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 897 matches)

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Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
2.19.aq_dy $2$ $\F_{19}$ $( 1 - 8 x + 19 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-3}) \) $C_2$ 1.19.ai 2
2.19.ap_dp $2$ $\F_{19}$ $1 - 15 x + 93 x^{2} - 285 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-9 +2 \sqrt{5}})\) $D_{4}$ simple
2.19.ap_dq $2$ $\F_{19}$ $( 1 - 8 x + 19 x^{2} )( 1 - 7 x + 19 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.19.ai $\times$ 1.19.ah
2.19.ao_dh $2$ $\F_{19}$ $1 - 14 x + 85 x^{2} - 266 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-19 +8 \sqrt{2}})\) $D_{4}$ simple
2.19.ao_di $2$ $\F_{19}$ $( 1 - 8 x + 19 x^{2} )( 1 - 6 x + 19 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-10}) \) $C_2$, $C_2$ 1.19.ai $\times$ 1.19.ag
2.19.ao_dj $2$ $\F_{19}$ $( 1 - 7 x + 19 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-3}) \) $C_2$ 1.19.ah 2
2.19.an_cy $2$ $\F_{19}$ $1 - 13 x + 76 x^{2} - 247 x^{3} + 361 x^{4}$ $1$ \(\Q(\sqrt{-26 +2 \sqrt{17}})\) $D_{4}$ simple
2.19.an_cz $2$ $\F_{19}$ $1 - 13 x + 77 x^{2} - 247 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-122 +26 \sqrt{13}})\) $D_{4}$ simple
2.19.an_da $2$ $\F_{19}$ $( 1 - 8 x + 19 x^{2} )( 1 - 5 x + 19 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-51}) \) $C_2$, $C_2$ 1.19.ai $\times$ 1.19.af
2.19.an_db $2$ $\F_{19}$ $1 - 13 x + 79 x^{2} - 247 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-130 +26 \sqrt{5}})\) $C_4$ simple
2.19.an_dc $2$ $\F_{19}$ $( 1 - 7 x + 19 x^{2} )( 1 - 6 x + 19 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-10}) \) $C_2$, $C_2$ 1.19.ah $\times$ 1.19.ag
2.19.am_cp $2$ $\F_{19}$ $1 - 12 x + 67 x^{2} - 228 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{7})\) $C_2^2$ simple
2.19.am_cq $2$ $\F_{19}$ $1 - 12 x + 68 x^{2} - 228 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-34 +12 \sqrt{6}})\) $D_{4}$ simple
2.19.am_cr $2$ $\F_{19}$ $1 - 12 x + 69 x^{2} - 228 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-90 +2 \sqrt{5}})\) $D_{4}$ simple
2.19.am_cs $2$ $\F_{19}$ $( 1 - 8 x + 19 x^{2} )( 1 - 4 x + 19 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-15}) \) $C_2$, $C_2$ 1.19.ai $\times$ 1.19.ae
2.19.am_ct $2$ $\F_{19}$ $1 - 12 x + 71 x^{2} - 228 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-37 +12 \sqrt{3}})\) $D_{4}$ simple
2.19.am_cu $2$ $\F_{19}$ $1 - 12 x + 72 x^{2} - 228 x^{3} + 361 x^{4}$ $2$ \(\Q(\zeta_{8})\) $C_2^2$ simple
2.19.am_cv $2$ $\F_{19}$ $( 1 - 7 x + 19 x^{2} )( 1 - 5 x + 19 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-51}) \) $C_2$, $C_2$ 1.19.ah $\times$ 1.19.af
2.19.am_cw $2$ $\F_{19}$ $( 1 - 6 x + 19 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-10}) \) $C_2$ 1.19.ag 2
2.19.al_cg $2$ $\F_{19}$ $1 - 11 x + 58 x^{2} - 209 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-13 +2 \sqrt{41}})\) $D_{4}$ simple
2.19.al_ch $2$ $\F_{19}$ $1 - 11 x + 59 x^{2} - 209 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-146 -22 \sqrt{37}})\) $D_{4}$ simple
2.19.al_ci $2$ $\F_{19}$ $1 - 11 x + 60 x^{2} - 209 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-150 -22 \sqrt{33}})\) $D_{4}$ simple
2.19.al_cj $2$ $\F_{19}$ $1 - 11 x + 61 x^{2} - 209 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-154 -22 \sqrt{29}})\) $D_{4}$ simple
2.19.al_ck $2$ $\F_{19}$ $( 1 - 8 x + 19 x^{2} )( 1 - 3 x + 19 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-67}) \) $C_2$, $C_2$ 1.19.ai $\times$ 1.19.ad
2.19.al_cl $2$ $\F_{19}$ $1 - 11 x + 63 x^{2} - 209 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-162 -22 \sqrt{21}})\) $D_{4}$ simple
