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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
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Newton elevation # Jacobians # Hyp. Jacobians # twists Max twist degree
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Results (1-50 of 401 matches)

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Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
2.11.am_cg $2$ $\F_{11}$ $( 1 - 6 x + 11 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-2}) \) $C_2$ 1.11.ag 2
2.11.al_bz $2$ $\F_{11}$ $1 - 11 x + 51 x^{2} - 121 x^{3} + 121 x^{4}$ $2$ \(\Q(\zeta_{5})\) $C_4$ simple
2.11.al_ca $2$ $\F_{11}$ $( 1 - 6 x + 11 x^{2} )( 1 - 5 x + 11 x^{2} )$ $2$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-19}) \) $C_2$, $C_2$ 1.11.ag $\times$ 1.11.af
2.11.ak_bt $2$ $\F_{11}$ $1 - 10 x + 45 x^{2} - 110 x^{3} + 121 x^{4}$ $2$ 4.0.5696.1 $D_{4}$ simple
2.11.ak_bu $2$ $\F_{11}$ $( 1 - 6 x + 11 x^{2} )( 1 - 4 x + 11 x^{2} )$ $2$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-7}) \) $C_2$, $C_2$ 1.11.ag $\times$ 1.11.ae
2.11.ak_bv $2$ $\F_{11}$ $( 1 - 5 x + 11 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-19}) \) $C_2$ 1.11.af 2
2.11.aj_bm $2$ $\F_{11}$ $1 - 9 x + 38 x^{2} - 99 x^{3} + 121 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{17})\) $C_2^2$ simple
2.11.aj_bn $2$ $\F_{11}$ $1 - 9 x + 39 x^{2} - 99 x^{3} + 121 x^{4}$ $2$ 4.0.26533.1 $D_{4}$ simple
2.11.aj_bo $2$ $\F_{11}$ $( 1 - 6 x + 11 x^{2} )( 1 - 3 x + 11 x^{2} )$ $2$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-35}) \) $C_2$, $C_2$ 1.11.ag $\times$ 1.11.ad
2.11.aj_bp $2$ $\F_{11}$ $1 - 9 x + 41 x^{2} - 99 x^{3} + 121 x^{4}$ $2$ \(\Q(\zeta_{5})\) $C_4$ simple
2.11.aj_bq $2$ $\F_{11}$ $( 1 - 5 x + 11 x^{2} )( 1 - 4 x + 11 x^{2} )$ $2$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-7}) \) $C_2$, $C_2$ 1.11.af $\times$ 1.11.ae
2.11.ai_bg $2$ $\F_{11}$ $1 - 8 x + 32 x^{2} - 88 x^{3} + 121 x^{4}$ $2$ \(\Q(i, \sqrt{6})\) $C_2^2$ simple
2.11.ai_bh $2$ $\F_{11}$ $1 - 8 x + 33 x^{2} - 88 x^{3} + 121 x^{4}$ $1$ 4.0.5225.1 $D_{4}$ simple
2.11.ai_bi $2$ $\F_{11}$ $( 1 - 6 x + 11 x^{2} )( 1 - 2 x + 11 x^{2} )$ $2$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-10}) \) $C_2$, $C_2$ 1.11.ag $\times$ 1.11.ac
2.11.ai_bj $2$ $\F_{11}$ $1 - 8 x + 35 x^{2} - 88 x^{3} + 121 x^{4}$ $2$ 4.0.62352.1 $D_{4}$ simple
2.11.ai_bk $2$ $\F_{11}$ $1 - 8 x + 36 x^{2} - 88 x^{3} + 121 x^{4}$ $2$ 4.0.35072.1 $D_{4}$ simple
2.11.ai_bl $2$ $\F_{11}$ $( 1 - 5 x + 11 x^{2} )( 1 - 3 x + 11 x^{2} )$ $2$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-35}) \) $C_2$, $C_2$ 1.11.af $\times$ 1.11.ad
2.11.ai_bm $2$ $\F_{11}$ $( 1 - 4 x + 11 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-7}) \) $C_2$ 1.11.ae 2
2.11.ah_z $2$ $\F_{11}$ $1 - 7 x + 25 x^{2} - 77 x^{3} + 121 x^{4}$ $2$ 4.0.72557.1 $D_{4}$ simple
2.11.ah_ba $2$ $\F_{11}$ $1 - 7 x + 26 x^{2} - 77 x^{3} + 121 x^{4}$ $2$ 4.0.40293.1 $D_{4}$ simple
2.11.ah_bb $2$ $\F_{11}$ $1 - 7 x + 27 x^{2} - 77 x^{3} + 121 x^{4}$ $2$ 4.0.206045.1 $D_{4}$ simple
2.11.ah_bc $2$ $\F_{11}$ $( 1 - 6 x + 11 x^{2} )( 1 - x + 11 x^{2} )$ $2$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-43}) \) $C_2$, $C_2$ 1.11.ag $\times$ 1.11.ab
2.11.ah_bd $2$ $\F_{11}$ $1 - 7 x + 29 x^{2} - 77 x^{3} + 121 x^{4}$ $2$ 4.0.196245.1 $D_{4}$ simple
