Properties

Label 2.19.am_cv
Base Field $\F_{19}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{19}$
Dimension:  $2$
L-polynomial:  $( 1 - 7 x + 19 x^{2} )( 1 - 5 x + 19 x^{2} )$
Frobenius angles:  $\pm0.203259864187$, $\pm0.305569972467$
Angle rank:  $2$ (numerical)
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 195 131625 48550320 17134547625 6138171800475 2213253727776000 798971085669032835 288438938659422383625 104127294467636946782640 37589973152955087548165625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 364 7076 131476 2478968 47044582 893831912 16983417316 322687524764 6131066208124

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{19}$
The isogeny class factors as 1.19.ah $\times$ 1.19.af 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.ac_d$2$(not in LMFDB)
2.19.c_d$2$(not in LMFDB)
2.19.m_cv$2$(not in LMFDB)
2.19.ag_br$3$(not in LMFDB)
2.19.d_ac$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.19.ac_d$2$(not in LMFDB)
2.19.c_d$2$(not in LMFDB)
2.19.m_cv$2$(not in LMFDB)
2.19.ag_br$3$(not in LMFDB)
2.19.d_ac$3$(not in LMFDB)
2.19.an_da$6$(not in LMFDB)
2.19.ae_bh$6$(not in LMFDB)
2.19.ad_ac$6$(not in LMFDB)
2.19.e_bh$6$(not in LMFDB)
2.19.g_br$6$(not in LMFDB)
2.19.n_da$6$(not in LMFDB)