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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Results (1-50 of 765 matches)

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Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
2.17.aq_du $2$ $\F_{17}$ $( 1 - 8 x + 17 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-1}) \) $C_2$ 1.17.ai 2
2.17.ap_dm $2$ $\F_{17}$ $( 1 - 8 x + 17 x^{2} )( 1 - 7 x + 17 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-19}) \) $C_2$, $C_2$ 1.17.ai $\times$ 1.17.ah
2.17.ao_de $2$ $\F_{17}$ $( 1 - 8 x + 17 x^{2} )( 1 - 6 x + 17 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) $C_2$, $C_2$ 1.17.ai $\times$ 1.17.ag
2.17.ao_df $2$ $\F_{17}$ $( 1 - 7 x + 17 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-19}) \) $C_2$ 1.17.ah 2
2.17.an_cw $2$ $\F_{17}$ $( 1 - 8 x + 17 x^{2} )( 1 - 5 x + 17 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-43}) \) $C_2$, $C_2$ 1.17.ai $\times$ 1.17.af
2.17.an_cx $2$ $\F_{17}$ $1 - 13 x + 75 x^{2} - 221 x^{3} + 289 x^{4}$ $2$ \(\Q(\sqrt{-82 +10 \sqrt{5}})\) $D_{4}$ simple
2.17.an_cy $2$ $\F_{17}$ $( 1 - 7 x + 17 x^{2} )( 1 - 6 x + 17 x^{2} )$ $2$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-2}) \) $C_2$, $C_2$ 1.17.ah $\times$ 1.17.ag
2.17.am_cn $2$ $\F_{17}$ $1 - 12 x + 65 x^{2} - 204 x^{3} + 289 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{5})\) $C_2^2$ simple
2.17.am_co $2$ $\F_{17}$ $( 1 - 8 x + 17 x^{2} )( 1 - 4 x + 17 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-13}) \) $C_2$, $C_2$ 1.17.ai $\times$ 1.17.ae
2.17.am_cp $2$ $\F_{17}$ $1 - 12 x + 67 x^{2} - 204 x^{3} + 289 x^{4}$ $2$ \(\Q(\sqrt{-29 +12 \sqrt{3}})\) $D_{4}$ simple
2.17.am_cq $2$ $\F_{17}$ $1 - 12 x + 68 x^{2} - 204 x^{3} + 289 x^{4}$ $1$ \(\Q(\sqrt{-30 +12 \sqrt{2}})\) $D_{4}$ simple
2.17.am_cr $2$ $\F_{17}$ $( 1 - 7 x + 17 x^{2} )( 1 - 5 x + 17 x^{2} )$ $2$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-43}) \) $C_2$, $C_2$ 1.17.ah $\times$ 1.17.af
2.17.am_cs $2$ $\F_{17}$ $( 1 - 6 x + 17 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-2}) \) $C_2$ 1.17.ag 2
2.17.al_cf $2$ $\F_{17}$ $1 - 11 x + 57 x^{2} - 187 x^{3} + 289 x^{4}$ $2$ \(\Q(\sqrt{-13 +2 \sqrt{29}})\) $D_{4}$ simple
2.17.al_cg $2$ $\F_{17}$ $( 1 - 8 x + 17 x^{2} )( 1 - 3 x + 17 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-59}) \) $C_2$, $C_2$ 1.17.ai $\times$ 1.17.ad
