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Results (1-50 of 1345256 matches)

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Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
2.2.ad_f $2$ $\F_{2}$ $1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{5})\) $C_2^2$ simple
2.2.ac_d $2$ $\F_{2}$ $1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4}$ $2$ 4.0.1088.2 $D_{4}$ simple
2.2.ac_f $2$ $\F_{2}$ $( 1 - x + 2 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-7}) \) $C_2$ 1.2.ab 2
2.2.ab_ab $2$ $\F_{2}$ $1 - x - x^{2} - 2 x^{3} + 4 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{-7})\) $C_2^2$ simple
2.2.ab_b $2$ $\F_{2}$ $1 - x + x^{2} - 2 x^{3} + 4 x^{4}$ $2$ 4.0.2873.1 $D_{4}$ simple
2.2.ab_d $2$ $\F_{2}$ $1 - x + 3 x^{2} - 2 x^{3} + 4 x^{4}$ $2$ 4.0.1025.1 $D_{4}$ simple
2.2.a_ad $2$ $\F_{2}$ $1 - 3 x^{2} + 4 x^{4}$ $2$ \(\Q(i, \sqrt{7})\) $C_2^2$ simple
2.2.a_ab $2$ $\F_{2}$ $1 - x^{2} + 4 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{5})\) $C_2^2$ simple
2.2.a_b $2$ $\F_{2}$ $1 + x^{2} + 4 x^{4}$ $2$ \(\Q(\sqrt{3}, \sqrt{-5})\) $C_2^2$ simple
2.2.a_d $2$ $\F_{2}$ $( 1 - x + 2 x^{2} )( 1 + x + 2 x^{2} )$ $2$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-7}) \) $C_2$, $C_2$ 1.2.ab $\times$ 1.2.b
2.2.b_ab $2$ $\F_{2}$ $1 + x - x^{2} + 2 x^{3} + 4 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{-7})\) $C_2^2$ simple
2.2.b_b $2$ $\F_{2}$ $1 + x + x^{2} + 2 x^{3} + 4 x^{4}$ $2$ 4.0.2873.1 $D_{4}$ simple
2.2.b_d $2$ $\F_{2}$ $1 + x + 3 x^{2} + 2 x^{3} + 4 x^{4}$ $2$ 4.0.1025.1 $D_{4}$ simple
2.2.c_d $2$ $\F_{2}$ $1 + 2 x + 3 x^{2} + 4 x^{3} + 4 x^{4}$ $2$ 4.0.1088.2 $D_{4}$ simple
2.2.c_f $2$ $\F_{2}$ $( 1 + x + 2 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-7}) \) $C_2$ 1.2.b 2
2.2.d_f $2$ $\F_{2}$ $1 + 3 x + 5 x^{2} + 6 x^{3} + 4 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{5})\) $C_2^2$ simple
2.3.ae_i $2$ $\F_{3}$ $1 - 4 x + 8 x^{2} - 12 x^{3} + 9 x^{4}$ $2$ \(\Q(\zeta_{8})\) $C_2^2$ simple
2.3.ae_k $2$ $\F_{3}$ $( 1 - 2 x + 3 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-2}) \) $C_2$ 1.3.ac 2
2.3.ad_f $2$ $\F_{3}$ $1 - 3 x + 5 x^{2} - 9 x^{3} + 9 x^{4}$ $2$ 4.0.2197.1 $C_4$ simple
2.3.ad_h $2$ $\F_{3}$ $1 - 3 x + 7 x^{2} - 9 x^{3} + 9 x^{4}$ $2$ 4.0.1525.1 $D_{4}$ simple
2.3.ad_i $2$ $\F_{3}$ $( 1 - 2 x + 3 x^{2} )( 1 - x + 3 x^{2} )$ $2$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-11}) \) $C_2$, $C_2$ 1.3.ac $\times$ 1.3.ab
2.3.ac_b $2$ $\F_{3}$ $1 - 2 x + x^{2} - 6 x^{3} + 9 x^{4}$ $2$ \(\Q(\sqrt{-2}, \sqrt{-3})\) $C_2^2$ simple
2.3.ac_c $2$ $\F_{3}$ $1 - 2 x + 2 x^{2} - 6 x^{3} + 9 x^{4}$ $2$ \(\Q(i, \sqrt{5})\) $C_2^2$ simple
2.3.ac_e $2$ $\F_{3}$ $1 - 2 x + 4 x^{2} - 6 x^{3} + 9 x^{4}$ $2$ 4.0.7488.1 $D_{4}$ simple
