↑

Learn more

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 1861 matches)

Next   displayed columns for results
Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
2.31.aw_hb $2$ $\F_{31}$ $( 1 - 11 x + 31 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-3}) \) $C_2$ 1.31.al 2
2.31.av_gq $2$ $\F_{31}$ $( 1 - 11 x + 31 x^{2} )( 1 - 10 x + 31 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-6}) \) $C_2$, $C_2$ 1.31.al $\times$ 1.31.ak
2.31.au_gf $2$ $\F_{31}$ $( 1 - 11 x + 31 x^{2} )( 1 - 9 x + 31 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-43}) \) $C_2$, $C_2$ 1.31.al $\times$ 1.31.aj
2.31.au_gg $2$ $\F_{31}$ $( 1 - 10 x + 31 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-6}) \) $C_2$ 1.31.ak 2
2.31.at_fu $2$ $\F_{31}$ $( 1 - 11 x + 31 x^{2} )( 1 - 8 x + 31 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-15}) \) $C_2$, $C_2$ 1.31.al $\times$ 1.31.ai
2.31.at_fv $2$ $\F_{31}$ $1 - 19 x + 151 x^{2} - 589 x^{3} + 961 x^{4}$ $2$ \(\Q(\zeta_{5})\) $C_4$ simple
2.31.at_fw $2$ $\F_{31}$ $( 1 - 10 x + 31 x^{2} )( 1 - 9 x + 31 x^{2} )$ $2$ \(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-43}) \) $C_2$, $C_2$ 1.31.ak $\times$ 1.31.aj
2.31.as_fj $2$ $\F_{31}$ $( 1 - 11 x + 31 x^{2} )( 1 - 7 x + 31 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.31.al $\times$ 1.31.ah
2.31.as_fk $2$ $\F_{31}$ $1 - 18 x + 140 x^{2} - 558 x^{3} + 961 x^{4}$ $2$ \(\Q(\sqrt{-40 -18 \sqrt{3}})\) $D_{4}$ simple
2.31.as_fl $2$ $\F_{31}$ $1 - 18 x + 141 x^{2} - 558 x^{3} + 961 x^{4}$ $2$ \(\Q(\sqrt{-41 -18 \sqrt{2}})\) $D_{4}$ simple
2.31.as_fm $2$ $\F_{31}$ $( 1 - 10 x + 31 x^{2} )( 1 - 8 x + 31 x^{2} )$ $2$ \(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-15}) \) $C_2$, $C_2$ 1.31.ak $\times$ 1.31.ai
2.31.as_fn $2$ $\F_{31}$ $( 1 - 9 x + 31 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-43}) \) $C_2$ 1.31.aj 2
2.31.ar_ey $2$ $\F_{31}$ $( 1 - 11 x + 31 x^{2} )( 1 - 6 x + 31 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-22}) \) $C_2$, $C_2$ 1.31.al $\times$ 1.31.ag
2.31.ar_ez $2$ $\F_{31}$ $1 - 17 x + 129 x^{2} - 527 x^{3} + 961 x^{4}$ $2$ \(\Q(\sqrt{-186 +34 \sqrt{21}})\) $D_{4}$ simple
2.31.ar_fa $2$ $\F_{31}$ $1 - 17 x + 130 x^{2} - 527 x^{3} + 961 x^{4}$ $2$ \(\Q(\sqrt{-23 +4 \sqrt{17}})\) $D_{4}$ simple
