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.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
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
2.3.ac_h	$2$	$\F_{3}$	$3$			✓	✓			✓	✓	$( 1 - x + 3 x^{2} )^{2}$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$2$	$[2, 20, 44, 68, 182, 710, 2354, 6788, 19412, 58100]$	$9$	$[9, 225, 1296, 5625, 45369, 518400, 5157441, 44555625, 382124304, 3431030625]$	$1$	$1$	$6$	$6$	$1$	$\Q(\sqrt{-11})$	$C_2$	1.3.ab^2
2.3.ab_ac	$2$	$\F_{3}$	$3$	✓		✓	✓			✓	✓	$1 - x - 2 x^{2} - 3 x^{3} + 9 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$3$	$[3, 5, 12, 89, 213, 710, 2271, 6449, 19956, 59525]$	$4$	$[4, 48, 400, 7104, 52204, 518400, 4969276, 42311424, 392832400, 3514999728]$	$1$	$1$	$6$	$12$	$3$	$\Q(\sqrt{-3}, \sqrt{-11})$	$C_2^2$	simple
2.3.ab_ab	$2$	$\F_{3}$	$3$	✓	✓	✓	✓			✓	✓	$1 - x - x^{2} - 3 x^{3} + 9 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$3$	$[3, 7, 15, 99, 248, 739, 2369, 6611, 19905, 59782]$	$5$	$[5, 65, 455, 8125, 60400, 538265, 5191555, 43363125, 391801865, 3530259200]$	$1$	$1$	$2$	$2$	$1$	4.0.10933.1	$D_{4}$	simple
2.3.ab_a	$2$	$\F_{3}$	$3$			✓		✓		✓	✓	$( 1 - 3 x + 3 x^{2} )( 1 + 2 x + 3 x^{2} )$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$1$	$1$	$3$	$[3, 9, 18, 105, 273, 738, 2355, 6609, 19494, 59289]$	$6$	$[6, 84, 504, 8736, 66666, 536256, 5159706, 43365504, 383719896, 3500898324]$	$1$	$1$	$6$	$6$	$6$	$\Q(\sqrt{-3})$, $\Q(\sqrt{-2})$	$C_2$, $C_2$	1.3.ad $\times$ 1.3.c
2.3.ab_b	$2$	$\F_{3}$	$3$	✓	✓	✓	✓			✓	✓	$1 - x + x^{2} - 3 x^{3} + 9 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$3$	$[3, 11, 21, 107, 288, 719, 2271, 6563, 19173, 58886]$	$7$	$[7, 105, 553, 8925, 70672, 522585, 4970413, 43063125, 377466187, 3477062400]$	$2$	$2$	$2$	$2$	$1$	4.0.16317.1	$D_{4}$	simple
2.3.ab_c	$2$	$\F_{3}$	$3$	✓	✓	✓	✓			✓	✓	$1 - x + 2 x^{2} - 3 x^{3} + 9 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$3$	$[3, 13, 24, 105, 293, 694, 2159, 6545, 19176, 58813]$	$8$	$[8, 128, 608, 8704, 72088, 505856, 4723384, 42928128, 377524832, 3472911488]$	$2$	$2$	$2$	$2$	$1$	4.0.3757.1	$D_{4}$	simple
2.3.ab_d	$2$	$\F_{3}$	$3$	✓	✓	✓		✓		✓	✓	$1 - x + 3 x^{2} - 3 x^{3} + 9 x^{4}$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$2$	$0$	$3$	$[3, 15, 27, 99, 288, 675, 2061, 6579, 19521, 58950]$	$9$	$[9, 153, 675, 8109, 70704, 493425, 4512951, 43147989, 384257925, 3480899328]$	$2$	$2$	$2$	$2$	$1$	4.0.11661.1	$D_{4}$	simple
