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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
Cyclic group of points Non-cyclic primes
Use Geometric decomposition in the following inputs
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Results (1-50 of 1683 matches)

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Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
2.29.au_gc $2$ $\F_{29}$ $( 1 - 10 x + 29 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-1}) \) $C_2$ 1.29.ak 2
2.29.at_fr $2$ $\F_{29}$ $1 - 19 x + 147 x^{2} - 551 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-13 +2 \sqrt{5}})\) $D_{4}$ simple
2.29.at_fs $2$ $\F_{29}$ $( 1 - 10 x + 29 x^{2} )( 1 - 9 x + 29 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-35}) \) $C_2$, $C_2$ 1.29.ak $\times$ 1.29.aj
2.29.as_fg $2$ $\F_{29}$ $1 - 18 x + 136 x^{2} - 522 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-8 -2 \sqrt{3}})\) $D_{4}$ simple
2.29.as_fh $2$ $\F_{29}$ $1 - 18 x + 137 x^{2} - 522 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{2}, \sqrt{-3})\) $C_2^2$ simple
2.29.as_fi $2$ $\F_{29}$ $( 1 - 10 x + 29 x^{2} )( 1 - 8 x + 29 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-13}) \) $C_2$, $C_2$ 1.29.ak $\times$ 1.29.ai
2.29.as_fj $2$ $\F_{29}$ $( 1 - 9 x + 29 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-35}) \) $C_2$ 1.29.aj 2
2.29.ar_ew $2$ $\F_{29}$ $1 - 17 x + 126 x^{2} - 493 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-10 + \sqrt{17}})\) $D_{4}$ simple
2.29.ar_ex $2$ $\F_{29}$ $1 - 17 x + 127 x^{2} - 493 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-162 +34 \sqrt{13}})\) $D_{4}$ simple
2.29.ar_ey $2$ $\F_{29}$ $( 1 - 10 x + 29 x^{2} )( 1 - 7 x + 29 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-67}) \) $C_2$, $C_2$ 1.29.ak $\times$ 1.29.ah
2.29.ar_ez $2$ $\F_{29}$ $1 - 17 x + 129 x^{2} - 493 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-170 +34 \sqrt{5}})\) $C_4$ simple
2.29.ar_fa $2$ $\F_{29}$ $( 1 - 9 x + 29 x^{2} )( 1 - 8 x + 29 x^{2} )$ $2$ \(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-13}) \) $C_2$, $C_2$ 1.29.aj $\times$ 1.29.ai
2.29.aq_el $2$ $\F_{29}$ $1 - 16 x + 115 x^{2} - 464 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-47 +4 \sqrt{7}})\) $D_{4}$ simple
2.29.aq_em $2$ $\F_{29}$ $1 - 16 x + 116 x^{2} - 464 x^{3} + 841 x^{4}$ $1$ \(\Q(\sqrt{-46 +16 \sqrt{6}})\) $D_{4}$ simple
2.29.aq_en $2$ $\F_{29}$ $1 - 16 x + 117 x^{2} - 464 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-122 +2 \sqrt{5}})\) $D_{4}$ simple
2.29.aq_eo $2$ $\F_{29}$ $( 1 - 10 x + 29 x^{2} )( 1 - 6 x + 29 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \) $C_2$, $C_2$ 1.29.ak $\times$ 1.29.ag
2.29.aq_ep $2$ $\F_{29}$ $1 - 16 x + 119 x^{2} - 464 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-49 +16 \sqrt{3}})\) $D_{4}$ simple
2.29.aq_eq $2$ $\F_{29}$ $1 - 16 x + 120 x^{2} - 464 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-50 +16 \sqrt{2}})\) $D_{4}$ simple
2.29.aq_er $2$ $\F_{29}$ $( 1 - 9 x + 29 x^{2} )( 1 - 7 x + 29 x^{2} )$ $2$ \(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-67}) \) $C_2$, $C_2$ 1.29.aj $\times$ 1.29.ah
2.29.aq_es $2$ $\F_{29}$ $( 1 - 8 x + 29 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-13}) \) $C_2$ 1.29.ai 2
2.29.ap_ea $2$ $\F_{29}$ $1 - 15 x + 104 x^{2} - 435 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-3}, \sqrt{41})\) $C_2^2$ simple
2.29.ap_eb $2$ $\F_{29}$ $1 - 15 x + 105 x^{2} - 435 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-202 -30 \sqrt{37}})\) $D_{4}$ simple
2.29.ap_ec $2$ $\F_{29}$ $1 - 15 x + 106 x^{2} - 435 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-206 -30 \sqrt{33}})\) $D_{4}$ simple
2.29.ap_ed $2$ $\F_{29}$ $1 - 15 x + 107 x^{2} - 435 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-42 -6 \sqrt{29}})\) $D_{4}$ simple
