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

Refine search

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
Cyclic group of points Non-cyclic primes
Use Geometric decomposition in the following inputs
Dim 1 factors Dim 2 factors Dim 3 factors Dim 4 factors Dim 5 factors
(distinct) (distinct) (distinct) Number field Galois group
Sort order Select

Results (1-50 of 2425 matches)

Next   displayed columns for results
Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
2.37.ay_ik $2$ $\F_{37}$ $( 1 - 12 x + 37 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-1}) \) $C_2$ 1.37.am 2
2.37.ax_hy $2$ $\F_{37}$ $( 1 - 12 x + 37 x^{2} )( 1 - 11 x + 37 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.37.am $\times$ 1.37.al
2.37.aw_hm $2$ $\F_{37}$ $( 1 - 12 x + 37 x^{2} )( 1 - 10 x + 37 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.37.am $\times$ 1.37.ak
2.37.aw_hn $2$ $\F_{37}$ $( 1 - 11 x + 37 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-3}) \) $C_2$ 1.37.al 2
2.37.av_ha $2$ $\F_{37}$ $( 1 - 12 x + 37 x^{2} )( 1 - 9 x + 37 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-67}) \) $C_2$, $C_2$ 1.37.am $\times$ 1.37.aj
2.37.av_hb $2$ $\F_{37}$ $1 - 21 x + 183 x^{2} - 777 x^{3} + 1369 x^{4}$ $2$ \(\Q(\sqrt{-114 +10 \sqrt{5}})\) $D_{4}$ simple
2.37.av_hc $2$ $\F_{37}$ $( 1 - 11 x + 37 x^{2} )( 1 - 10 x + 37 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.37.al $\times$ 1.37.ak
2.37.au_go $2$ $\F_{37}$ $( 1 - 12 x + 37 x^{2} )( 1 - 8 x + 37 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-21}) \) $C_2$, $C_2$ 1.37.am $\times$ 1.37.ai
2.37.au_gp $2$ $\F_{37}$ $1 - 20 x + 171 x^{2} - 740 x^{3} + 1369 x^{4}$ $2$ \(\Q(\sqrt{-45 +20 \sqrt{3}})\) $D_{4}$ simple
2.37.au_gq $2$ $\F_{37}$ $1 - 20 x + 172 x^{2} - 740 x^{3} + 1369 x^{4}$ $2$ \(\Q(\sqrt{-46 +20 \sqrt{2}})\) $D_{4}$ simple
2.37.au_gr $2$ $\F_{37}$ $( 1 - 11 x + 37 x^{2} )( 1 - 9 x + 37 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-67}) \) $C_2$, $C_2$ 1.37.al $\times$ 1.37.aj
2.37.au_gs $2$ $\F_{37}$ $( 1 - 10 x + 37 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-3}) \) $C_2$ 1.37.ak 2
2.37.at_gc $2$ $\F_{37}$ $( 1 - 12 x + 37 x^{2} )( 1 - 7 x + 37 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-11}) \) $C_2$, $C_2$ 1.37.am $\times$ 1.37.ah
2.37.at_gd $2$ $\F_{37}$ $1 - 19 x + 159 x^{2} - 703 x^{3} + 1369 x^{4}$ $2$ \(\Q(\sqrt{-210 -38 \sqrt{21}})\) $D_{4}$ simple