2.3.ab_e	$2$	$\F_{3}$	$3$			✓	✓			✓	✓	$( 1 - 2 x + 3 x^{2} )( 1 + x + 3 x^{2} )$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$3$	$[3, 17, 30, 89, 273, 674, 2019, 6641, 20010, 59057]$	$10$	$[10, 180, 760, 7200, 66550, 492480, 4424710, 43574400, 393902680, 3487086900]$	$1$	$1$	$4$	$2$	$1$	$\Q(\sqrt{-2})$, $\Q(\sqrt{-11})$	$C_2$, $C_2$	1.3.ac $\times$ 1.3.b
2.3.ab_f	$2$	$\F_{3}$	$3$	✓	✓	✓	✓			✓	✓	$1 - x + 5 x^{2} - 3 x^{3} + 9 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$3$	$[3, 19, 33, 75, 248, 703, 2075, 6659, 20229, 59014]$	$11$	$[11, 209, 869, 6061, 60016, 511841, 4542241, 43693749, 398261831, 3484769024]$	$1$	$1$	$2$	$2$	$1$	4.0.2725.1	$D_{4}$	simple
2.3.ab_g	$2$	$\F_{3}$	$3$			✓		✓		✓		$( 1 - x + 3 x^{2} )( 1 + 3 x^{2} )$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$1$	$1$	$3$	$[3, 21, 36, 57, 213, 774, 2271, 6513, 19548, 59061]$	$12$	$[12, 240, 1008, 4800, 51972, 564480, 4968948, 42720000, 384782832, 3487321200]$	$0$	$0$	$6$	$6$	$2$	$\Q(\sqrt{-11})$, $\Q(\sqrt{-3})$	$C_2$, $C_2$	1.3.ab $\times$ 1.3.a
2.3.a_ag	$2$	$\F_{3}$	$3$	✓		✓			✓	✓		$( 1 - 3 x^{2} )^{2}$	$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$	$2$	$0$	$2$	$0$	$2$	$4$	$[4, -2, 28, 46, 244, 622, 2188, 6238, 19684, 58078]$	$4$	$[4, 16, 676, 4096, 58564, 456976, 4778596, 40960000, 387381124, 3429742096]$	$0$	$0$	$9$	$12$	$2$	$\Q(\sqrt{3})$	$C_2$	simple
2.3.a_af	$2$	$\F_{3}$	$3$	✓		✓	✓			✓		$1 - 5 x^{2} + 9 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$4$	$[4, 0, 28, 68, 244, 750, 2188, 6788, 19684, 60000]$	$5$	$[5, 25, 740, 5625, 59525, 547600, 4785485, 44555625, 387399620, 3543225625]$	$0$	$0$	$6$	$12$	$2$	$\Q(i, \sqrt{11})$	$C_2^2$	simple
2.3.a_ae	$2$	$\F_{3}$	$3$	✓		✓	✓			✓		$1 - 4 x^{2} + 9 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$4$	$[4, 2, 28, 86, 244, 818, 2188, 6878, 19684, 59522]$	$6$	$[6, 36, 774, 7056, 59286, 599076, 4778934, 45158400, 387409446, 3514829796]$	$0$	$0$	$4$	$8$	$2$	$\Q(\sqrt{-2}, \sqrt{-5})$	$C_2^2$	simple
2.3.a_ad	$2$	$\F_{3}$	$3$			✓			✓	✓		$( 1 - 3 x + 3 x^{2} )( 1 + 3 x + 3 x^{2} )$	$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$	$2$	$0$	$2$	$0$	$2$	$4$	$[4, 4, 28, 100, 244, 838, 2188, 6724, 19684, 58564]$	$7$	$[7, 49, 784, 8281, 58807, 614656, 4780783, 44129449, 387459856, 3458263249]$	$0$	$0$	$9$	$24$	$6$	$\Q(\sqrt{-3})$, $\Q(\sqrt{-3})$	$C_2$, $C_2$	1.3.ad $\times$ 1.3.d
