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Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
2.2.ae_i $2$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )^{2}$ $0$ \(\Q(\sqrt{-1}) \) $C_2$ 1.2.ac 2
2.2.ac_c $2$ $\F_{2}$ $1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4}$ $0$ \(\Q(\zeta_{12})\) $C_2^2$ simple
2.2.ac_e $2$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} )$ $0$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) $C_2$, $C_2$ 1.2.ac $\times$ 1.2.a
2.2.a_ae $2$ $\F_{2}$ $( 1 - 2 x^{2} )^{2}$ $0$ \(\Q(\sqrt{2}) \) $C_2$ simple
2.2.a_ac $2$ $\F_{2}$ $1 - 2 x^{2} + 4 x^{4}$ $0$ \(\Q(\sqrt{-2}, \sqrt{-3})\) $C_2^2$ simple
2.2.a_a $2$ $\F_{2}$ $( 1 - 2 x + 2 x^{2} )( 1 + 2 x + 2 x^{2} )$ $0$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.2.ac $\times$ 1.2.c
2.2.a_c $2$ $\F_{2}$ $1 + 2 x^{2} + 4 x^{4}$ $0$ \(\Q(\sqrt{2}, \sqrt{-3})\) $C_2^2$ simple
2.2.a_e $2$ $\F_{2}$ $( 1 + 2 x^{2} )^{2}$ $0$ \(\Q(\sqrt{-2}) \) $C_2$ 1.2.a 2
2.2.c_c $2$ $\F_{2}$ $1 + 2 x + 2 x^{2} + 4 x^{3} + 4 x^{4}$ $0$ \(\Q(\zeta_{12})\) $C_2^2$ simple
2.2.c_e $2$ $\F_{2}$ $( 1 + 2 x^{2} )( 1 + 2 x + 2 x^{2} )$ $0$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.2.a $\times$ 1.2.c
2.2.e_i $2$ $\F_{2}$ $( 1 + 2 x + 2 x^{2} )^{2}$ $0$ \(\Q(\sqrt{-1}) \) $C_2$ 1.2.c 2
2.3.ag_p $2$ $\F_{3}$ $( 1 - 3 x + 3 x^{2} )^{2}$ $0$ \(\Q(\sqrt{-3}) \) $C_2$ 1.3.ad 2
2.3.ad_g $2$ $\F_{3}$ $( 1 - 3 x + 3 x^{2} )( 1 + 3 x^{2} )$ $0$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.3.ad $\times$ 1.3.a
2.3.a_ag $2$ $\F_{3}$ $( 1 - 3 x^{2} )^{2}$ $0$ \(\Q(\sqrt{3}) \) $C_2$ simple
2.3.a_ad $2$ $\F_{3}$ $( 1 - 3 x + 3 x^{2} )( 1 + 3 x + 3 x^{2} )$ $0$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.3.ad $\times$ 1.3.d
2.3.a_a $2$ $\F_{3}$ $1 + 9 x^{4}$ $0$ \(\Q(i, \sqrt{6})\) $C_2^2$ simple
2.3.a_d $2$ $\F_{3}$ $1 + 3 x^{2} + 9 x^{4}$ $0$ \(\Q(\zeta_{12})\) $C_2^2$ simple
2.3.a_g $2$ $\F_{3}$ $( 1 + 3 x^{2} )^{2}$ $0$ \(\Q(\sqrt{-3}) \) $C_2$ 1.3.a 2
2.3.d_g $2$ $\F_{3}$ $( 1 + 3 x^{2} )( 1 + 3 x + 3 x^{2} )$ $0$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.3.a $\times$ 1.3.d
2.3.g_p $2$ $\F_{3}$ $( 1 + 3 x + 3 x^{2} )^{2}$ $0$ \(\Q(\sqrt{-3}) \) $C_2$ 1.3.d 2
2.4.ai_y $2$ $\F_{2^{2}}$ $( 1 - 2 x )^{4}$ $0$ \(\Q\) Trivial 1.4.ae 2
2.4.ag_q $2$ $\F_{2^{2}}$ $( 1 - 2 x )^{2}( 1 - 2 x + 4 x^{2} )$ $0$ \(\Q\), \(\Q(\sqrt{-3}) \) Trivial, $C_2$ 1.4.ae $\times$ 1.4.ac
2.4.ae_i $2$ $\F_{2^{2}}$ $( 1 - 2 x )^{2}( 1 + 4 x^{2} )$ $0$ \(\Q\), \(\Q(\sqrt{-1}) \) Trivial, $C_2$ 1.4.ae $\times$ 1.4.a
2.4.ae_m $2$ $\F_{2^{2}}$ $( 1 - 2 x + 4 x^{2} )^{2}$ $0$ \(\Q(\sqrt{-3}) \) $C_2$ 1.4.ac 2
