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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Results (1-50 of 10223 matches)

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Label Dimension Base field L-polynomial $p$-rank Number fields Galois groups Isogeny factors
2.97.abm_vj $2$ $\F_{97}$ $( 1 - 19 x + 97 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-3}) \) $C_2$ 1.97.at 2
2.97.abl_up $2$ $\F_{97}$ $1 - 37 x + 535 x^{2} - 3589 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-17 +2 \sqrt{5}})\) $D_{4}$ simple
2.97.abl_uq $2$ $\F_{97}$ $( 1 - 19 x + 97 x^{2} )( 1 - 18 x + 97 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \) $C_2$, $C_2$ 1.97.at $\times$ 1.97.as
2.97.abk_tw $2$ $\F_{97}$ $1 - 36 x + 516 x^{2} - 3492 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-42 +16 \sqrt{2}})\) $D_{4}$ simple
2.97.abk_tx $2$ $\F_{97}$ $( 1 - 19 x + 97 x^{2} )( 1 - 17 x + 97 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-11}) \) $C_2$, $C_2$ 1.97.at $\times$ 1.97.ar
2.97.abk_ty $2$ $\F_{97}$ $( 1 - 18 x + 97 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-1}) \) $C_2$ 1.97.as 2
2.97.abj_tc $2$ $\F_{97}$ $1 - 35 x + 496 x^{2} - 3395 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-70 +10 \sqrt{17}})\) $D_{4}$ simple
2.97.abj_td $2$ $\F_{97}$ $1 - 35 x + 497 x^{2} - 3395 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-314 -70 \sqrt{13}})\) $D_{4}$ simple
2.97.abj_te $2$ $\F_{97}$ $( 1 - 19 x + 97 x^{2} )( 1 - 16 x + 97 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-33}) \) $C_2$, $C_2$ 1.97.at $\times$ 1.97.aq
2.97.abj_tf $2$ $\F_{97}$ $1 - 35 x + 499 x^{2} - 3395 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-77 +14 \sqrt{5}})\) $D_{4}$ simple
2.97.abj_tg $2$ $\F_{97}$ $( 1 - 18 x + 97 x^{2} )( 1 - 17 x + 97 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-11}) \) $C_2$, $C_2$ 1.97.as $\times$ 1.97.ar
2.97.abi_si $2$ $\F_{97}$ $1 - 34 x + 476 x^{2} - 3298 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-11 +2 \sqrt{7}})\) $D_{4}$ simple
2.97.abi_sj $2$ $\F_{97}$ $1 - 34 x + 477 x^{2} - 3298 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-93 -34 \sqrt{6}})\) $D_{4}$ simple
2.97.abi_sk $2$ $\F_{97}$ $1 - 34 x + 478 x^{2} - 3298 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-14 + \sqrt{5}})\) $D_{4}$ simple
2.97.abi_sl $2$ $\F_{97}$ $( 1 - 19 x + 97 x^{2} )( 1 - 15 x + 97 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-163}) \) $C_2$, $C_2$ 1.97.at $\times$ 1.97.ap
2.97.abi_sm $2$ $\F_{97}$ $1 - 34 x + 480 x^{2} - 3298 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-96 -34 \sqrt{3}})\) $D_{4}$ simple
2.97.abi_sn $2$ $\F_{97}$ $1 - 34 x + 481 x^{2} - 3298 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-97 -34 \sqrt{2}})\) $D_{4}$ simple
2.97.abi_so $2$ $\F_{97}$ $( 1 - 18 x + 97 x^{2} )( 1 - 16 x + 97 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-33}) \) $C_2$, $C_2$ 1.97.as $\times$ 1.97.aq
2.97.abi_sp $2$ $\F_{97}$ $( 1 - 17 x + 97 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-11}) \) $C_2$ 1.97.ar 2
2.97.abh_rp $2$ $\F_{97}$ $1 - 33 x + 457 x^{2} - 3201 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-17 +2 \sqrt{37}})\) $D_{4}$ simple
2.97.abh_rq $2$ $\F_{97}$ $1 - 33 x + 458 x^{2} - 3201 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-430 +66 \sqrt{33}})\) $D_{4}$ simple
2.97.abh_rr $2$ $\F_{97}$ $1 - 33 x + 459 x^{2} - 3201 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-434 +66 \sqrt{29}})\) $D_{4}$ simple
2.97.abh_rs $2$ $\F_{97}$ $( 1 - 19 x + 97 x^{2} )( 1 - 14 x + 97 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.97.at $\times$ 1.97.ao
2.97.abh_rt $2$ $\F_{97}$ $1 - 33 x + 461 x^{2} - 3201 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-442 +66 \sqrt{21}})\) $D_{4}$ simple
