# Properties

 Label 2.13.al_cc Base Field $\F_{13}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{13}$ Dimension: $2$ L-polynomial: $( 1 - 7 x + 13 x^{2} )( 1 - 4 x + 13 x^{2} )$ Frobenius angles: $\pm0.0772104791556$, $\pm0.312832958189$ Angle rank: $2$ (numerical) Jacobians: 1

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 contains the Jacobians of 1 curves, and hence is principally polarizable:

• $y^2=5x^6+2x^5+3x^4+11x^3+5x^2+3x+5$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 70 26460 4873120 817084800 137610200350 23276009352960 3936680039061070 665433838241625600 112458489573068467360 19005135175967126514300

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 3 157 2220 28609 370623 4822234 62737419 815751841 10604790060 137859735157

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
 The isogeny class factors as 1.13.ah $\times$ 1.13.ae 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.ad_ac $2$ 2.169.an_ee 2.13.d_ac $2$ 2.169.an_ee 2.13.l_cc $2$ 2.169.an_ee 2.13.ac_s $3$ (not in LMFDB) 2.13.b_g $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.13.ad_ac $2$ 2.169.an_ee 2.13.d_ac $2$ 2.169.an_ee 2.13.l_cc $2$ 2.169.an_ee 2.13.ac_s $3$ (not in LMFDB) 2.13.b_g $3$ (not in LMFDB) 2.13.an_cq $4$ (not in LMFDB) 2.13.ab_aq $4$ (not in LMFDB) 2.13.b_aq $4$ (not in LMFDB) 2.13.n_cq $4$ (not in LMFDB) 2.13.aj_bu $6$ (not in LMFDB) 2.13.ag_bi $6$ (not in LMFDB) 2.13.ab_g $6$ (not in LMFDB) 2.13.c_s $6$ (not in LMFDB) 2.13.g_bi $6$ (not in LMFDB) 2.13.j_bu $6$ (not in LMFDB) 2.13.al_ce $12$ (not in LMFDB) 2.13.ai_bm $12$ (not in LMFDB) 2.13.ae_o $12$ (not in LMFDB) 2.13.ab_ae $12$ (not in LMFDB) 2.13.b_ae $12$ (not in LMFDB) 2.13.e_o $12$ (not in LMFDB) 2.13.i_bm $12$ (not in LMFDB) 2.13.l_ce $12$ (not in LMFDB)