2.31.ar_fb $2$ $\F_{31}$ $1 - 17 x + 131 x^{2} - 527 x^{3} + 961 x^{4}$ $2$ \(\Q(\sqrt{-82 +18 \sqrt{13}})\) $D_{4}$ simple
2.31.ar_fc $2$ $\F_{31}$ $( 1 - 10 x + 31 x^{2} )( 1 - 7 x + 31 x^{2} )$ $2$ \(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.31.ak $\times$ 1.31.ah
2.31.ar_fd $2$ $\F_{31}$ $1 - 17 x + 133 x^{2} - 527 x^{3} + 961 x^{4}$ $2$ \(\Q(\sqrt{-202 +34 \sqrt{5}})\) $D_{4}$ simple
2.31.ar_fe $2$ $\F_{31}$ $( 1 - 9 x + 31 x^{2} )( 1 - 8 x + 31 x^{2} )$ $2$ \(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-15}) \) $C_2$, $C_2$ 1.31.aj $\times$ 1.31.ai
2.31.aq_en $2$ $\F_{31}$ $( 1 - 11 x + 31 x^{2} )( 1 - 5 x + 31 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-11}) \) $C_2$, $C_2$ 1.31.al $\times$ 1.31.af
2.31.aq_eo $2$ $\F_{31}$ $1 - 16 x + 118 x^{2} - 496 x^{3} + 961 x^{4}$ $2$ \(\Q(\sqrt{-14 +4 \sqrt{2}})\) $D_{4}$ simple
2.31.aq_ep $2$ $\F_{31}$ $1 - 16 x + 119 x^{2} - 496 x^{3} + 961 x^{4}$ $2$ \(\Q(\sqrt{-15 +4 \sqrt{7}})\) $D_{4}$ simple
2.31.aq_eq $2$ $\F_{31}$ $1 - 16 x + 120 x^{2} - 496 x^{3} + 961 x^{4}$ $2$ \(\Q(\sqrt{-54 +16 \sqrt{6}})\) $D_{4}$ simple
2.31.aq_er $2$ $\F_{31}$ $1 - 16 x + 121 x^{2} - 496 x^{3} + 961 x^{4}$ $2$ \(\Q(\sqrt{-170 -14 \sqrt{5}})\) $D_{4}$ simple
2.31.aq_es $2$ $\F_{31}$ $( 1 - 10 x + 31 x^{2} )( 1 - 6 x + 31 x^{2} )$ $2$ \(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-22}) \) $C_2$, $C_2$ 1.31.ak $\times$ 1.31.ag
2.31.aq_et $2$ $\F_{31}$ $1 - 16 x + 123 x^{2} - 496 x^{3} + 961 x^{4}$ $2$ \(\Q(\sqrt{-57 +16 \sqrt{3}})\) $D_{4}$ simple
2.31.aq_eu $2$ $\F_{31}$ $1 - 16 x + 124 x^{2} - 496 x^{3} + 961 x^{4}$ $1$ \(\Q(\sqrt{-58 +16 \sqrt{2}})\) $D_{4}$ simple
2.31.aq_ev $2$ $\F_{31}$ $( 1 - 9 x + 31 x^{2} )( 1 - 7 x + 31 x^{2} )$ $2$ \(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.31.aj $\times$ 1.31.ah
2.31.aq_ew $2$ $\F_{31}$ $( 1 - 8 x + 31 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-15}) \) $C_2$ 1.31.ai 2
2.31.ap_ec $2$ $\F_{31}$ $( 1 - 11 x + 31 x^{2} )( 1 - 4 x + 31 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.31.al $\times$ 1.31.ae
2.31.ap_ed $2$ $\F_{31}$ $1 - 15 x + 107 x^{2} - 465 x^{3} + 961 x^{4}$ $2$ \(\Q(\sqrt{-29 +6 \sqrt{5}})\) $D_{4}$ simple
2.31.ap_ee $2$ $\F_{31}$ $1 - 15 x + 108 x^{2} - 465 x^{3} + 961 x^{4}$ $2$ \(\Q(\sqrt{-18 +2 \sqrt{41}})\) $D_{4}$ simple
2.31.ap_ef $2$ $\F_{31}$ $1 - 15 x + 109 x^{2} - 465 x^{3} + 961 x^{4}$ $2$ \(\Q(\sqrt{-234 -30 \sqrt{37}})\) $D_{4}$ simple
