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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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Use Geometric decomposition in the following inputs
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Results (1-50 of 8987 matches)

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Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
2.89.abk_ti $2$ $\F_{89}$ $( 1 - 18 x + 89 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-2}) \) $C_2$ 1.89.as 2
2.89.abj_sp $2$ $\F_{89}$ $1 - 35 x + 483 x^{2} - 3115 x^{3} + 7921 x^{4}$ $2$ 4.0.20525.1 $D_{4}$ simple
2.89.abj_sq $2$ $\F_{89}$ $( 1 - 18 x + 89 x^{2} )( 1 - 17 x + 89 x^{2} )$ $2$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-67}) \) $C_2$, $C_2$ 1.89.as $\times$ 1.89.ar
2.89.abi_rw $2$ $\F_{89}$ $1 - 34 x + 464 x^{2} - 3026 x^{3} + 7921 x^{4}$ $2$ 4.0.90432.3 $D_{4}$ simple
2.89.abi_rx $2$ $\F_{89}$ $1 - 34 x + 465 x^{2} - 3026 x^{3} + 7921 x^{4}$ $2$ 4.0.122432.2 $D_{4}$ simple
2.89.abi_ry $2$ $\F_{89}$ $( 1 - 18 x + 89 x^{2} )( 1 - 16 x + 89 x^{2} )$ $2$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.89.as $\times$ 1.89.aq
2.89.abi_rz $2$ $\F_{89}$ $( 1 - 17 x + 89 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-67}) \) $C_2$ 1.89.ar 2
2.89.abh_rd $2$ $\F_{89}$ $1 - 33 x + 445 x^{2} - 2937 x^{3} + 7921 x^{4}$ $1$ 4.0.196245.2 $D_{4}$ simple
2.89.abh_re $2$ $\F_{89}$ $1 - 33 x + 446 x^{2} - 2937 x^{3} + 7921 x^{4}$ $2$ 4.0.488988.1 $D_{4}$ simple
2.89.abh_rf $2$ $\F_{89}$ $1 - 33 x + 447 x^{2} - 2937 x^{3} + 7921 x^{4}$ $2$ 4.0.497029.2 $D_{4}$ simple
2.89.abh_rg $2$ $\F_{89}$ $( 1 - 18 x + 89 x^{2} )( 1 - 15 x + 89 x^{2} )$ $2$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-131}) \) $C_2$, $C_2$ 1.89.as $\times$ 1.89.ap
2.89.abh_rh $2$ $\F_{89}$ $1 - 33 x + 449 x^{2} - 2937 x^{3} + 7921 x^{4}$ $2$ 4.0.136125.2 $C_4$ simple
2.89.abh_ri $2$ $\F_{89}$ $( 1 - 17 x + 89 x^{2} )( 1 - 16 x + 89 x^{2} )$ $2$ \(\Q(\sqrt{-67}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.89.ar $\times$ 1.89.aq
2.89.abg_qk $2$ $\F_{89}$ $1 - 32 x + 426 x^{2} - 2848 x^{3} + 7921 x^{4}$ $2$ 4.0.1088.2 $D_{4}$ simple
2.89.abg_ql $2$ $\F_{89}$ $1 - 32 x + 427 x^{2} - 2848 x^{3} + 7921 x^{4}$ $2$ 4.0.1161104.1 $D_{4}$ simple
2.89.abg_qm $2$ $\F_{89}$ $1 - 32 x + 428 x^{2} - 2848 x^{3} + 7921 x^{4}$ $2$ 4.0.1550592.2 $D_{4}$ simple
2.89.abg_qn $2$ $\F_{89}$ $1 - 32 x + 429 x^{2} - 2848 x^{3} + 7921 x^{4}$ $2$ 4.0.97625.1 $D_{4}$ simple
2.89.abg_qo $2$ $\F_{89}$ $( 1 - 18 x + 89 x^{2} )( 1 - 14 x + 89 x^{2} )$ $2$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-10}) \) $C_2$, $C_2$ 1.89.as $\times$ 1.89.ao
2.89.abg_qp $2$ $\F_{89}$ $1 - 32 x + 431 x^{2} - 2848 x^{3} + 7921 x^{4}$ $2$ 4.0.912528.1 $D_{4}$ simple
2.89.abg_qq $2$ $\F_{89}$ $1 - 32 x + 432 x^{2} - 2848 x^{3} + 7921 x^{4}$ $2$ 4.0.483584.2 $D_{4}$ simple
2.89.abg_qr $2$ $\F_{89}$ $( 1 - 17 x + 89 x^{2} )( 1 - 15 x + 89 x^{2} )$ $2$ \(\Q(\sqrt{-67}) \), \(\Q(\sqrt{-131}) \) $C_2$, $C_2$ 1.89.ar $\times$ 1.89.ap
2.89.abg_qs $2$ $\F_{89}$ $( 1 - 16 x + 89 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-1}) \) $C_2$ 1.89.aq 2
2.89.abf_pr $2$ $\F_{89}$ $1 - 31 x + 407 x^{2} - 2759 x^{3} + 7921 x^{4}$ $2$ 4.0.2725.1 $D_{4}$ simple
