4.ab_c	$2$	$\F_{2^{2}}$	$2$			✓		✓		✓	✓	$( 1 - 3 x + 4 x^{2} )( 1 + 2 x + 4 x^{2} )$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$1$	$1$	$4$	$[4, 20, 58, 304, 1114, 4016, 16426, 65344, 260122, 1048400]$	$14$	$[14, 336, 3626, 78624, 1143674, 16447536, 269128874, 4282334784, 68190704666, 1099326896976]$	$2$	$2$	$10$	$12$	$3$	$\Q(\sqrt{-7})$, $\Q(\sqrt{-3})$	$C_2$, $C_2$	1.4.ad $\times$ 1.4.c
2.4.ab_d	$2$	$\F_{2^{2}}$	$2$	✓	✓	✓	✓			✓	✓	$1 - x + 3 x^{2} - 4 x^{3} + 16 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$4$	$[4, 22, 61, 298, 1114, 3967, 16216, 65458, 260629, 1048702]$	$15$	$[15, 375, 3780, 76875, 1143825, 16254000, 265693695, 4289701875, 68323148460, 1099644759375]$	$4$	$4$	$2$	$2$	$1$	4.0.46305.1	$D_{4}$	simple
2.4.ab_e	$2$	$\F_{2^{2}}$	$2$	✓	✓			✓		✓	✓	$1 - x + 4 x^{2} - 4 x^{3} + 16 x^{4}$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$2$	$0$	$4$	$[4, 24, 64, 288, 1104, 3936, 16048, 65664, 261712, 1048864]$	$16$	$[16, 416, 3952, 74048, 1132816, 16132064, 262967728, 4303225472, 68606478928, 1099812538656]$	$1$	$1$	$2$	$2$	$1$	4.0.2312.1	$D_{4}$	simple
2.4.ab_f	$2$	$\F_{2^{2}}$	$2$	✓	✓	✓	✓			✓	✓	$1 - x + 5 x^{2} - 4 x^{3} + 16 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$4$	$[4, 26, 67, 274, 1084, 3935, 15964, 65890, 263011, 1048586]$	$17$	$[17, 459, 4148, 70227, 1110797, 16127424, 261613901, 4318188003, 68947130996, 1099519078059]$	$3$	$3$	$2$	$2$	$1$	4.0.2873.1	$D_{4}$	simple
2.4.ab_g	$2$	$\F_{2^{2}}$	$2$			✓		✓		✓	✓	$( 1 - 2 x + 4 x^{2} )( 1 + x + 4 x^{2} )$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$1$	$1$	$4$	$[4, 28, 70, 256, 1054, 3976, 16006, 66016, 263950, 1047928]$	$18$	$[18, 504, 4374, 65520, 1078398, 16288776, 262290438, 4326547680, 69193972494, 1098831485304]$	$2$	$2$	$10$	$12$	$3$	$\Q(\sqrt{-3})$, $\Q(\sqrt{-15})$	$C_2$, $C_2$	1.4.ac $\times$ 1.4.b
2.4.ab_h	$2$	$\F_{2^{2}}$	$2$	✓	✓	✓	✓			✓	✓	$1 - x + 7 x^{2} - 4 x^{3} + 16 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$4$	$[4, 30, 73, 234, 1014, 4071, 16216, 65874, 263737, 1047550]$	$19$	$[19, 551, 4636, 60059, 1036849, 16671056, 265686139, 4317100979, 69137924356, 1098436793751]$	$2$	$2$	$2$	$2$	$1$	4.0.5225.1	$D_{4}$	simple
2.4.ab_i	$2$	$\F_{2^{2}}$	$2$			✓		✓		✓		$( 1 - x + 4 x^{2} )( 1 + 4 x^{2} )$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$1$	$1$	$4$	$[4, 32, 76, 208, 964, 4232, 16636, 65248, 261364, 1048952]$	$20$	$[20, 600, 4940, 54000, 988100, 17339400, 272580860, 4276044000, 68515265780, 1099903515000]$	$0$	$0$	$10$	$12$	$2$	$\Q(\sqrt{-15})$, $\Q(\sqrt{-1})$	$C_2$, $C_2$	1.4.ab $\times$ 1.4.a
2.4.a_ai	$2$	$\F_{2^{2}}$	$2$			✓			✓	✓		$( 1 - 2 x )^{2}( 1 + 2 x )^{2}$	$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$	$2$	$0$	$2$	$0$	$2$	$5$	$[5, 1, 65, 193, 1025, 3841, 16385, 64513, 262145, 1044481]$	$9$	$[9, 81, 3969, 50625, 1046529, 15752961, 268402689, 4228250625, 68718952449, 1095222947841]$	$0$	$0$	$19$	$12$	$2$	$\Q$, $\Q$	Trivial, Trivial	1.4.ae $\times$ 1.4.e
2.4.a_ah	$2$	$\F_{2^{2}}$	$2$	✓		✓	✓			✓		$1 - 7 x^{2} + 16 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$5$	$[5, 3, 65, 223, 1025, 4083, 16385, 65983, 262145, 1051923]$	$10$	$[10, 100, 4090, 57600, 1050250, 16728100, 268465690, 4324377600, 68719562410, 1103025062500]$	$0$	$0$	$6$	$12$	$2$	$\Q(i, \sqrt{15})$	$C_2^2$	simple

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