# Properties

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

## 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 3422 27410220 151069747328 806544627091200 4297818566709710222 22902229270463447024640 122045142227108802027816398 650377954015134451833778560000 3465863756149416204295912916972672 18469587783236067300871131693689141100

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