2.31.ap_eg $2$ $\F_{31}$ $1 - 15 x + 110 x^{2} - 465 x^{3} + 961 x^{4}$ $2$ \(\Q(\sqrt{-61 +10 \sqrt{33}})\) $D_{4}$ simple
2.31.ap_eh $2$ $\F_{31}$ $1 - 15 x + 111 x^{2} - 465 x^{3} + 961 x^{4}$ $2$ \(\Q(\sqrt{-242 -30 \sqrt{29}})\) $D_{4}$ simple
2.31.ap_ei $2$ $\F_{31}$ $( 1 - 10 x + 31 x^{2} )( 1 - 5 x + 31 x^{2} )$ $2$ \(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-11}) \) $C_2$, $C_2$ 1.31.ak $\times$ 1.31.af
2.31.ap_ej $2$ $\F_{31}$ $1 - 15 x + 113 x^{2} - 465 x^{3} + 961 x^{4}$ $2$ \(\Q(\sqrt{-250 -30 \sqrt{21}})\) $D_{4}$ simple
2.31.ap_ek $2$ $\F_{31}$ $1 - 15 x + 114 x^{2} - 465 x^{3} + 961 x^{4}$ $2$ \(\Q(\sqrt{-222 +2 \sqrt{17}})\) $D_{4}$ simple
2.31.ap_el $2$ $\F_{31}$ $1 - 15 x + 115 x^{2} - 465 x^{3} + 961 x^{4}$ $2$ \(\Q(\sqrt{-122 +26 \sqrt{13}})\) $D_{4}$ simple
2.31.ap_em $2$ $\F_{31}$ $( 1 - 9 x + 31 x^{2} )( 1 - 6 x + 31 x^{2} )$ $2$ \(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-22}) \) $C_2$, $C_2$ 1.31.aj $\times$ 1.31.ag
2.31.ap_en $2$ $\F_{31}$ $1 - 15 x + 117 x^{2} - 465 x^{3} + 961 x^{4}$ $2$ \(\Q(\sqrt{-266 -30 \sqrt{5}})\) $D_{4}$ simple
2.31.ap_eo $2$ $\F_{31}$ $( 1 - 8 x + 31 x^{2} )( 1 - 7 x + 31 x^{2} )$ $2$ \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.31.ai $\times$ 1.31.ah
2.31.ao_dq $2$ $\F_{31}$ $1 - 14 x + 94 x^{2} - 434 x^{3} + 961 x^{4}$ $2$ \(\Q(\sqrt{-14 +2 \sqrt{17}})\) $D_{4}$ simple
2.31.ao_dr $2$ $\F_{31}$ $( 1 - 11 x + 31 x^{2} )( 1 - 3 x + 31 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-115}) \) $C_2$, $C_2$ 1.31.al $\times$ 1.31.ad
2.31.ao_ds $2$ $\F_{31}$ $1 - 14 x + 96 x^{2} - 434 x^{3} + 961 x^{4}$ $2$ \(\Q(\sqrt{-60 -14 \sqrt{15}})\) $D_{4}$ simple
2.31.ao_dt $2$ $\F_{31}$ $1 - 14 x + 97 x^{2} - 434 x^{3} + 961 x^{4}$ $2$ \(\Q(\sqrt{-61 -14 \sqrt{14}})\) $D_{4}$ simple
2.31.ao_du $2$ $\F_{31}$ $1 - 14 x + 98 x^{2} - 434 x^{3} + 961 x^{4}$ $2$ \(\Q(i, \sqrt{13})\) $C_2^2$ simple
2.31.ao_dv $2$ $\F_{31}$ $1 - 14 x + 99 x^{2} - 434 x^{3} + 961 x^{4}$ $2$ \(\Q(\sqrt{-63 +28 \sqrt{3}})\) $D_{4}$ simple
2.31.ao_dw $2$ $\F_{31}$ $1 - 14 x + 100 x^{2} - 434 x^{3} + 961 x^{4}$ $2$ \(\Q(\sqrt{-64 -14 \sqrt{11}})\) $D_{4}$ simple
2.31.ao_dx $2$ $\F_{31}$ $1 - 14 x + 101 x^{2} - 434 x^{3} + 961 x^{4}$ $2$ \(\Q(\sqrt{-65 -14 \sqrt{10}})\) $D_{4}$ simple
Next   displayed columns for results