# Properties

 Label 2.5.ai_ba Base Field $\F_{5}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{5}$ Dimension: $2$ L-polynomial: $( 1 - 4 x + 5 x^{2} )^{2}$ Frobenius angles: $\pm0.147583617650$, $\pm0.147583617650$ Angle rank: $1$ (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 $A(\F_{q^r})$ 4 400 14884 409600 10252804 251539600 6190857124 153413222400 3820312611844 95376709210000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -2 14 118 654 3278 16094 79238 392734 1955998 9766574

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
 The isogeny class factors as 1.5.ae 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-1})$$$)$
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_ag $2$ 2.25.am_di 2.5.i_ba $2$ 2.25.am_di 2.5.e_l $3$ 2.125.ai_kg
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.5.a_ag $2$ 2.25.am_di 2.5.i_ba $2$ 2.25.am_di 2.5.e_l $3$ 2.125.ai_kg 2.5.ag_s $4$ 2.625.bc_cdq 2.5.ae_o $4$ 2.625.bc_cdq 2.5.ac_c $4$ 2.625.bc_cdq 2.5.a_g $4$ 2.625.bc_cdq 2.5.c_c $4$ 2.625.bc_cdq 2.5.e_o $4$ 2.625.bc_cdq 2.5.g_s $4$ 2.625.bc_cdq 2.5.ae_l $6$ (not in LMFDB) 2.5.a_ai $8$ (not in LMFDB) 2.5.a_i $8$ (not in LMFDB) 2.5.ac_ab $12$ (not in LMFDB) 2.5.c_ab $12$ (not in LMFDB)