2.29.ap_ee $2$ $\F_{29}$ $( 1 - 10 x + 29 x^{2} )( 1 - 5 x + 29 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-91}) \) $C_2$, $C_2$ 1.29.ak $\times$ 1.29.af
2.29.ap_ef $2$ $\F_{29}$ $1 - 15 x + 109 x^{2} - 435 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-218 -30 \sqrt{21}})\) $D_{4}$ simple
2.29.ap_eg $2$ $\F_{29}$ $1 - 15 x + 110 x^{2} - 435 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-222 -30 \sqrt{17}})\) $D_{4}$ simple
2.29.ap_eh $2$ $\F_{29}$ $1 - 15 x + 111 x^{2} - 435 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-226 -30 \sqrt{13}})\) $D_{4}$ simple
2.29.ap_ei $2$ $\F_{29}$ $( 1 - 9 x + 29 x^{2} )( 1 - 6 x + 29 x^{2} )$ $2$ \(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-5}) \) $C_2$, $C_2$ 1.29.aj $\times$ 1.29.ag
2.29.ap_ej $2$ $\F_{29}$ $1 - 15 x + 113 x^{2} - 435 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-234 -30 \sqrt{5}})\) $D_{4}$ simple
2.29.ap_ek $2$ $\F_{29}$ $( 1 - 8 x + 29 x^{2} )( 1 - 7 x + 29 x^{2} )$ $2$ \(\Q(\sqrt{-13}) \), \(\Q(\sqrt{-67}) \) $C_2$, $C_2$ 1.29.ai $\times$ 1.29.ah
2.29.ao_dp $2$ $\F_{29}$ $1 - 14 x + 93 x^{2} - 406 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-22 +4 \sqrt{14}})\) $D_{4}$ simple
2.29.ao_dq $2$ $\F_{29}$ $1 - 14 x + 94 x^{2} - 406 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-6 + \sqrt{13}})\) $D_{4}$ simple
2.29.ao_dr $2$ $\F_{29}$ $1 - 14 x + 95 x^{2} - 406 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-49 +24 \sqrt{3}})\) $D_{4}$ simple
2.29.ao_ds $2$ $\F_{29}$ $1 - 14 x + 96 x^{2} - 406 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-56 -14 \sqrt{11}})\) $D_{4}$ simple
2.29.ao_dt $2$ $\F_{29}$ $1 - 14 x + 97 x^{2} - 406 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-57 -14 \sqrt{10}})\) $D_{4}$ simple
2.29.ao_du $2$ $\F_{29}$ $( 1 - 10 x + 29 x^{2} )( 1 - 4 x + 29 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.29.ak $\times$ 1.29.ae
2.29.ao_dv $2$ $\F_{29}$ $1 - 14 x + 99 x^{2} - 406 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-59 +28 \sqrt{2}})\) $D_{4}$ simple
2.29.ao_dw $2$ $\F_{29}$ $1 - 14 x + 100 x^{2} - 406 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-60 -14 \sqrt{7}})\) $D_{4}$ simple
2.29.ao_dx $2$ $\F_{29}$ $1 - 14 x + 101 x^{2} - 406 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-61 -14 \sqrt{6}})\) $D_{4}$ simple
2.29.ao_dy $2$ $\F_{29}$ $1 - 14 x + 102 x^{2} - 406 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-58 +10 \sqrt{5}})\) $D_{4}$ simple
2.29.ao_dz $2$ $\F_{29}$ $( 1 - 9 x + 29 x^{2} )( 1 - 5 x + 29 x^{2} )$ $2$ \(\Q(\sqrt{-35}) \), \(\Q(\sqrt{-91}) \) $C_2$, $C_2$ 1.29.aj $\times$ 1.29.af
2.29.ao_ea $2$ $\F_{29}$ $1 - 14 x + 104 x^{2} - 406 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-64 -14 \sqrt{3}})\) $D_{4}$ simple
2.29.ao_eb $2$ $\F_{29}$ $1 - 14 x + 105 x^{2} - 406 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-65 -14 \sqrt{2}})\) $D_{4}$ simple
2.29.ao_ec $2$ $\F_{29}$ $( 1 - 8 x + 29 x^{2} )( 1 - 6 x + 29 x^{2} )$ $2$ \(\Q(\sqrt{-13}) \), \(\Q(\sqrt{-5}) \) $C_2$, $C_2$ 1.29.ai $\times$ 1.29.ag
2.29.ao_ed $2$ $\F_{29}$ $( 1 - 7 x + 29 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-67}) \) $C_2$ 1.29.ah 2
2.29.an_df $2$ $\F_{29}$ $1 - 13 x + 83 x^{2} - 377 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-226 +26 \sqrt{69}})\) $D_{4}$ simple
2.29.an_dg $2$ $\F_{29}$ $1 - 13 x + 84 x^{2} - 377 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-10 + \sqrt{65}})\) $D_{4}$ simple
2.29.an_dh $2$ $\F_{29}$ $1 - 13 x + 85 x^{2} - 377 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-234 +26 \sqrt{61}})\) $D_{4}$ simple
2.29.an_di $2$ $\F_{29}$ $1 - 13 x + 86 x^{2} - 377 x^{3} + 841 x^{4}$ $2$ \(\Q(\sqrt{-238 +26 \sqrt{57}})\) $D_{4}$ simple
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