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The results below are complete, since the LMFDB contains all isogeny classes of abelian varieties of dimension at most 2 over fields of cardinality at most 211 or 243, 256, 343, 512, 625, 729, 1024

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Base field Base char. Dimension $p$-rank Initial coefficients
Simple Geom. simple Primitive Princ. polarizable Jacobian
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Use Geometric decomposition in the following inputs
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Results (1-50 of 3031 matches)

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Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
2.43.aba_jv $2$ $\F_{43}$ $( 1 - 13 x + 43 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-3}) \) $C_2$ 1.43.an 2
2.43.az_ji $2$ $\F_{43}$ $( 1 - 13 x + 43 x^{2} )( 1 - 12 x + 43 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \) $C_2$, $C_2$ 1.43.an $\times$ 1.43.am
2.43.ay_iv $2$ $\F_{43}$ $( 1 - 13 x + 43 x^{2} )( 1 - 11 x + 43 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-51}) \) $C_2$, $C_2$ 1.43.an $\times$ 1.43.al
2.43.ay_iw $2$ $\F_{43}$ $( 1 - 12 x + 43 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-7}) \) $C_2$ 1.43.am 2
2.43.ax_ii $2$ $\F_{43}$ $( 1 - 13 x + 43 x^{2} )( 1 - 10 x + 43 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \) $C_2$, $C_2$ 1.43.an $\times$ 1.43.ak
2.43.ax_ij $2$ $\F_{43}$ $1 - 23 x + 217 x^{2} - 989 x^{3} + 1849 x^{4}$ $2$ \(\Q(\sqrt{-29 +2 \sqrt{5}})\) $D_{4}$ simple
2.43.ax_ik $2$ $\F_{43}$ $( 1 - 12 x + 43 x^{2} )( 1 - 11 x + 43 x^{2} )$ $2$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-51}) \) $C_2$, $C_2$ 1.43.am $\times$ 1.43.al
2.43.aw_hv $2$ $\F_{43}$ $( 1 - 13 x + 43 x^{2} )( 1 - 9 x + 43 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-91}) \) $C_2$, $C_2$ 1.43.an $\times$ 1.43.aj
2.43.aw_hw $2$ $\F_{43}$ $1 - 22 x + 204 x^{2} - 946 x^{3} + 1849 x^{4}$ $2$ \(\Q(\sqrt{-48 -22 \sqrt{3}})\) $D_{4}$ simple
2.43.aw_hx $2$ $\F_{43}$ $1 - 22 x + 205 x^{2} - 946 x^{3} + 1849 x^{4}$ $2$ \(\Q(\sqrt{-49 -22 \sqrt{2}})\) $D_{4}$ simple
2.43.aw_hy $2$ $\F_{43}$ $( 1 - 12 x + 43 x^{2} )( 1 - 10 x + 43 x^{2} )$ $2$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-2}) \) $C_2$, $C_2$ 1.43.am $\times$ 1.43.ak
2.43.aw_hz $2$ $\F_{43}$ $( 1 - 11 x + 43 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-51}) \) $C_2$ 1.43.al 2
2.43.av_hi $2$ $\F_{43}$ $( 1 - 13 x + 43 x^{2} )( 1 - 8 x + 43 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.43.an $\times$ 1.43.ai
