# Properties

 Label 2.137.abo_zu Base Field $\F_{137}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{137}$ Dimension: $2$ L-polynomial: $( 1 - 22 x + 137 x^{2} )( 1 - 18 x + 137 x^{2} )$ Frobenius angles: $\pm0.111017258455$, $\pm0.220793476886$ Angle rank: $2$ (numerical) Jacobians: 100

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 contains the Jacobians of 100 curves, and hence is principally polarizable:

• $y^2=116x^6+44x^5+82x^4+123x^3+82x^2+44x+116$
• $y^2=46x^6+133x^5+114x^4+36x^3+113x^2+78x+23$
• $y^2=110x^6+10x^5+125x^4+44x^3+113x^2+40x+58$
• $y^2=96x^6+94x^5+115x^4+92x^3+115x^2+94x+96$
• $y^2=52x^6+38x^5+114x^4+128x^3+114x^2+38x+52$
• $y^2=104x^6+34x^5+96x^4+55x^3+33x^2+74x+43$
• $y^2=118x^6+44x^5+128x^4+73x^3+128x^2+44x+118$
• $y^2=116x^6+87x^5+56x^4+74x^3+41x^2+55x+29$
• $y^2=45x^6+110x^5+62x^4+14x^3+66x^2+26x+29$
• $y^2=94x^6+50x^5+61x^4+15x^3+61x^2+50x+94$
• $y^2=92x^6+75x^5+119x^4+60x^3+102x^2+24x+31$
• $y^2=66x^6+78x^5+28x^4+11x^3+29x^2+80x+56$
• $y^2=6x^6+20x^5+126x^4+33x^3+87x^2+26x+23$
• $y^2=31x^6+105x^5+70x^4+30x^3+46x^2+61x+43$
• $y^2=29x^6+51x^5+11x^4+75x^3+43x^2+105x+78$
• $y^2=94x^6+134x^5+109x^4+75x^3+135x^2+58x+92$
• $y^2=13x^6+92x^5+46x^4+95x^3+79x^2+45x+70$
• $y^2=87x^6+83x^5+77x^4+72x^3+70x^2+101x+27$
• $y^2=117x^6+22x^5+29x^4+42x^3+79x^2+88x+23$
• $y^2=91x^6+107x^5+54x^4+101x^3+54x^2+107x+91$
• and 80 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 13920 347443200 6611756024160 124107961835520000 2329217782807488309600 43716677816240030336716800 820517707863979692153919839840 15400296239435980287083188715520000 289048159795773569922802694284313309280 5425144911237691373986986507475366279680000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 98 18510 2571314 352303838 48262216258 6611861504430 905824343779474 124097930106060478 17001416405578902818 2329194047577540545550

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
 The isogeny class factors as 1.137.aw $\times$ 1.137.as 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.ae_aes $2$ (not in LMFDB) 2.137.e_aes $2$ (not in LMFDB) 2.137.bo_zu $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.137.ae_aes $2$ (not in LMFDB) 2.137.e_aes $2$ (not in LMFDB) 2.137.bo_zu $2$ (not in LMFDB) 2.137.aba_qc $4$ (not in LMFDB) 2.137.ak_fa $4$ (not in LMFDB) 2.137.k_fa $4$ (not in LMFDB) 2.137.ba_qc $4$ (not in LMFDB)