Properties

 Label 2.13.al_ce Base Field $\F_{13}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian No

Invariants

 Base field: $\F_{13}$ Dimension: $2$ L-polynomial: $( 1 - 6 x + 13 x^{2} )( 1 - 5 x + 13 x^{2} )$ Frobenius angles: $\pm0.187167041811$, $\pm0.256122854178$ Angle rank: $2$ (numerical) Jacobians: 0

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

 $p$-rank: $2$ Slopes: $[0, 0, 1, 1]$

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 72 27360 5025888 832291200 138591237672 23315295467520 3937143790280808 665370955154880000 112452955480771954272 19004889181346053336800

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 3 161 2286 29137 373263 4830374 62744811 815674753 10604268198 137857950761

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
 The isogeny class factors as 1.13.ag $\times$ 1.13.af and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{13}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.13.ab_ae $2$ 2.169.aj_mq 2.13.b_ae $2$ 2.169.aj_mq 2.13.l_ce $2$ 2.169.aj_mq 2.13.ai_bm $3$ (not in LMFDB) 2.13.b_aq $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.13.ab_ae $2$ 2.169.aj_mq 2.13.b_ae $2$ 2.169.aj_mq 2.13.l_ce $2$ 2.169.aj_mq 2.13.ai_bm $3$ (not in LMFDB) 2.13.b_aq $3$ (not in LMFDB) 2.13.aj_bu $4$ (not in LMFDB) 2.13.ab_g $4$ (not in LMFDB) 2.13.b_g $4$ (not in LMFDB) 2.13.j_bu $4$ (not in LMFDB) 2.13.an_cq $6$ (not in LMFDB) 2.13.ae_o $6$ (not in LMFDB) 2.13.ab_aq $6$ (not in LMFDB) 2.13.e_o $6$ (not in LMFDB) 2.13.i_bm $6$ (not in LMFDB) 2.13.n_cq $6$ (not in LMFDB) 2.13.al_cc $12$ (not in LMFDB) 2.13.ag_bi $12$ (not in LMFDB) 2.13.ad_ac $12$ (not in LMFDB) 2.13.ac_s $12$ (not in LMFDB) 2.13.c_s $12$ (not in LMFDB) 2.13.d_ac $12$ (not in LMFDB) 2.13.g_bi $12$ (not in LMFDB) 2.13.l_cc $12$ (not in LMFDB)