2.3.a_ac	$2$	$\F_{3}$	$3$	✓		✓	✓			✓	✓	$1 - 2 x^{2} + 9 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$4$	$[4, 6, 28, 110, 244, 822, 2188, 6494, 19684, 58086]$	$8$	$[8, 64, 776, 9216, 58568, 602176, 4785992, 42614784, 387417224, 3430210624]$	$2$	$2$	$8$	$12$	$2$	$\Q(\zeta_{8})$	$C_2^2$	simple
2.3.a_ab	$2$	$\F_{3}$	$3$	✓		✓	✓			✓	✓	$1 - x^{2} + 9 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$4$	$[4, 8, 28, 116, 244, 782, 2188, 6308, 19684, 58328]$	$9$	$[9, 81, 756, 9801, 58689, 571536, 4787001, 41409225, 387381204, 3444398721]$	$1$	$1$	$2$	$4$	$2$	$\Q(\sqrt{-5}, \sqrt{7})$	$C_2^2$	simple
2.3.a_a	$2$	$\F_{3}$	$3$	✓		✓			✓	✓	✓	$1 + 9 x^{4}$	$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$	$2$	$0$	$2$	$0$	$2$	$4$	$[4, 10, 28, 118, 244, 730, 2188, 6238, 19684, 59050]$	$10$	$[10, 100, 730, 10000, 59050, 532900, 4782970, 40960000, 387420490, 3486902500]$	$2$	$2$	$9$	$24$	$4$	$\Q(i, \sqrt{6})$	$C_2^2$	simple
2.3.a_b	$2$	$\F_{3}$	$3$	✓		✓	✓			✓	✓	$1 + x^{2} + 9 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$4$	$[4, 12, 28, 116, 244, 678, 2188, 6308, 19684, 59772]$	$11$	$[11, 121, 704, 9801, 59411, 495616, 4778939, 41409225, 387459776, 3529666921]$	$1$	$1$	$2$	$4$	$2$	$\Q(\sqrt{5}, \sqrt{-7})$	$C_2^2$	simple
2.3.a_c	$2$	$\F_{3}$	$3$			✓	✓			✓	✓	$( 1 - 2 x + 3 x^{2} )( 1 + 2 x + 3 x^{2} )$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$4$	$[4, 14, 28, 110, 244, 638, 2188, 6494, 19684, 60014]$	$12$	$[12, 144, 684, 9216, 59532, 467856, 4779948, 42614784, 387423756, 3544059024]$	$2$	$2$	$8$	$8$	$2$	$\Q(\sqrt{-2})$, $\Q(\sqrt{-2})$	$C_2$, $C_2$	1.3.ac $\times$ 1.3.c
2.3.a_d	$2$	$\F_{3}$	$3$	✓		✓			✓	✓	✓	$1 + 3 x^{2} + 9 x^{4}$	$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$	$2$	$0$	$2$	$0$	$2$	$4$	$[4, 16, 28, 100, 244, 622, 2188, 6724, 19684, 59536]$	$13$	$[13, 169, 676, 8281, 59293, 456976, 4785157, 44129449, 387381124, 3515659849]$	$2$	$2$	$9$	$24$	$6$	$\Q(\zeta_{12})$	$C_2^2$	simple
2.3.a_e	$2$	$\F_{3}$	$3$	✓		✓	✓			✓	✓	$1 + 4 x^{2} + 9 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$4$	$[4, 18, 28, 86, 244, 642, 2188, 6878, 19684, 58578]$	$14$	$[14, 196, 686, 7056, 58814, 470596, 4787006, 45158400, 387431534, 3459086596]$	$1$	$1$	$4$	$8$	$2$	$\Q(\sqrt{2}, \sqrt{-5})$	$C_2^2$	simple
