# Properties

 Label 2.13.am_ck 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: $( 1 - 6 x + 13 x^{2} )^{2}$ Frobenius angles: $\pm0.187167041811$, $\pm0.187167041811$ Angle rank: $1$ (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:

• $y^2=6x^6+4x^4+4x^2+6$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 64 25600 4910656 829440000 138747310144 23337401574400 3938493262997056 665417390653440000 112453014483578818624 19004775447137357440000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 2 150 2234 29038 373682 4834950 62766314 815731678 10604273762 137857125750

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
 The isogeny class factors as 1.13.ag 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-1})$$$)$
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.a_ak $2$ 2.169.au_qw 2.13.m_ck $2$ 2.169.au_qw 2.13.g_x $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.13.a_ak $2$ 2.169.au_qw 2.13.m_ck $2$ 2.169.au_qw 2.13.g_x $3$ (not in LMFDB) 2.13.ak_by $4$ (not in LMFDB) 2.13.ai_bq $4$ (not in LMFDB) 2.13.ac_c $4$ (not in LMFDB) 2.13.a_k $4$ (not in LMFDB) 2.13.c_c $4$ (not in LMFDB) 2.13.i_bq $4$ (not in LMFDB) 2.13.k_by $4$ (not in LMFDB) 2.13.ag_x $6$ (not in LMFDB) 2.13.a_ay $8$ (not in LMFDB) 2.13.a_y $8$ (not in LMFDB) 2.13.ae_d $12$ (not in LMFDB) 2.13.e_d $12$ (not in LMFDB)