Properties

Label 2.19.an_dc
Base Field $\F_{19}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{19}$
Dimension:  $2$
L-polynomial:  $( 1 - 7 x + 19 x^{2} )( 1 - 6 x + 19 x^{2} )$
Frobenius angles:  $\pm0.203259864187$, $\pm0.258380448083$
Angle rank:  $2$ (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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 182 127764 48315176 17156149920 6143598863402 2213711304831936 798975439788211322 288435376972587761280 104126843995038193192136 37589951156111042988102804

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 353 7042 131641 2481157 47054306 893836783 16983207601 322686128758 6131062620353

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{19}$
The isogeny class factors as 1.19.ah $\times$ 1.19.ag and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{19}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.19.ab_ae$2$(not in LMFDB)
2.19.b_ae$2$(not in LMFDB)
2.19.n_dc$2$(not in LMFDB)
2.19.ah_bs$3$(not in LMFDB)
2.19.c_ak$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.19.ab_ae$2$(not in LMFDB)
2.19.b_ae$2$(not in LMFDB)
2.19.n_dc$2$(not in LMFDB)
2.19.ah_bs$3$(not in LMFDB)
2.19.c_ak$3$(not in LMFDB)
2.19.ao_di$6$(not in LMFDB)
2.19.af_bg$6$(not in LMFDB)
2.19.ac_ak$6$(not in LMFDB)
2.19.f_bg$6$(not in LMFDB)
2.19.h_bs$6$(not in LMFDB)
2.19.o_di$6$(not in LMFDB)