# Properties

 Label 2.5.ag_t Base Field $\F_{5}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{5}$ Dimension: $2$ L-polynomial: $( 1 - 3 x + 5 x^{2} )^{2}$ Frobenius angles: $\pm0.265942140215$, $\pm0.265942140215$ 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:

• $y^2=2x^6+4x^5+4x^4+2x^3+4x^2+4x+2$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 9 729 20736 455625 10131489 241864704 6024709161 151690775625 3811116075264 95426073465129

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 0 28 162 724 3240 15478 77112 388324 1951290 9771628

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
 The isogeny class factors as 1.5.ad 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-11})$$$)$
All geometric endomorphisms are defined over $\F_{5}$.

## 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 2.5.a_b $2$ 2.25.c_bz 2.5.g_t $2$ 2.25.c_bz 2.5.d_e $3$ 2.125.bk_wc
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.5.a_b $2$ 2.25.c_bz 2.5.g_t $2$ 2.25.c_bz 2.5.d_e $3$ 2.125.bk_wc 2.5.a_ab $4$ 2.625.du_fkl 2.5.ad_e $6$ (not in LMFDB)