2.11.ah_be $2$ $\F_{11}$ $1 - 7 x + 30 x^{2} - 77 x^{3} + 121 x^{4}$ $2$ 4.0.39593.1 $D_{4}$ simple
2.11.ah_bf $2$ $\F_{11}$ $1 - 7 x + 31 x^{2} - 77 x^{3} + 121 x^{4}$ $2$ 4.0.110357.1 $D_{4}$ simple
2.11.ah_bg $2$ $\F_{11}$ $( 1 - 5 x + 11 x^{2} )( 1 - 2 x + 11 x^{2} )$ $2$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-10}) \) $C_2$, $C_2$ 1.11.af $\times$ 1.11.ac
2.11.ah_bh $2$ $\F_{11}$ $1 - 7 x + 33 x^{2} - 77 x^{3} + 121 x^{4}$ $1$ 4.0.21725.1 $D_{4}$ simple
2.11.ah_bi $2$ $\F_{11}$ $( 1 - 4 x + 11 x^{2} )( 1 - 3 x + 11 x^{2} )$ $2$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-35}) \) $C_2$, $C_2$ 1.11.ae $\times$ 1.11.ad
2.11.ag_s $2$ $\F_{11}$ $1 - 6 x + 18 x^{2} - 66 x^{3} + 121 x^{4}$ $2$ \(\Q(i, \sqrt{13})\) $C_2^2$ simple
2.11.ag_t $2$ $\F_{11}$ $1 - 6 x + 19 x^{2} - 66 x^{3} + 121 x^{4}$ $2$ 4.0.13968.2 $D_{4}$ simple
2.11.ag_u $2$ $\F_{11}$ $1 - 6 x + 20 x^{2} - 66 x^{3} + 121 x^{4}$ $2$ 4.0.348480.1 $D_{4}$ simple
2.11.ag_v $2$ $\F_{11}$ $1 - 6 x + 21 x^{2} - 66 x^{3} + 121 x^{4}$ $2$ 4.0.424000.2 $D_{4}$ simple
2.11.ag_w $2$ $\F_{11}$ $( 1 - 6 x + 11 x^{2} )( 1 + 11 x^{2} )$ $1$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-11}) \) $C_2$, $C_2$ 1.11.ag $\times$ 1.11.a
2.11.ag_x $2$ $\F_{11}$ $1 - 6 x + 23 x^{2} - 66 x^{3} + 121 x^{4}$ $2$ \(\Q(\sqrt{2}, \sqrt{-3})\) $C_2^2$ simple
2.11.ag_y $2$ $\F_{11}$ $1 - 6 x + 24 x^{2} - 66 x^{3} + 121 x^{4}$ $2$ 4.0.417088.1 $D_{4}$ simple
2.11.ag_z $2$ $\F_{11}$ $1 - 6 x + 25 x^{2} - 66 x^{3} + 121 x^{4}$ $2$ \(\Q(\sqrt{-2}, \sqrt{-3})\) $C_2^2$ simple
2.11.ag_ba $2$ $\F_{11}$ $1 - 6 x + 26 x^{2} - 66 x^{3} + 121 x^{4}$ $2$ 4.0.18000.1 $C_4$ simple
2.11.ag_bb $2$ $\F_{11}$ $( 1 - 5 x + 11 x^{2} )( 1 - x + 11 x^{2} )$ $2$ \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-43}) \) $C_2$, $C_2$ 1.11.af $\times$ 1.11.ab
2.11.ag_bc $2$ $\F_{11}$ $1 - 6 x + 28 x^{2} - 66 x^{3} + 121 x^{4}$ $2$ 4.0.131904.1 $D_{4}$ simple
2.11.ag_bd $2$ $\F_{11}$ $1 - 6 x + 29 x^{2} - 66 x^{3} + 121 x^{4}$ $2$ 4.0.65088.2 $D_{4}$ simple
2.11.ag_be $2$ $\F_{11}$ $( 1 - 4 x + 11 x^{2} )( 1 - 2 x + 11 x^{2} )$ $2$ \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-10}) \) $C_2$, $C_2$ 1.11.ae $\times$ 1.11.ac
2.11.ag_bf $2$ $\F_{11}$ $( 1 - 3 x + 11 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-35}) \) $C_2$ 1.11.ad 2
2.11.af_m $2$ $\F_{11}$ $1 - 5 x + 12 x^{2} - 55 x^{3} + 121 x^{4}$ $2$ 4.0.236600.1 $D_{4}$ simple
2.11.af_n $2$ $\F_{11}$ $1 - 5 x + 13 x^{2} - 55 x^{3} + 121 x^{4}$ $2$ 4.0.18605.1 $D_{4}$ simple
2.11.af_o $2$ $\F_{11}$ $1 - 5 x + 14 x^{2} - 55 x^{3} + 121 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{-19})\) $C_2^2$ simple
2.11.af_p $2$ $\F_{11}$ $1 - 5 x + 15 x^{2} - 55 x^{3} + 121 x^{4}$ $2$ 4.0.755621.1 $D_{4}$ simple
2.11.af_q $2$ $\F_{11}$ $( 1 - 6 x + 11 x^{2} )( 1 + x + 11 x^{2} )$ $2$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-43}) \) $C_2$, $C_2$ 1.11.ag $\times$ 1.11.b
2.11.af_r $2$ $\F_{11}$ $1 - 5 x + 17 x^{2} - 55 x^{3} + 121 x^{4}$ $2$ 4.0.10525.1 $D_{4}$ simple
2.11.af_s $2$ $\F_{11}$ $1 - 5 x + 18 x^{2} - 55 x^{3} + 121 x^{4}$ $2$ 4.0.8405.1 $D_{4}$ simple
2.11.af_t $2$ $\F_{11}$ $1 - 5 x + 19 x^{2} - 55 x^{3} + 121 x^{4}$ $2$ 4.0.795389.1 $D_{4}$ simple
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