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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
Slopes Points on variety Points on curve Simple factors
Newton elevation # Jacobians # Hyp. Jacobians # twists Max twist degree
Angle rank Angle corank End. degree $p$-corank (Geom.) Sq.free
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Use Geometric decomposition in the following inputs
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Results (1-50 of 1193 matches)

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Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
2.23.as_ex $2$ $\F_{23}$ $( 1 - 9 x + 23 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-11}) \) $C_2$ 1.23.aj 2
2.23.ar_eo $2$ $\F_{23}$ $( 1 - 9 x + 23 x^{2} )( 1 - 8 x + 23 x^{2} )$ $2$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-7}) \) $C_2$, $C_2$ 1.23.aj $\times$ 1.23.ai
2.23.aq_ee $2$ $\F_{23}$ $1 - 16 x + 108 x^{2} - 368 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-14 +4 \sqrt{2}})\) $D_{4}$ simple
2.23.aq_ef $2$ $\F_{23}$ $( 1 - 9 x + 23 x^{2} )( 1 - 7 x + 23 x^{2} )$ $2$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-43}) \) $C_2$, $C_2$ 1.23.aj $\times$ 1.23.ah
2.23.aq_eg $2$ $\F_{23}$ $( 1 - 8 x + 23 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-7}) \) $C_2$ 1.23.ai 2
2.23.ap_du $2$ $\F_{23}$ $1 - 15 x + 98 x^{2} - 345 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{17})\) $C_2^2$ simple
2.23.ap_dv $2$ $\F_{23}$ $1 - 15 x + 99 x^{2} - 345 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-130 -30 \sqrt{13}})\) $C_4$ simple
2.23.ap_dw $2$ $\F_{23}$ $( 1 - 9 x + 23 x^{2} )( 1 - 6 x + 23 x^{2} )$ $2$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-14}) \) $C_2$, $C_2$ 1.23.aj $\times$ 1.23.ag
2.23.ap_dx $2$ $\F_{23}$ $1 - 15 x + 101 x^{2} - 345 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-33 +6 \sqrt{5}})\) $D_{4}$ simple
2.23.ap_dy $2$ $\F_{23}$ $( 1 - 8 x + 23 x^{2} )( 1 - 7 x + 23 x^{2} )$ $2$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-43}) \) $C_2$, $C_2$ 1.23.ai $\times$ 1.23.ah
2.23.ao_dl $2$ $\F_{23}$ $1 - 14 x + 89 x^{2} - 322 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-34 +8 \sqrt{6}})\) $D_{4}$ simple
2.23.ao_dm $2$ $\F_{23}$ $1 - 14 x + 90 x^{2} - 322 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-22 +2 \sqrt{5}})\) $D_{4}$ simple
2.23.ao_dn $2$ $\F_{23}$ $( 1 - 9 x + 23 x^{2} )( 1 - 5 x + 23 x^{2} )$ $2$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-67}) \) $C_2$, $C_2$ 1.23.aj $\times$ 1.23.af
2.23.ao_do $2$ $\F_{23}$ $1 - 14 x + 92 x^{2} - 322 x^{3} + 529 x^{4}$ $1$ \(\Q(\sqrt{-40 -14 \sqrt{3}})\) $D_{4}$ simple
2.23.ao_dp $2$ $\F_{23}$ $1 - 14 x + 93 x^{2} - 322 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-41 -14 \sqrt{2}})\) $D_{4}$ simple
2.23.ao_dq $2$ $\F_{23}$ $( 1 - 8 x + 23 x^{2} )( 1 - 6 x + 23 x^{2} )$ $2$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) $C_2$, $C_2$ 1.23.ai $\times$ 1.23.ag
2.23.ao_dr $2$ $\F_{23}$ $( 1 - 7 x + 23 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-43}) \) $C_2$ 1.23.ah 2
2.23.an_db $2$ $\F_{23}$ $1 - 13 x + 79 x^{2} - 299 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-29 +2 \sqrt{37}})\) $D_{4}$ simple
2.23.an_dc $2$ $\F_{23}$ $1 - 13 x + 80 x^{2} - 299 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-166 +26 \sqrt{33}})\) $D_{4}$ simple
2.23.an_dd $2$ $\F_{23}$ $1 - 13 x + 81 x^{2} - 299 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-170 +26 \sqrt{29}})\) $D_{4}$ simple
2.23.an_de $2$ $\F_{23}$ $( 1 - 9 x + 23 x^{2} )( 1 - 4 x + 23 x^{2} )$ $2$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-19}) \) $C_2$, $C_2$ 1.23.aj $\times$ 1.23.ae
2.23.an_df $2$ $\F_{23}$ $1 - 13 x + 83 x^{2} - 299 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-178 +26 \sqrt{21}})\) $D_{4}$ simple
2.23.an_dg $2$ $\F_{23}$ $1 - 13 x + 84 x^{2} - 299 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-182 +26 \sqrt{17}})\) $D_{4}$ simple
