# Properties

 Label 2.137.abt_bea Base Field $\F_{137}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{137}$ Dimension: $2$ L-polynomial: $( 1 - 23 x + 137 x^{2} )( 1 - 22 x + 137 x^{2} )$ Frobenius angles: $\pm0.0596181899068$, $\pm0.111017258455$ 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 $A(\F_{q^r})$ 13340 343638400 6600757502720 124085936228800000 2329185132493164832700 43716645329268458883481600 820517701637845826515029336380 15400296298025874010242193708800000 289048159951931795261687853947266108160 5425144911483129864790165269668556834160000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 93 18305 2567034 352241313 48261539733 6611856590990 905824336906029 124097930578186753 17001416414763915498 2329194047682915403025

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
 The isogeny class factors as 1.137.ax $\times$ 1.137.aw 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 $\F_{137}$.

## 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 2.137.ab_aiy $2$ (not in LMFDB) 2.137.b_aiy $2$ (not in LMFDB) 2.137.bt_bea $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.137.ab_aiy $2$ (not in LMFDB) 2.137.b_aiy $2$ (not in LMFDB) 2.137.bt_bea $2$ (not in LMFDB) 2.137.abf_rq $4$ (not in LMFDB) 2.137.ap_dm $4$ (not in LMFDB) 2.137.p_dm $4$ (not in LMFDB) 2.137.bf_rq $4$ (not in LMFDB)