Properties

Label 2.73.abf_ow
Base Field $\F_{73}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{73}$
Dimension:  $2$
L-polynomial:  $( 1 - 16 x + 73 x^{2} )( 1 - 15 x + 73 x^{2} )$
Frobenius angles:  $\pm0.114200251220$, $\pm0.159004799845$
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
$A(\F_{q^r})$ 3422 27410220 151069747328 806544627091200 4297818566709710222 22902229270463447024640 122045142227108802027816398 650377954015134451833778560000 3465863756149416204295912916972672 18469587783236067300871131693689141100

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 43 5141 388336 28401217 2073164563 151335423794 11047410122491 806460183897793 58871587295993008 4297625832286582661

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The isogeny class factors as 1.73.aq $\times$ 1.73.ap 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 $\F_{73}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.73.ab_adq$2$(not in LMFDB)
2.73.b_adq$2$(not in LMFDB)
2.73.bf_ow$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.73.ab_adq$2$(not in LMFDB)
2.73.b_adq$2$(not in LMFDB)
2.73.bf_ow$2$(not in LMFDB)
2.73.av_jc$4$(not in LMFDB)
2.73.aj_ce$4$(not in LMFDB)
2.73.j_ce$4$(not in LMFDB)
2.73.v_jc$4$(not in LMFDB)