2.89.abf_ps $2$ $\F_{89}$ $1 - 31 x + 408 x^{2} - 2759 x^{3} + 7921 x^{4}$ $2$ 4.0.8405.1 $D_{4}$ simple
2.89.abf_pt $2$ $\F_{89}$ $1 - 31 x + 409 x^{2} - 2759 x^{3} + 7921 x^{4}$ $2$ 4.0.3358157.1 $D_{4}$ simple
2.89.abf_pu $2$ $\F_{89}$ $1 - 31 x + 410 x^{2} - 2759 x^{3} + 7921 x^{4}$ $2$ 4.0.3950892.2 $D_{4}$ simple
2.89.abf_pv $2$ $\F_{89}$ $1 - 31 x + 411 x^{2} - 2759 x^{3} + 7921 x^{4}$ $2$ 4.0.4041005.3 $D_{4}$ simple
2.89.abf_pw $2$ $\F_{89}$ $( 1 - 18 x + 89 x^{2} )( 1 - 13 x + 89 x^{2} )$ $2$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-187}) \) $C_2$, $C_2$ 1.89.as $\times$ 1.89.an
2.89.abf_px $2$ $\F_{89}$ $1 - 31 x + 413 x^{2} - 2759 x^{3} + 7921 x^{4}$ $2$ 4.0.3159765.2 $D_{4}$ simple
2.89.abf_py $2$ $\F_{89}$ $1 - 31 x + 414 x^{2} - 2759 x^{3} + 7921 x^{4}$ $2$ 4.0.2412572.1 $D_{4}$ simple
2.89.abf_pz $2$ $\F_{89}$ $1 - 31 x + 415 x^{2} - 2759 x^{3} + 7921 x^{4}$ $2$ 4.0.1611077.3 $D_{4}$ simple
2.89.abf_qa $2$ $\F_{89}$ $( 1 - 17 x + 89 x^{2} )( 1 - 14 x + 89 x^{2} )$ $2$ \(\Q(\sqrt{-67}) \), \(\Q(\sqrt{-10}) \) $C_2$, $C_2$ 1.89.ar $\times$ 1.89.ao
2.89.abf_qb $2$ $\F_{89}$ $1 - 31 x + 417 x^{2} - 2759 x^{3} + 7921 x^{4}$ $2$ 4.0.297725.1 $D_{4}$ simple
2.89.abf_qc $2$ $\F_{89}$ $( 1 - 16 x + 89 x^{2} )( 1 - 15 x + 89 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-131}) \) $C_2$, $C_2$ 1.89.aq $\times$ 1.89.ap
2.89.abe_oz $2$ $\F_{89}$ $1 - 30 x + 389 x^{2} - 2670 x^{3} + 7921 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{14})\) $C_2^2$ simple
2.89.abe_pa $2$ $\F_{89}$ $1 - 30 x + 390 x^{2} - 2670 x^{3} + 7921 x^{4}$ $2$ 4.0.375856.1 $D_{4}$ simple
2.89.abe_pb $2$ $\F_{89}$ $1 - 30 x + 391 x^{2} - 2670 x^{3} + 7921 x^{4}$ $2$ 4.0.483984.2 $D_{4}$ simple
2.89.abe_pc $2$ $\F_{89}$ $1 - 30 x + 392 x^{2} - 2670 x^{3} + 7921 x^{4}$ $2$ 4.0.348480.1 $D_{4}$ simple
2.89.abe_pd $2$ $\F_{89}$ $1 - 30 x + 393 x^{2} - 2670 x^{3} + 7921 x^{4}$ $2$ 4.0.9025600.2 $D_{4}$ simple
2.89.abe_pe $2$ $\F_{89}$ $( 1 - 18 x + 89 x^{2} )( 1 - 12 x + 89 x^{2} )$ $2$ \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-53}) \) $C_2$, $C_2$ 1.89.as $\times$ 1.89.am
2.89.abe_pf $2$ $\F_{89}$ $1 - 30 x + 395 x^{2} - 2670 x^{3} + 7921 x^{4}$ $2$ 4.0.507456.2 $D_{4}$ simple
2.89.abe_pg $2$ $\F_{89}$ $1 - 30 x + 396 x^{2} - 2670 x^{3} + 7921 x^{4}$ $2$ 4.0.7115584.1 $D_{4}$ simple
2.89.abe_ph $2$ $\F_{89}$ $1 - 30 x + 397 x^{2} - 2670 x^{3} + 7921 x^{4}$ $2$ 4.0.5889600.9 $D_{4}$ simple
2.89.abe_pi $2$ $\F_{89}$ $1 - 30 x + 398 x^{2} - 2670 x^{3} + 7921 x^{4}$ $2$ 4.0.284400.2 $D_{4}$ simple
2.89.abe_pj $2$ $\F_{89}$ $( 1 - 17 x + 89 x^{2} )( 1 - 13 x + 89 x^{2} )$ $2$ \(\Q(\sqrt{-67}) \), \(\Q(\sqrt{-187}) \) $C_2$, $C_2$ 1.89.ar $\times$ 1.89.an
2.89.abe_pk $2$ $\F_{89}$ $1 - 30 x + 400 x^{2} - 2670 x^{3} + 7921 x^{4}$ $2$ 4.0.1970496.2 $D_{4}$ simple
2.89.abe_pl $2$ $\F_{89}$ $1 - 30 x + 401 x^{2} - 2670 x^{3} + 7921 x^{4}$ $2$ 4.0.949824.3 $D_{4}$ simple
2.89.abe_pm $2$ $\F_{89}$ $( 1 - 16 x + 89 x^{2} )( 1 - 14 x + 89 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-10}) \) $C_2$, $C_2$ 1.89.aq $\times$ 1.89.ao
2.89.abe_pn $2$ $\F_{89}$ $( 1 - 15 x + 89 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-131}) \) $C_2$ 1.89.ap 2
2.89.abd_og $2$ $\F_{89}$ $1 - 29 x + 370 x^{2} - 2581 x^{3} + 7921 x^{4}$ $2$ 4.0.4838732.1 $D_{4}$ simple
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