Properties

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

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Invariants

Base field:  $\F_{5}$
Dimension:  $2$
L-polynomial:  $( 1 - x + 5 x^{2} )^{2}$
Frobenius angles:  $\pm0.428216853436$, $\pm0.428216853436$
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:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 25 1225 19600 354025 9150625 245862400 6191329225 152814537225 3804918384400 95290298805625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 44 154 564 2924 15734 79244 391204 1948114 9757724

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
The isogeny class factors as 1.5.ab 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-19}) \)$)$
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.
TwistExtension DegreeCommon base change
2.5.a_j$2$2.25.s_fb
2.5.c_l$2$2.25.s_fb
2.5.b_ae$3$2.125.bc_re
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.5.a_j$2$2.25.s_fb
2.5.c_l$2$2.25.s_fb
2.5.b_ae$3$2.125.bc_re
2.5.a_aj$4$2.625.ack_dhb
2.5.ab_ae$6$(not in LMFDB)