2.97.abh_ru $2$ $\F_{97}$ $1 - 33 x + 462 x^{2} - 3201 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-446 +66 \sqrt{17}})\) $D_{4}$ simple
2.97.abh_rv $2$ $\F_{97}$ $1 - 33 x + 463 x^{2} - 3201 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-450 +66 \sqrt{13}})\) $D_{4}$ simple
2.97.abh_rw $2$ $\F_{97}$ $( 1 - 18 x + 97 x^{2} )( 1 - 15 x + 97 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-163}) \) $C_2$, $C_2$ 1.97.as $\times$ 1.97.ap
2.97.abh_rx $2$ $\F_{97}$ $1 - 33 x + 465 x^{2} - 3201 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-458 +66 \sqrt{5}})\) $D_{4}$ simple
2.97.abh_ry $2$ $\F_{97}$ $( 1 - 17 x + 97 x^{2} )( 1 - 16 x + 97 x^{2} )$ $2$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-33}) \) $C_2$, $C_2$ 1.97.ar $\times$ 1.97.aq
2.97.abg_qv $2$ $\F_{97}$ $1 - 32 x + 437 x^{2} - 3104 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-122 +10 \sqrt{13}})\) $D_{4}$ simple
2.97.abg_qw $2$ $\F_{97}$ $1 - 32 x + 438 x^{2} - 3104 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-6 + \sqrt{3}})\) $D_{4}$ simple
2.97.abg_qx $2$ $\F_{97}$ $1 - 32 x + 439 x^{2} - 3104 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-121 +32 \sqrt{11}})\) $D_{4}$ simple
2.97.abg_qy $2$ $\F_{97}$ $1 - 32 x + 440 x^{2} - 3104 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-17 +4 \sqrt{10}})\) $D_{4}$ simple
2.97.abg_qz $2$ $\F_{97}$ $( 1 - 19 x + 97 x^{2} )( 1 - 13 x + 97 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-219}) \) $C_2$, $C_2$ 1.97.at $\times$ 1.97.an
2.97.abg_ra $2$ $\F_{97}$ $1 - 32 x + 442 x^{2} - 3104 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-31 +16 \sqrt{2}})\) $D_{4}$ simple
2.97.abg_rb $2$ $\F_{97}$ $1 - 32 x + 443 x^{2} - 3104 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-125 +32 \sqrt{7}})\) $D_{4}$ simple
2.97.abg_rc $2$ $\F_{97}$ $1 - 32 x + 444 x^{2} - 3104 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-126 +32 \sqrt{6}})\) $D_{4}$ simple
2.97.abg_rd $2$ $\F_{97}$ $1 - 32 x + 445 x^{2} - 3104 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-442 -62 \sqrt{5}})\) $D_{4}$ simple
2.97.abg_re $2$ $\F_{97}$ $( 1 - 18 x + 97 x^{2} )( 1 - 14 x + 97 x^{2} )$ $2$ \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}) \) $C_2$, $C_2$ 1.97.as $\times$ 1.97.ao
2.97.abg_rf $2$ $\F_{97}$ $1 - 32 x + 447 x^{2} - 3104 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-129 +32 \sqrt{3}})\) $D_{4}$ simple
2.97.abg_rg $2$ $\F_{97}$ $1 - 32 x + 448 x^{2} - 3104 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-130 +32 \sqrt{2}})\) $D_{4}$ simple
2.97.abg_rh $2$ $\F_{97}$ $( 1 - 17 x + 97 x^{2} )( 1 - 15 x + 97 x^{2} )$ $2$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-163}) \) $C_2$, $C_2$ 1.97.ar $\times$ 1.97.ap
2.97.abg_ri $2$ $\F_{97}$ $( 1 - 16 x + 97 x^{2} )^{2}$ $2$ \(\Q(\sqrt{-33}) \) $C_2$ 1.97.aq 2
2.97.abf_qb $2$ $\F_{97}$ $1 - 31 x + 417 x^{2} - 3007 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-81 +6 \sqrt{69}})\) $D_{4}$ simple
2.97.abf_qc $2$ $\F_{97}$ $1 - 31 x + 418 x^{2} - 3007 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-526 -62 \sqrt{65}})\) $D_{4}$ simple
2.97.abf_qd $2$ $\F_{97}$ $1 - 31 x + 419 x^{2} - 3007 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-530 -62 \sqrt{61}})\) $D_{4}$ simple
2.97.abf_qe $2$ $\F_{97}$ $1 - 31 x + 420 x^{2} - 3007 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-33 + \sqrt{57}})\) $D_{4}$ simple
2.97.abf_qf $2$ $\F_{97}$ $1 - 31 x + 421 x^{2} - 3007 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-538 -62 \sqrt{53}})\) $D_{4}$ simple
2.97.abf_qg $2$ $\F_{97}$ $( 1 - 19 x + 97 x^{2} )( 1 - 12 x + 97 x^{2} )$ $2$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-61}) \) $C_2$, $C_2$ 1.97.at $\times$ 1.97.am
2.97.abf_qh $2$ $\F_{97}$ $1 - 31 x + 423 x^{2} - 3007 x^{3} + 9409 x^{4}$ $2$ \(\Q(\sqrt{-354 -6 \sqrt{5}})\) $D_{4}$ simple
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