2.17.al_ch $2$ $\F_{17}$ $1 - 11 x + 59 x^{2} - 187 x^{3} + 289 x^{4}$ $2$ \(\Q(\sqrt{-130 -22 \sqrt{21}})\) $D_{4}$ simple
2.17.al_ci $2$ $\F_{17}$ $1 - 11 x + 60 x^{2} - 187 x^{3} + 289 x^{4}$ $2$ \(\Q(\sqrt{-26 +2 \sqrt{17}})\) $D_{4}$ simple
2.17.al_cj $2$ $\F_{17}$ $1 - 11 x + 61 x^{2} - 187 x^{3} + 289 x^{4}$ $2$ \(\Q(\sqrt{-138 -22 \sqrt{13}})\) $D_{4}$ simple
2.17.al_ck $2$ $\F_{17}$ $( 1 - 7 x + 17 x^{2} )( 1 - 4 x + 17 x^{2} )$ $2$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-13}) \) $C_2$, $C_2$ 1.17.ah $\times$ 1.17.ae
2.17.al_cl $2$ $\F_{17}$ $1 - 11 x + 63 x^{2} - 187 x^{3} + 289 x^{4}$ $2$ \(\Q(\sqrt{-146 -22 \sqrt{5}})\) $D_{4}$ simple
2.17.al_cm $2$ $\F_{17}$ $( 1 - 6 x + 17 x^{2} )( 1 - 5 x + 17 x^{2} )$ $2$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-43}) \) $C_2$, $C_2$ 1.17.ag $\times$ 1.17.af
2.17.ak_bx $2$ $\F_{17}$ $1 - 10 x + 49 x^{2} - 170 x^{3} + 289 x^{4}$ $2$ \(\Q(\sqrt{-27 +8 \sqrt{10}})\) $D_{4}$ simple
2.17.ak_by $2$ $\F_{17}$ $( 1 - 8 x + 17 x^{2} )( 1 - 2 x + 17 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.17.ai $\times$ 1.17.ac
2.17.ak_bz $2$ $\F_{17}$ $1 - 10 x + 51 x^{2} - 170 x^{3} + 289 x^{4}$ $1$ \(\Q(\sqrt{-25 -10 \sqrt{2}})\) $D_{4}$ simple
2.17.ak_ca $2$ $\F_{17}$ $1 - 10 x + 52 x^{2} - 170 x^{3} + 289 x^{4}$ $2$ \(\Q(\sqrt{-36 -10 \sqrt{7}})\) $D_{4}$ simple
2.17.ak_cb $2$ $\F_{17}$ $1 - 10 x + 53 x^{2} - 170 x^{3} + 289 x^{4}$ $2$ \(\Q(\sqrt{-37 -10 \sqrt{6}})\) $D_{4}$ simple
2.17.ak_cc $2$ $\F_{17}$ $1 - 10 x + 54 x^{2} - 170 x^{3} + 289 x^{4}$ $2$ \(\Q(\sqrt{-8 + \sqrt{5}})\) $D_{4}$ simple
2.17.ak_cd $2$ $\F_{17}$ $( 1 - 7 x + 17 x^{2} )( 1 - 3 x + 17 x^{2} )$ $2$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-59}) \) $C_2$, $C_2$ 1.17.ah $\times$ 1.17.ad
2.17.ak_ce $2$ $\F_{17}$ $1 - 10 x + 56 x^{2} - 170 x^{3} + 289 x^{4}$ $2$ \(\Q(\sqrt{-40 -10 \sqrt{3}})\) $D_{4}$ simple
2.17.ak_cf $2$ $\F_{17}$ $1 - 10 x + 57 x^{2} - 170 x^{3} + 289 x^{4}$ $2$ \(\Q(\sqrt{-41 -10 \sqrt{2}})\) $D_{4}$ simple
2.17.ak_cg $2$ $\F_{17}$ $( 1 - 6 x + 17 x^{2} )( 1 - 4 x + 17 x^{2} )$ $2$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-13}) \) $C_2$, $C_2$ 1.17.ag $\times$ 1.17.ae
2.17.ak_ch $2$ $\F_{17}$ $( 1 - 5 x + 17 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-43}) \) $C_2$ 1.17.af 2
2.17.aj_bp $2$ $\F_{17}$ $1 - 9 x + 41 x^{2} - 153 x^{3} + 289 x^{4}$ $2$ \(\Q(\sqrt{-45 +6 \sqrt{53}})\) $D_{4}$ simple
