# Properties

 Label 2.73.abb_mq 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: $( 1 - 14 x + 73 x^{2} )( 1 - 13 x + 73 x^{2} )$ Frobenius angles: $\pm0.194368965322$, $\pm0.224822766824$ 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 $A(\F_{q^r})$ 3660 28020960 151713339120 806979549974400 4297988490122748300 22902203903730989967360 122045028321101009140057740 650377835013597824624209804800 3465863672899846277724153175557360 18469587741925119242937477426782776800

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 47 5257 389990 28416529 2073246527 151335256174 11047399811831 806460036337441 58871585881905590 4297625822674078057

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
 The isogeny class factors as 1.73.ao $\times$ 1.73.an 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 is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.73.ab_abk $2$ (not in LMFDB) 2.73.b_abk $2$ (not in LMFDB) 2.73.bb_mq $2$ (not in LMFDB)