2.43.av_hj $2$ $\F_{43}$ $1 - 21 x + 191 x^{2} - 903 x^{3} + 1849 x^{4}$ $2$ \(\Q(\sqrt{-226 +42 \sqrt{21}})\) $D_{4}$ simple
2.43.av_hk $2$ $\F_{43}$ $1 - 21 x + 192 x^{2} - 903 x^{3} + 1849 x^{4}$ $2$ \(\Q(\sqrt{-230 +42 \sqrt{17}})\) $D_{4}$ simple
2.43.av_hl $2$ $\F_{43}$ $1 - 21 x + 193 x^{2} - 903 x^{3} + 1849 x^{4}$ $2$ \(\Q(\sqrt{-234 +42 \sqrt{13}})\) $D_{4}$ simple
2.43.av_hm $2$ $\F_{43}$ $( 1 - 12 x + 43 x^{2} )( 1 - 9 x + 43 x^{2} )$ $2$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-91}) \) $C_2$, $C_2$ 1.43.am $\times$ 1.43.aj
2.43.av_hn $2$ $\F_{43}$ $1 - 21 x + 195 x^{2} - 903 x^{3} + 1849 x^{4}$ $2$ \(\Q(\sqrt{-242 +42 \sqrt{5}})\) $D_{4}$ simple
2.43.av_ho $2$ $\F_{43}$ $( 1 - 11 x + 43 x^{2} )( 1 - 10 x + 43 x^{2} )$ $2$ \(\Q(\sqrt{-51}) \), \(\Q(\sqrt{-2}) \) $C_2$, $C_2$ 1.43.al $\times$ 1.43.ak
2.43.au_gv $2$ $\F_{43}$ $( 1 - 13 x + 43 x^{2} )( 1 - 7 x + 43 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-123}) \) $C_2$, $C_2$ 1.43.an $\times$ 1.43.ah
2.43.au_gw $2$ $\F_{43}$ $1 - 20 x + 178 x^{2} - 860 x^{3} + 1849 x^{4}$ $2$ \(\Q(\sqrt{-4 + \sqrt{2}})\) $D_{4}$ simple
2.43.au_gx $2$ $\F_{43}$ $1 - 20 x + 179 x^{2} - 860 x^{3} + 1849 x^{4}$ $2$ \(\Q(\sqrt{-65 +20 \sqrt{7}})\) $D_{4}$ simple
2.43.au_gy $2$ $\F_{43}$ $1 - 20 x + 180 x^{2} - 860 x^{3} + 1849 x^{4}$ $2$ \(\Q(\sqrt{-66 +20 \sqrt{6}})\) $D_{4}$ simple
2.43.au_gz $2$ $\F_{43}$ $1 - 20 x + 181 x^{2} - 860 x^{3} + 1849 x^{4}$ $2$ \(\Q(\sqrt{-202 -14 \sqrt{5}})\) $D_{4}$ simple
2.43.au_ha $2$ $\F_{43}$ $( 1 - 12 x + 43 x^{2} )( 1 - 8 x + 43 x^{2} )$ $2$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.43.am $\times$ 1.43.ai
2.43.au_hb $2$ $\F_{43}$ $1 - 20 x + 183 x^{2} - 860 x^{3} + 1849 x^{4}$ $2$ \(\Q(\sqrt{-69 +20 \sqrt{3}})\) $D_{4}$ simple
2.43.au_hc $2$ $\F_{43}$ $1 - 20 x + 184 x^{2} - 860 x^{3} + 1849 x^{4}$ $2$ \(\Q(\sqrt{-70 +20 \sqrt{2}})\) $D_{4}$ simple
2.43.au_hd $2$ $\F_{43}$ $( 1 - 11 x + 43 x^{2} )( 1 - 9 x + 43 x^{2} )$ $2$ \(\Q(\sqrt{-51}) \), \(\Q(\sqrt{-91}) \) $C_2$, $C_2$ 1.43.al $\times$ 1.43.aj
2.43.au_he $2$ $\F_{43}$ $( 1 - 10 x + 43 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-2}) \) $C_2$ 1.43.ak 2
2.43.at_gi $2$ $\F_{43}$ $( 1 - 13 x + 43 x^{2} )( 1 - 6 x + 43 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-34}) \) $C_2$, $C_2$ 1.43.an $\times$ 1.43.ag
2.43.at_gj $2$ $\F_{43}$ $1 - 19 x + 165 x^{2} - 817 x^{3} + 1849 x^{4}$ $2$ \(\Q(\sqrt{-33 +6 \sqrt{5}})\) $D_{4}$ simple
2.43.at_gk $2$ $\F_{43}$ $1 - 19 x + 166 x^{2} - 817 x^{3} + 1849 x^{4}$ $2$ \(\Q(\sqrt{-206 -22 \sqrt{41}})\) $D_{4}$ simple