2.3.ac_f $2$ $\F_{3}$ $1 - 2 x + 5 x^{2} - 6 x^{3} + 9 x^{4}$ $2$ 4.0.4672.2 $D_{4}$ simple
2.3.ac_h $2$ $\F_{3}$ $( 1 - x + 3 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-11}) \) $C_2$ 1.3.ab 2
2.3.ab_ac $2$ $\F_{3}$ $1 - x - 2 x^{2} - 3 x^{3} + 9 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{-11})\) $C_2^2$ simple
2.3.ab_ab $2$ $\F_{3}$ $1 - x - x^{2} - 3 x^{3} + 9 x^{4}$ $2$ 4.0.10933.1 $D_{4}$ simple
2.3.ab_b $2$ $\F_{3}$ $1 - x + x^{2} - 3 x^{3} + 9 x^{4}$ $2$ 4.0.16317.1 $D_{4}$ simple
2.3.ab_c $2$ $\F_{3}$ $1 - x + 2 x^{2} - 3 x^{3} + 9 x^{4}$ $2$ 4.0.3757.1 $D_{4}$ simple
2.3.ab_e $2$ $\F_{3}$ $( 1 - 2 x + 3 x^{2} )( 1 + x + 3 x^{2} )$ $2$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-11}) \) $C_2$, $C_2$ 1.3.ac $\times$ 1.3.b
2.3.ab_f $2$ $\F_{3}$ $1 - x + 5 x^{2} - 3 x^{3} + 9 x^{4}$ $2$ 4.0.2725.1 $D_{4}$ simple
2.3.a_af $2$ $\F_{3}$ $1 - 5 x^{2} + 9 x^{4}$ $2$ \(\Q(i, \sqrt{11})\) $C_2^2$ simple
2.3.a_ae $2$ $\F_{3}$ $1 - 4 x^{2} + 9 x^{4}$ $2$ \(\Q(\sqrt{-2}, \sqrt{-5})\) $C_2^2$ simple
2.3.a_ac $2$ $\F_{3}$ $1 - 2 x^{2} + 9 x^{4}$ $2$ \(\Q(\zeta_{8})\) $C_2^2$ simple
2.3.a_ab $2$ $\F_{3}$ $1 - x^{2} + 9 x^{4}$ $2$ \(\Q(\sqrt{-5}, \sqrt{7})\) $C_2^2$ simple
2.3.a_b $2$ $\F_{3}$ $1 + x^{2} + 9 x^{4}$ $2$ \(\Q(\sqrt{5}, \sqrt{-7})\) $C_2^2$ simple
2.3.a_c $2$ $\F_{3}$ $( 1 - 2 x + 3 x^{2} )( 1 + 2 x + 3 x^{2} )$ $2$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-2}) \) $C_2$, $C_2$ 1.3.ac $\times$ 1.3.c
2.3.a_e $2$ $\F_{3}$ $1 + 4 x^{2} + 9 x^{4}$ $2$ \(\Q(\sqrt{2}, \sqrt{-5})\) $C_2^2$ simple
2.3.a_f $2$ $\F_{3}$ $( 1 - x + 3 x^{2} )( 1 + x + 3 x^{2} )$ $2$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-11}) \) $C_2$, $C_2$ 1.3.ab $\times$ 1.3.b
2.3.b_ac $2$ $\F_{3}$ $1 + x - 2 x^{2} + 3 x^{3} + 9 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{-11})\) $C_2^2$ simple
2.3.b_ab $2$ $\F_{3}$ $1 + x - x^{2} + 3 x^{3} + 9 x^{4}$ $2$ 4.0.10933.1 $D_{4}$ simple
2.3.b_b $2$ $\F_{3}$ $1 + x + x^{2} + 3 x^{3} + 9 x^{4}$ $2$ 4.0.16317.1 $D_{4}$ simple
2.3.b_c $2$ $\F_{3}$ $1 + x + 2 x^{2} + 3 x^{3} + 9 x^{4}$ $2$ 4.0.3757.1 $D_{4}$ simple
2.3.b_e $2$ $\F_{3}$ $( 1 - x + 3 x^{2} )( 1 + 2 x + 3 x^{2} )$ $2$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-2}) \) $C_2$, $C_2$ 1.3.ab $\times$ 1.3.c
2.3.b_f $2$ $\F_{3}$ $1 + x + 5 x^{2} + 3 x^{3} + 9 x^{4}$ $2$ 4.0.2725.1 $D_{4}$ simple
2.3.c_b $2$ $\F_{3}$ $1 + 2 x + x^{2} + 6 x^{3} + 9 x^{4}$ $2$ \(\Q(\sqrt{-2}, \sqrt{-3})\) $C_2^2$ simple
2.3.c_c $2$ $\F_{3}$ $1 + 2 x + 2 x^{2} + 6 x^{3} + 9 x^{4}$ $2$ \(\Q(i, \sqrt{5})\) $C_2^2$ simple
2.3.c_e $2$ $\F_{3}$ $1 + 2 x + 4 x^{2} + 6 x^{3} + 9 x^{4}$ $2$ 4.0.7488.1 $D_{4}$ simple
2.3.c_f $2$ $\F_{3}$ $1 + 2 x + 5 x^{2} + 6 x^{3} + 9 x^{4}$ $2$ 4.0.4672.2 $D_{4}$ simple
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