Properties

Label 2.193.abz_bnw
Base Field $\F_{193}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{193}$
Dimension:  $2$
L-polynomial:  $( 1 - 26 x + 193 x^{2} )( 1 - 25 x + 193 x^{2} )$
Frobenius angles:  $\pm0.114714697559$, $\pm0.143734387197$
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
$A(\F_{q^r})$ 28392 1367926560 51656159606688 1925133743246313600 71709144131730866632872 2671086086743762700997304320 99495248691459170475365098881768 3706098393781014250585761146952000000 138048458723132223598046575601804495201952 5142167038166852790383443738071910867359712800

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 143 36721 7185386 1387495777 267786077663 51682561622494 9974730688414271 1925122958074769473 371548729974995004458 71708904873863036092561

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The isogeny class factors as 1.193.aba $\times$ 1.193.az 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 $\F_{193}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.193.ab_ake$2$(not in LMFDB)
2.193.b_ake$2$(not in LMFDB)
2.193.bz_bnw$2$(not in LMFDB)
2.193.ay_mw$3$(not in LMFDB)
2.193.ad_aie$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.193.ab_ake$2$(not in LMFDB)
2.193.b_ake$2$(not in LMFDB)
2.193.bz_bnw$2$(not in LMFDB)
2.193.ay_mw$3$(not in LMFDB)
2.193.ad_aie$3$(not in LMFDB)
2.193.abx_blw$6$(not in LMFDB)
2.193.abc_qw$6$(not in LMFDB)
2.193.d_aie$6$(not in LMFDB)
2.193.y_mw$6$(not in LMFDB)
2.193.bc_qw$6$(not in LMFDB)
2.193.bx_blw$6$(not in LMFDB)