2.3.a_f	$2$	$\F_{3}$	$3$			✓	✓			✓	✓	$( 1 - x + 3 x^{2} )( 1 + x + 3 x^{2} )$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$4$	$[4, 20, 28, 68, 244, 710, 2188, 6788, 19684, 58100]$	$15$	$[15, 225, 720, 5625, 58575, 518400, 4780455, 44555625, 387441360, 3431030625]$	$2$	$2$	$6$	$6$	$2$	$\Q(\sqrt{-11})$, $\Q(\sqrt{-11})$	$C_2$, $C_2$	1.3.ab $\times$ 1.3.b
2.3.a_g	$2$	$\F_{3}$	$3$			✓			✓	✓		$( 1 + 3 x^{2} )^{2}$	$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$	$2$	$0$	$2$	$0$	$2$	$4$	$[4, 22, 28, 46, 244, 838, 2188, 6238, 19684, 60022]$	$16$	$[16, 256, 784, 4096, 59536, 614656, 4787344, 40960000, 387459856, 3544535296]$	$0$	$0$	$9$	$12$	$2$	$\Q(\sqrt{-3})$	$C_2$	1.3.a^2
2.3.b_ac	$2$	$\F_{3}$	$3$	✓		✓	✓			✓	✓	$1 + x - 2 x^{2} + 3 x^{3} + 9 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$1$	$1$	$5$	$[5, 5, 44, 89, 275, 710, 2105, 6449, 19412, 59525]$	$12$	$[12, 48, 1296, 7104, 67332, 518400, 4606068, 42311424, 382124304, 3514999728]$	$1$	$1$	$6$	$12$	$3$	$\Q(\sqrt{-3}, \sqrt{-11})$	$C_2^2$	simple
2.3.b_ab	$2$	$\F_{3}$	$3$	✓	✓	✓	✓			✓	✓	$1 + x - x^{2} + 3 x^{3} + 9 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$5$	$[5, 7, 41, 99, 240, 739, 2007, 6611, 19463, 59782]$	$13$	$[13, 65, 1183, 8125, 58448, 538265, 4399499, 43363125, 383101537, 3530259200]$	$1$	$1$	$2$	$2$	$1$	4.0.10933.1	$D_{4}$	simple
2.3.b_a	$2$	$\F_{3}$	$3$			✓		✓		✓	✓	$( 1 - 2 x + 3 x^{2} )( 1 + 3 x + 3 x^{2} )$	$[0,\frac{1}{2},\frac{1}{2},1]$	$1$	$1$	$1$	$1$	$1$	$5$	$[5, 9, 38, 105, 215, 738, 2021, 6609, 19874, 59289]$	$14$	$[14, 84, 1064, 8736, 52514, 536256, 4428914, 43365504, 391199816, 3500898324]$	$1$	$1$	$6$	$6$	$6$	$\Q(\sqrt{-2})$, $\Q(\sqrt{-3})$	$C_2$, $C_2$	1.3.ac $\times$ 1.3.d
2.3.b_b	$2$	$\F_{3}$	$3$	✓	✓	✓	✓			✓	✓	$1 + x + x^{2} + 3 x^{3} + 9 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$5$	$[5, 11, 35, 107, 200, 719, 2105, 6563, 20195, 58886]$	$15$	$[15, 105, 945, 8925, 49200, 522585, 4607205, 43063125, 397583235, 3477062400]$	$2$	$2$	$2$	$2$	$1$	4.0.16317.1	$D_{4}$	simple
2.3.b_c	$2$	$\F_{3}$	$3$	✓	✓	✓	✓			✓	✓	$1 + x + 2 x^{2} + 3 x^{3} + 9 x^{4}$	$[0,0,1,1]$	$0$	$2$	$0$	$2$	$0$	$5$	$[5, 13, 32, 105, 195, 694, 2217, 6545, 20192, 58813]$	$16$	$[16, 128, 832, 8704, 48176, 505856, 4850288, 42928128, 397523776, 3472911488]$	$2$	$2$	$2$	$2$	$1$	4.0.3757.1	$D_{4}$	simple

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