Properties

Label 2.5.ag_t
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:  $( 1 - 3 x + 5 x^{2} )^{2}$
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:

Point counts of the abelian variety

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

Point counts of the curve

$r$ 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.
TwistExtension DegreeCommon 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.
TwistExtension DegreeCommon 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)