2.37.at_ge $2$ $\F_{37}$ $1 - 19 x + 160 x^{2} - 703 x^{3} + 1369 x^{4}$ $2$ \(\Q(\sqrt{-10 + \sqrt{17}})\) $D_{4}$ simple
2.37.at_gf $2$ $\F_{37}$ $1 - 19 x + 161 x^{2} - 703 x^{3} + 1369 x^{4}$ $2$ \(\Q(\sqrt{-218 -38 \sqrt{13}})\) $D_{4}$ simple
2.37.at_gg $2$ $\F_{37}$ $( 1 - 11 x + 37 x^{2} )( 1 - 8 x + 37 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-21}) \) $C_2$, $C_2$ 1.37.al $\times$ 1.37.ai
2.37.at_gh $2$ $\F_{37}$ $1 - 19 x + 163 x^{2} - 703 x^{3} + 1369 x^{4}$ $2$ \(\Q(\sqrt{-226 -38 \sqrt{5}})\) $D_{4}$ simple
2.37.at_gi $2$ $\F_{37}$ $( 1 - 10 x + 37 x^{2} )( 1 - 9 x + 37 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-67}) \) $C_2$, $C_2$ 1.37.ak $\times$ 1.37.aj
2.37.as_fp $2$ $\F_{37}$ $1 - 18 x + 145 x^{2} - 666 x^{3} + 1369 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{10})\) $C_2^2$ simple
2.37.as_fq $2$ $\F_{37}$ $( 1 - 12 x + 37 x^{2} )( 1 - 6 x + 37 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) $C_2$, $C_2$ 1.37.am $\times$ 1.37.ag
2.37.as_fr $2$ $\F_{37}$ $1 - 18 x + 147 x^{2} - 666 x^{3} + 1369 x^{4}$ $2$ \(\Q(\sqrt{-33 -10 \sqrt{2}})\) $D_{4}$ simple
2.37.as_fs $2$ $\F_{37}$ $1 - 18 x + 148 x^{2} - 666 x^{3} + 1369 x^{4}$ $1$ \(\Q(\sqrt{-60 -18 \sqrt{7}})\) $D_{4}$ simple
2.37.as_ft $2$ $\F_{37}$ $1 - 18 x + 149 x^{2} - 666 x^{3} + 1369 x^{4}$ $2$ \(\Q(\sqrt{-61 -18 \sqrt{6}})\) $D_{4}$ simple
2.37.as_fu $2$ $\F_{37}$ $1 - 18 x + 150 x^{2} - 666 x^{3} + 1369 x^{4}$ $2$ \(\Q(\sqrt{-12 + \sqrt{5}})\) $D_{4}$ simple
2.37.as_fv $2$ $\F_{37}$ $( 1 - 11 x + 37 x^{2} )( 1 - 7 x + 37 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-11}) \) $C_2$, $C_2$ 1.37.al $\times$ 1.37.ah
2.37.as_fw $2$ $\F_{37}$ $1 - 18 x + 152 x^{2} - 666 x^{3} + 1369 x^{4}$ $2$ \(\Q(\sqrt{-64 -18 \sqrt{3}})\) $D_{4}$ simple
2.37.as_fx $2$ $\F_{37}$ $1 - 18 x + 153 x^{2} - 666 x^{3} + 1369 x^{4}$ $2$ \(\Q(\sqrt{-9 -2 \sqrt{2}})\) $D_{4}$ simple
2.37.as_fy $2$ $\F_{37}$ $( 1 - 10 x + 37 x^{2} )( 1 - 8 x + 37 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-21}) \) $C_2$, $C_2$ 1.37.ak $\times$ 1.37.ai
2.37.as_fz $2$ $\F_{37}$ $( 1 - 9 x + 37 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-67}) \) $C_2$ 1.37.aj 2
2.37.ar_fd $2$ $\F_{37}$ $1 - 17 x + 133 x^{2} - 629 x^{3} + 1369 x^{4}$ $2$ \(\Q(\sqrt{-17 +2 \sqrt{53}})\) $D_{4}$ simple
2.37.ar_fe $2$ $\F_{37}$ $( 1 - 12 x + 37 x^{2} )( 1 - 5 x + 37 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-123}) \) $C_2$, $C_2$ 1.37.am $\times$ 1.37.af