2.23.an_dh $2$ $\F_{23}$ $1 - 13 x + 85 x^{2} - 299 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-186 +26 \sqrt{13}})\) $D_{4}$ simple
2.23.an_di $2$ $\F_{23}$ $( 1 - 8 x + 23 x^{2} )( 1 - 5 x + 23 x^{2} )$ $2$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-67}) \) $C_2$, $C_2$ 1.23.ai $\times$ 1.23.af
2.23.an_dj $2$ $\F_{23}$ $1 - 13 x + 87 x^{2} - 299 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-194 +26 \sqrt{5}})\) $D_{4}$ simple
2.23.an_dk $2$ $\F_{23}$ $( 1 - 7 x + 23 x^{2} )( 1 - 6 x + 23 x^{2} )$ $2$ \(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-14}) \) $C_2$, $C_2$ 1.23.ah $\times$ 1.23.ag
2.23.am_cs $2$ $\F_{23}$ $1 - 12 x + 70 x^{2} - 276 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-8 -2 \sqrt{3}})\) $D_{4}$ simple
2.23.am_ct $2$ $\F_{23}$ $1 - 12 x + 71 x^{2} - 276 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{11})\) $C_2^2$ simple
2.23.am_cu $2$ $\F_{23}$ $1 - 12 x + 72 x^{2} - 276 x^{3} + 529 x^{4}$ $2$ \(\Q(i, \sqrt{10})\) $C_2^2$ simple
2.23.am_cv $2$ $\F_{23}$ $( 1 - 9 x + 23 x^{2} )( 1 - 3 x + 23 x^{2} )$ $2$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-83}) \) $C_2$, $C_2$ 1.23.aj $\times$ 1.23.ad
2.23.am_cw $2$ $\F_{23}$ $1 - 12 x + 74 x^{2} - 276 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-6 +3 \sqrt{2}})\) $C_4$ simple
2.23.am_cx $2$ $\F_{23}$ $1 - 12 x + 75 x^{2} - 276 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-49 +12 \sqrt{7}})\) $D_{4}$ simple
2.23.am_cy $2$ $\F_{23}$ $1 - 12 x + 76 x^{2} - 276 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-50 +12 \sqrt{6}})\) $D_{4}$ simple
2.23.am_cz $2$ $\F_{23}$ $1 - 12 x + 77 x^{2} - 276 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-186 -30 \sqrt{5}})\) $D_{4}$ simple
2.23.am_da $2$ $\F_{23}$ $( 1 - 8 x + 23 x^{2} )( 1 - 4 x + 23 x^{2} )$ $2$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-19}) \) $C_2$, $C_2$ 1.23.ai $\times$ 1.23.ae
2.23.am_db $2$ $\F_{23}$ $1 - 12 x + 79 x^{2} - 276 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-53 +12 \sqrt{3}})\) $D_{4}$ simple
2.23.am_dc $2$ $\F_{23}$ $1 - 12 x + 80 x^{2} - 276 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-54 +12 \sqrt{2}})\) $D_{4}$ simple
2.23.am_dd $2$ $\F_{23}$ $( 1 - 7 x + 23 x^{2} )( 1 - 5 x + 23 x^{2} )$ $2$ \(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-67}) \) $C_2$, $C_2$ 1.23.ah $\times$ 1.23.af
2.23.am_de $2$ $\F_{23}$ $( 1 - 6 x + 23 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-14}) \) $C_2$ 1.23.ag 2
2.23.al_ci $2$ $\F_{23}$ $1 - 11 x + 60 x^{2} - 253 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-13 + \sqrt{65}})\) $D_{4}$ simple
2.23.al_cj $2$ $\F_{23}$ $1 - 11 x + 61 x^{2} - 253 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-186 -22 \sqrt{61}})\) $D_{4}$ simple
2.23.al_ck $2$ $\F_{23}$ $1 - 11 x + 62 x^{2} - 253 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-57 +6 \sqrt{57}})\) $D_{4}$ simple
2.23.al_cl $2$ $\F_{23}$ $1 - 11 x + 63 x^{2} - 253 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-194 -22 \sqrt{53}})\) $D_{4}$ simple
2.23.al_cm $2$ $\F_{23}$ $( 1 - 9 x + 23 x^{2} )( 1 - 2 x + 23 x^{2} )$ $2$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-22}) \) $C_2$, $C_2$ 1.23.aj $\times$ 1.23.ac
2.23.al_cn $2$ $\F_{23}$ $1 - 11 x + 65 x^{2} - 253 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-138 +2 \sqrt{5}})\) $D_{4}$ simple
2.23.al_co $2$ $\F_{23}$ $1 - 11 x + 66 x^{2} - 253 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-206 -22 \sqrt{41}})\) $D_{4}$ simple
2.23.al_cp $2$ $\F_{23}$ $1 - 11 x + 67 x^{2} - 253 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-210 -22 \sqrt{37}})\) $D_{4}$ simple
2.23.al_cq $2$ $\F_{23}$ $1 - 11 x + 68 x^{2} - 253 x^{3} + 529 x^{4}$ $2$ \(\Q(\sqrt{-214 -22 \sqrt{33}})\) $D_{4}$ simple
2.23.al_cr $2$ $\F_{23}$ $1 - 11 x + 69 x^{2} - 253 x^{3} + 529 x^{4}$ $1$ \(\Q(\sqrt{-218 -22 \sqrt{29}})\) $D_{4}$ simple
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