2.19.al_cm $2$ $\F_{19}$ $1 - 11 x + 64 x^{2} - 209 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-166 -22 \sqrt{17}})\) $D_{4}$ simple
2.19.al_cn $2$ $\F_{19}$ $1 - 11 x + 65 x^{2} - 209 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-82 +18 \sqrt{13}})\) $D_{4}$ simple
2.19.al_co $2$ $\F_{19}$ $( 1 - 7 x + 19 x^{2} )( 1 - 4 x + 19 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-15}) \) $C_2$, $C_2$ 1.19.ah $\times$ 1.19.ae
2.19.al_cp $2$ $\F_{19}$ $1 - 11 x + 67 x^{2} - 209 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-178 -22 \sqrt{5}})\) $D_{4}$ simple
2.19.al_cq $2$ $\F_{19}$ $( 1 - 6 x + 19 x^{2} )( 1 - 5 x + 19 x^{2} )$ $2$ \(\Q(\sqrt{-10}) \), \(\Q(\sqrt{-51}) \) $C_2$, $C_2$ 1.19.ag $\times$ 1.19.af
2.19.ak_by $2$ $\F_{19}$ $1 - 10 x + 50 x^{2} - 190 x^{3} + 361 x^{4}$ $2$ \(\Q(i, \sqrt{13})\) $C_2^2$ simple
2.19.ak_bz $2$ $\F_{19}$ $1 - 10 x + 51 x^{2} - 190 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-33 +16 \sqrt{3}})\) $D_{4}$ simple
2.19.ak_ca $2$ $\F_{19}$ $1 - 10 x + 52 x^{2} - 190 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-8 +2 \sqrt{11}})\) $D_{4}$ simple
2.19.ak_cb $2$ $\F_{19}$ $1 - 10 x + 53 x^{2} - 190 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-41 -10 \sqrt{10}})\) $D_{4}$ simple
2.19.ak_cc $2$ $\F_{19}$ $( 1 - 8 x + 19 x^{2} )( 1 - 2 x + 19 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \) $C_2$, $C_2$ 1.19.ai $\times$ 1.19.ac
2.19.ak_cd $2$ $\F_{19}$ $1 - 10 x + 55 x^{2} - 190 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-43 +20 \sqrt{2}})\) $D_{4}$ simple
2.19.ak_ce $2$ $\F_{19}$ $1 - 10 x + 56 x^{2} - 190 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-44 -10 \sqrt{7}})\) $D_{4}$ simple
2.19.ak_cf $2$ $\F_{19}$ $1 - 10 x + 57 x^{2} - 190 x^{3} + 361 x^{4}$ $1$ \(\Q(\sqrt{-45 -10 \sqrt{6}})\) $D_{4}$ simple
2.19.ak_cg $2$ $\F_{19}$ $1 - 10 x + 58 x^{2} - 190 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-11 +2 \sqrt{5}})\) $D_{4}$ simple
2.19.ak_ch $2$ $\F_{19}$ $( 1 - 7 x + 19 x^{2} )( 1 - 3 x + 19 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-67}) \) $C_2$, $C_2$ 1.19.ah $\times$ 1.19.ad
2.19.ak_ci $2$ $\F_{19}$ $1 - 10 x + 60 x^{2} - 190 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-48 -10 \sqrt{3}})\) $D_{4}$ simple
2.19.ak_cj $2$ $\F_{19}$ $1 - 10 x + 61 x^{2} - 190 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-49 -10 \sqrt{2}})\) $D_{4}$ simple
2.19.ak_ck $2$ $\F_{19}$ $( 1 - 6 x + 19 x^{2} )( 1 - 4 x + 19 x^{2} )$ $2$ \(\Q(\sqrt{-10}) \), \(\Q(\sqrt{-15}) \) $C_2$, $C_2$ 1.19.ag $\times$ 1.19.ae
2.19.ak_cl $2$ $\F_{19}$ $( 1 - 5 x + 19 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-51}) \) $C_2$ 1.19.af 2
2.19.aj_bp $2$ $\F_{19}$ $1 - 9 x + 41 x^{2} - 171 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-49 +2 \sqrt{69}})\) $D_{4}$ simple
2.19.aj_bq $2$ $\F_{19}$ $1 - 9 x + 42 x^{2} - 171 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-102 +10 \sqrt{65}})\) $D_{4}$ simple
2.19.aj_br $2$ $\F_{19}$ $1 - 9 x + 43 x^{2} - 171 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-17 +2 \sqrt{61}})\) $D_{4}$ simple
2.19.aj_bs $2$ $\F_{19}$ $1 - 9 x + 44 x^{2} - 171 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-166 +18 \sqrt{57}})\) $D_{4}$ simple
2.19.aj_bt $2$ $\F_{19}$ $1 - 9 x + 45 x^{2} - 171 x^{3} + 361 x^{4}$ $2$ \(\Q(\sqrt{-170 +18 \sqrt{53}})\) $D_{4}$ simple
2.19.aj_bu $2$ $\F_{19}$ $( 1 - 8 x + 19 x^{2} )( 1 - x + 19 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.19.ai $\times$ 1.19.ab
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