# Properties

 Label 2.137.abn_zc 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: $( 1 - 21 x + 137 x^{2} )( 1 - 18 x + 137 x^{2} )$ Frobenius angles: $\pm0.145687313345$, $\pm0.220793476886$ Angle rank: $2$ (numerical) Jacobians: 36

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 36 curves, and hence is principally polarizable:

• $y^2=29x^6+136x^5+49x^4+21x^3+99x^2+81x+43$
• $y^2=38x^6+61x^5+88x^4+60x^3+14x^2+28x+42$
• $y^2=129x^6+21x^5+55x^4+100x^3+15x^2+53x+133$
• $y^2=49x^6+93x^5+114x^4+22x^3+133x^2+103x+69$
• $y^2=62x^6+56x^5+87x^4+125x^3+127x^2+34x+79$
• $y^2=19x^6+29x^5+2x^4+102x^3+105x^2+67x+60$
• $y^2=55x^6+133x^5+32x^4+9x^3+52x^2+15x+47$
• $y^2=24x^6+10x^5+83x^4+101x^3+6x^2+50x+60$
• $y^2=88x^6+99x^5+121x^4+123x^3+47x^2+59x+116$
• $y^2=72x^6+36x^5+122x^4+58x^3+126x^2+47x+113$
• $y^2=136x^6+114x^5+67x^4+8x^3+71x^2+56x+71$
• $y^2=11x^6+20x^5+115x^4+94x^3+113x^2+70x+77$
• $y^2=81x^6+94x^5+12x^4+113x^3+98x^2+45x+90$
• $y^2=53x^6+87x^5+93x^4+126x^3+29x^2+67x+84$
• $y^2=10x^6+83x^5+134x^4+4x^3+123x^2+100x+86$
• $y^2=78x^6+2x^5+105x^4+105x^3+54x^2+94x+124$
• $y^2=84x^6+5x^5+90x^4+101x^3+33x^2+64x+102$
• $y^2=11x^6+122x^5+122x^4+70x^3+56x^2+82x+2$
• $y^2=75x^6+83x^5+112x^4+76x^3+25x^2+90x+8$
• $y^2=65x^6+61x^5+131x^4+32x^3+82x^2+136x+18$
• and 16 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 14040 348248160 6614267194080 124113673139414400 2329228076205097618200 43716692245537824115599360 820517720587268396688760316760 15400296233225703300927780511372800 289048159733944254232573564887030927840 5425144911056569488430413066887345053672800

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 99 18553 2572290 352320049 48262429539 6611863686766 905824357825563 124097930056017121 17001416401942187250 2329194047499778932793

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
 The isogeny class factors as 1.137.av $\times$ 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 is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.137.ad_aea $2$ (not in LMFDB) 2.137.d_aea $2$ (not in LMFDB) 2.137.bn_zc $2$ (not in LMFDB)