Properties

 Label 2.193.acb_bpw 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: $( 1 - 27 x + 193 x^{2} )( 1 - 26 x + 193 x^{2} )$ Frobenius angles: $\pm0.0758389534121$, $\pm0.114714697559$ 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 $A(\F_{q^r})$ 28056 1364082720 51635318652288 1925049761953718400 71708865687914240527896 2671085307370930312446904320 99495246892347096065464184109912 3706098390777728740262530482400780800 138048458722253713680162453500685725089152 5142167038187204629222796458466871500708493600

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 141 36617 7182486 1387435249 267785037861 51682546542494 9974730508047285 1925122956514720801 371548729972630550358 71708904874146847968857

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
 The isogeny class factors as 1.193.abb $\times$ 1.193.aba 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 is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.193.ab_ame $2$ (not in LMFDB) 2.193.b_ame $2$ (not in LMFDB) 2.193.cb_bpw $2$ (not in LMFDB)