2.43.at_gl $2$ $\F_{43}$ $1 - 19 x + 167 x^{2} - 817 x^{3} + 1849 x^{4}$ $2$ \(\Q(\sqrt{-146 -22 \sqrt{37}})\) $D_{4}$ simple
2.43.at_gm $2$ $\F_{43}$ $1 - 19 x + 168 x^{2} - 817 x^{3} + 1849 x^{4}$ $2$ \(\Q(\sqrt{-294 -38 \sqrt{33}})\) $D_{4}$ simple
2.43.at_gn $2$ $\F_{43}$ $1 - 19 x + 169 x^{2} - 817 x^{3} + 1849 x^{4}$ $2$ \(\Q(\sqrt{-298 -38 \sqrt{29}})\) $D_{4}$ simple
2.43.at_go $2$ $\F_{43}$ $( 1 - 12 x + 43 x^{2} )( 1 - 7 x + 43 x^{2} )$ $2$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-123}) \) $C_2$, $C_2$ 1.43.am $\times$ 1.43.ah
2.43.at_gp $2$ $\F_{43}$ $1 - 19 x + 171 x^{2} - 817 x^{3} + 1849 x^{4}$ $2$ \(\Q(\sqrt{-306 -38 \sqrt{21}})\) $D_{4}$ simple
2.43.at_gq $2$ $\F_{43}$ $1 - 19 x + 172 x^{2} - 817 x^{3} + 1849 x^{4}$ $1$ \(\Q(\sqrt{-310 -38 \sqrt{17}})\) $D_{4}$ simple
2.43.at_gr $2$ $\F_{43}$ $1 - 19 x + 173 x^{2} - 817 x^{3} + 1849 x^{4}$ $2$ \(\Q(\sqrt{-314 -38 \sqrt{13}})\) $D_{4}$ simple
2.43.at_gs $2$ $\F_{43}$ $( 1 - 11 x + 43 x^{2} )( 1 - 8 x + 43 x^{2} )$ $2$ \(\Q(\sqrt{-51}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.43.al $\times$ 1.43.ai
2.43.at_gt $2$ $\F_{43}$ $1 - 19 x + 175 x^{2} - 817 x^{3} + 1849 x^{4}$ $2$ \(\Q(\sqrt{-322 -38 \sqrt{5}})\) $D_{4}$ simple
2.43.at_gu $2$ $\F_{43}$ $( 1 - 10 x + 43 x^{2} )( 1 - 9 x + 43 x^{2} )$ $2$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-91}) \) $C_2$, $C_2$ 1.43.ak $\times$ 1.43.aj
2.43.as_fv $2$ $\F_{43}$ $( 1 - 13 x + 43 x^{2} )( 1 - 5 x + 43 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.43.an $\times$ 1.43.af
2.43.as_fw $2$ $\F_{43}$ $1 - 18 x + 152 x^{2} - 774 x^{3} + 1849 x^{4}$ $2$ \(\Q(\sqrt{-76 -18 \sqrt{15}})\) $D_{4}$ simple
2.43.as_fx $2$ $\F_{43}$ $1 - 18 x + 153 x^{2} - 774 x^{3} + 1849 x^{4}$ $2$ \(\Q(\sqrt{-77 -18 \sqrt{14}})\) $D_{4}$ simple
2.43.as_fy $2$ $\F_{43}$ $1 - 18 x + 154 x^{2} - 774 x^{3} + 1849 x^{4}$ $2$ \(\Q(\sqrt{-78 +18 \sqrt{13}})\) $C_4$ simple
2.43.as_fz $2$ $\F_{43}$ $1 - 18 x + 155 x^{2} - 774 x^{3} + 1849 x^{4}$ $2$ \(\Q(\sqrt{-79 +36 \sqrt{3}})\) $D_{4}$ simple
2.43.as_ga $2$ $\F_{43}$ $1 - 18 x + 156 x^{2} - 774 x^{3} + 1849 x^{4}$ $2$ \(\Q(\sqrt{-80 -18 \sqrt{11}})\) $D_{4}$ simple
2.43.as_gb $2$ $\F_{43}$ $1 - 18 x + 157 x^{2} - 774 x^{3} + 1849 x^{4}$ $2$ \(\Q(\sqrt{-9 +2 \sqrt{10}})\) $D_{4}$ simple
2.43.as_gc $2$ $\F_{43}$ $( 1 - 12 x + 43 x^{2} )( 1 - 6 x + 43 x^{2} )$ $2$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-34}) \) $C_2$, $C_2$ 1.43.am $\times$ 1.43.ag
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