2.17.aj_bq $2$ $\F_{17}$ $( 1 - 8 x + 17 x^{2} )( 1 - x + 17 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-67}) \) $C_2$, $C_2$ 1.17.ai $\times$ 1.17.ab
2.17.aj_br $2$ $\F_{17}$ $1 - 9 x + 43 x^{2} - 153 x^{3} + 289 x^{4}$ $2$ \(\Q(\sqrt{-21 +2 \sqrt{5}})\) $D_{4}$ simple
2.17.aj_bs $2$ $\F_{17}$ $1 - 9 x + 44 x^{2} - 153 x^{3} + 289 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{41})\) $C_2^2$ simple
2.17.aj_bt $2$ $\F_{17}$ $1 - 9 x + 45 x^{2} - 153 x^{3} + 289 x^{4}$ $2$ \(\Q(\sqrt{-154 +18 \sqrt{37}})\) $D_{4}$ simple
2.17.aj_bu $2$ $\F_{17}$ $1 - 9 x + 46 x^{2} - 153 x^{3} + 289 x^{4}$ $2$ \(\Q(\sqrt{-158 +18 \sqrt{33}})\) $D_{4}$ simple
2.17.aj_bv $2$ $\F_{17}$ $1 - 9 x + 47 x^{2} - 153 x^{3} + 289 x^{4}$ $2$ \(\Q(\sqrt{-18 +2 \sqrt{29}})\) $D_{4}$ simple
2.17.aj_bw $2$ $\F_{17}$ $( 1 - 7 x + 17 x^{2} )( 1 - 2 x + 17 x^{2} )$ $2$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.17.ah $\times$ 1.17.ac
2.17.aj_bx $2$ $\F_{17}$ $1 - 9 x + 49 x^{2} - 153 x^{3} + 289 x^{4}$ $2$ \(\Q(\sqrt{-170 +18 \sqrt{21}})\) $D_{4}$ simple
2.17.aj_by $2$ $\F_{17}$ $1 - 9 x + 50 x^{2} - 153 x^{3} + 289 x^{4}$ $2$ \(\Q(\sqrt{-174 +18 \sqrt{17}})\) $D_{4}$ simple
2.17.aj_bz $2$ $\F_{17}$ $1 - 9 x + 51 x^{2} - 153 x^{3} + 289 x^{4}$ $1$ \(\Q(\sqrt{-178 +18 \sqrt{13}})\) $D_{4}$ simple
2.17.aj_ca $2$ $\F_{17}$ $( 1 - 6 x + 17 x^{2} )( 1 - 3 x + 17 x^{2} )$ $2$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-59}) \) $C_2$, $C_2$ 1.17.ag $\times$ 1.17.ad
2.17.aj_cb $2$ $\F_{17}$ $1 - 9 x + 53 x^{2} - 153 x^{3} + 289 x^{4}$ $2$ \(\Q(\sqrt{-186 +18 \sqrt{5}})\) $D_{4}$ simple
2.17.aj_cc $2$ $\F_{17}$ $( 1 - 5 x + 17 x^{2} )( 1 - 4 x + 17 x^{2} )$ $2$ \(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-13}) \) $C_2$, $C_2$ 1.17.af $\times$ 1.17.ae
2.17.ai_bg $2$ $\F_{17}$ $1 - 8 x + 32 x^{2} - 136 x^{3} + 289 x^{4}$ $2$ \(\Q(\zeta_{8})\) $C_2^2$ simple
2.17.ai_bh $2$ $\F_{17}$ $1 - 8 x + 33 x^{2} - 136 x^{3} + 289 x^{4}$ $2$ \(\Q(\sqrt{-94 +2 \sqrt{17}})\) $D_{4}$ simple
2.17.ai_bi $2$ $\F_{17}$ $( 1 - 8 x + 17 x^{2} )( 1 + 17 x^{2} )$ $1$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-17}) \) $C_2$, $C_2$ 1.17.ai $\times$ 1.17.a
2.17.ai_bj $2$ $\F_{17}$ $1 - 8 x + 35 x^{2} - 136 x^{3} + 289 x^{4}$ $2$ \(\Q(\sqrt{-37 +8 \sqrt{15}})\) $D_{4}$ simple
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