2.37.ar_ff $2$ $\F_{37}$ $1 - 17 x + 135 x^{2} - 629 x^{3} + 1369 x^{4}$ $2$ \(\Q(\sqrt{-33 +6 \sqrt{5}})\) $D_{4}$ simple
2.37.ar_fg $2$ $\F_{37}$ $1 - 17 x + 136 x^{2} - 629 x^{3} + 1369 x^{4}$ $2$ \(\Q(\sqrt{-74 +2 \sqrt{41}})\) $D_{4}$ simple
2.37.ar_fh $2$ $\F_{37}$ $1 - 17 x + 137 x^{2} - 629 x^{3} + 1369 x^{4}$ $2$ \(\Q(\sqrt{-266 +34 \sqrt{37}})\) $D_{4}$ simple
2.37.ar_fi $2$ $\F_{37}$ $1 - 17 x + 138 x^{2} - 629 x^{3} + 1369 x^{4}$ $2$ \(\Q(\sqrt{-270 +34 \sqrt{33}})\) $D_{4}$ simple
2.37.ar_fj $2$ $\F_{37}$ $1 - 17 x + 139 x^{2} - 629 x^{3} + 1369 x^{4}$ $2$ \(\Q(\sqrt{-13 +2 \sqrt{29}})\) $D_{4}$ simple
2.37.ar_fk $2$ $\F_{37}$ $( 1 - 11 x + 37 x^{2} )( 1 - 6 x + 37 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \) $C_2$, $C_2$ 1.37.al $\times$ 1.37.ag
2.37.ar_fl $2$ $\F_{37}$ $1 - 17 x + 141 x^{2} - 629 x^{3} + 1369 x^{4}$ $2$ \(\Q(\sqrt{-282 +34 \sqrt{21}})\) $D_{4}$ simple
2.37.ar_fm $2$ $\F_{37}$ $1 - 17 x + 142 x^{2} - 629 x^{3} + 1369 x^{4}$ $2$ \(\Q(\sqrt{-286 +34 \sqrt{17}})\) $D_{4}$ simple
2.37.ar_fn $2$ $\F_{37}$ $1 - 17 x + 143 x^{2} - 629 x^{3} + 1369 x^{4}$ $2$ \(\Q(\sqrt{-290 +34 \sqrt{13}})\) $D_{4}$ simple
2.37.ar_fo $2$ $\F_{37}$ $( 1 - 10 x + 37 x^{2} )( 1 - 7 x + 37 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-11}) \) $C_2$, $C_2$ 1.37.ak $\times$ 1.37.ah
2.37.ar_fp $2$ $\F_{37}$ $1 - 17 x + 145 x^{2} - 629 x^{3} + 1369 x^{4}$ $2$ \(\Q(\sqrt{-298 +34 \sqrt{5}})\) $D_{4}$ simple
2.37.ar_fq $2$ $\F_{37}$ $( 1 - 9 x + 37 x^{2} )( 1 - 8 x + 37 x^{2} )$ $2$ \(\Q(\sqrt{-67}) \), \(\Q(\sqrt{-21}) \) $C_2$, $C_2$ 1.37.aj $\times$ 1.37.ai
2.37.aq_er $2$ $\F_{37}$ $1 - 16 x + 121 x^{2} - 592 x^{3} + 1369 x^{4}$ $2$ \(\Q(\sqrt{-94 +2 \sqrt{17}})\) $D_{4}$ simple
2.37.aq_es $2$ $\F_{37}$ $( 1 - 12 x + 37 x^{2} )( 1 - 4 x + 37 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-33}) \) $C_2$, $C_2$ 1.37.am $\times$ 1.37.ae
2.37.aq_et $2$ $\F_{37}$ $1 - 16 x + 123 x^{2} - 592 x^{3} + 1369 x^{4}$ $2$ \(\Q(\sqrt{-69 +16 \sqrt{15}})\) $D_{4}$ simple
2.37.aq_eu $2$ $\F_{37}$ $1 - 16 x + 124 x^{2} - 592 x^{3} + 1369 x^{4}$ $2$ \(\Q(\sqrt{-70 +16 \sqrt{14}})\) $D_{4}$ simple
2.37.aq_ev $2$ $\F_{37}$ $1 - 16 x + 125 x^{2} - 592 x^{3} + 1369 x^{4}$ $2$ \(\Q(\sqrt{-71 +16 \sqrt{13}})\) $D_{4}$ simple
2.37.aq_ew $2$ $\F_{37}$ $1 - 16 x + 126 x^{2} - 592 x^{3} + 1369 x^{4}$ $2$ \(\Q(\sqrt{-6 + \sqrt{3}})\) $D_{4}$ simple
Next   displayed columns for results