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Some interesting isogeny classes of abelian varieties over $\Fq$
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Labeling convention
Label
Description
1.2.ac
Jacobian of a function field of class number $1$ with $g=1$ and $q=2$
1.3.ad
Jacobian of a function field of class number $1$ with $g=1$ and $q=3$
1.4.ae
Jacobian of a function field of class number $1$ with $g=1$ and $q=4$
2.2.ad_f
Jacobian of a function field of class number $1$ with $g=2$ and $q=2$
2.2.ac_c
Jacobian of a function field of class number $1$ with $g=2$ and $q=2$
2.2.a_ae
Abelian surface with only one rational point
2.167.a_hi
Most Jacobians
3.2.ae_j_ap
Abelian threefold with only one rational point
3.2.ad_c_b
Jacobian of a function field of class number $1$ with $g=3$ and $q=2$
3.2.ad_d_ac
Jacobian of a function field of class number $1$ with $g=3$ and $q=2$
3.8.ag_bk_aea
Hyperspecial example
4.2.af_n_az_bn
Abelian fourfold with only one rational point
4.2.ae_e_h_av
Abelian fourfold with only one rational point
4.2.ad_c_a_b
Jacobian of a function field of class number $1$ with $g=4$ and $q=2$
6.2.ak_cb_ahg_sy_abme_ciq
Largest twist class
6.2.ag_r_abd_bg_ay_u
Largest endomorphism degree