2.4.ac_a $2$ $\F_{2^{2}}$ $( 1 - 2 x )^{2}( 1 + 2 x + 4 x^{2} )$ $0$ \(\Q\), \(\Q(\sqrt{-3}) \) Trivial, $C_2$ 1.4.ae $\times$ 1.4.c
2.4.ac_e $2$ $\F_{2^{2}}$ $1 - 2 x + 4 x^{2} - 8 x^{3} + 16 x^{4}$ $0$ \(\Q(\zeta_{5})\) $C_4$ simple
2.4.ac_i $2$ $\F_{2^{2}}$ $( 1 - 2 x + 4 x^{2} )( 1 + 4 x^{2} )$ $0$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.4.ac $\times$ 1.4.a
2.4.a_ai $2$ $\F_{2^{2}}$ $( 1 - 2 x )^{2}( 1 + 2 x )^{2}$ $0$ \(\Q\), \(\Q\) Trivial, Trivial 1.4.ae $\times$ 1.4.e
2.4.a_ae $2$ $\F_{2^{2}}$ $1 - 4 x^{2} + 16 x^{4}$ $0$ \(\Q(\zeta_{12})\) $C_2^2$ simple
2.4.a_a $2$ $\F_{2^{2}}$ $1 + 16 x^{4}$ $0$ \(\Q(\zeta_{8})\) $C_2^2$ simple
2.4.a_e $2$ $\F_{2^{2}}$ $( 1 - 2 x + 4 x^{2} )( 1 + 2 x + 4 x^{2} )$ $0$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.4.ac $\times$ 1.4.c
2.4.a_i $2$ $\F_{2^{2}}$ $( 1 + 4 x^{2} )^{2}$ $0$ \(\Q(\sqrt{-1}) \) $C_2$ 1.4.a 2
2.4.c_a $2$ $\F_{2^{2}}$ $( 1 + 2 x )^{2}( 1 - 2 x + 4 x^{2} )$ $0$ \(\Q(\sqrt{-3}) \), \(\Q\) $C_2$, Trivial 1.4.ac $\times$ 1.4.e
2.4.c_e $2$ $\F_{2^{2}}$ $1 + 2 x + 4 x^{2} + 8 x^{3} + 16 x^{4}$ $0$ \(\Q(\zeta_{5})\) $C_4$ simple
2.4.c_i $2$ $\F_{2^{2}}$ $( 1 + 4 x^{2} )( 1 + 2 x + 4 x^{2} )$ $0$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.4.a $\times$ 1.4.c
2.4.e_i $2$ $\F_{2^{2}}$ $( 1 + 2 x )^{2}( 1 + 4 x^{2} )$ $0$ \(\Q(\sqrt{-1}) \), \(\Q\) $C_2$, Trivial 1.4.a $\times$ 1.4.e
2.4.e_m $2$ $\F_{2^{2}}$ $( 1 + 2 x + 4 x^{2} )^{2}$ $0$ \(\Q(\sqrt{-3}) \) $C_2$ 1.4.c 2
2.4.g_q $2$ $\F_{2^{2}}$ $( 1 + 2 x )^{2}( 1 + 2 x + 4 x^{2} )$ $0$ \(\Q(\sqrt{-3}) \), \(\Q\) $C_2$, Trivial 1.4.c $\times$ 1.4.e
2.4.i_y $2$ $\F_{2^{2}}$ $( 1 + 2 x )^{4}$ $0$ \(\Q\) Trivial 1.4.e 2
2.5.af_p $2$ $\F_{5}$ $1 - 5 x + 15 x^{2} - 25 x^{3} + 25 x^{4}$ $0$ \(\Q(\zeta_{5})\) $C_4$ simple
2.5.a_ak $2$ $\F_{5}$ $( 1 - 5 x^{2} )^{2}$ $0$ \(\Q(\sqrt{5}) \) $C_2$ simple
2.5.a_af $2$ $\F_{5}$ $1 - 5 x^{2} + 25 x^{4}$ $0$ \(\Q(\sqrt{-3}, \sqrt{-5})\) $C_2^2$ simple
2.5.a_a $2$ $\F_{5}$ $1 + 25 x^{4}$ $0$ \(\Q(i, \sqrt{10})\) $C_2^2$ simple
2.5.a_f $2$ $\F_{5}$ $1 + 5 x^{2} + 25 x^{4}$ $0$ \(\Q(\sqrt{-3}, \sqrt{5})\) $C_2^2$ simple
2.5.a_k $2$ $\F_{5}$ $( 1 + 5 x^{2} )^{2}$ $0$ \(\Q(\sqrt{-5}) \) $C_2$ 1.5.a 2
2.5.f_p $2$ $\F_{5}$ $1 + 5 x + 15 x^{2} + 25 x^{3} + 25 x^{4}$ $0$ \(\Q(\zeta_{5})\) $C_4$ simple
2.7.a_ao $2$ $\F_{7}$ $( 1 - 7 x^{2} )^{2}$ $0$ \(\Q(\sqrt{7}) \) $C_2$ simple
2.7.a_ah $2$ $\F_{7}$ $1 - 7 x^{2} + 49 x^{4}$ $0$ \(\Q(\sqrt{-3}, \sqrt{-7})\) $C_2^2$ simple
2.7.a_a $2$ $\F_{7}$ $1 + 49 x^{4}$ $0$ \(\Q(i, \sqrt{14})\) $C_2^2$ simple
2.7.a_h $2$ $\F_{7}$ $1 + 7 x^{2} + 49 x^{4}$ $0$ \(\Q(\sqrt{-3}, \sqrt{7})\) $C_2^2$ simple
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