# Properties

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

## 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 28392 1367926560 51656159606688 1925133743246313600 71709144131730866632872 2671086086743762700997304320 99495248691459170475365098881768 3706098393781014250585761146952000000 138048458723132223598046575601804495201952 5142167038166852790383443738071910867359712800

 $r$ 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.
 Twist Extension Degree Common 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.
 Twist Extension Degree Common 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)