# Properties

 Label 2.139.abn_yu Base Field $\F_{139}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{139}$ Dimension: $2$ L-polynomial: $1 - 39 x + 644 x^{2} - 5421 x^{3} + 19321 x^{4}$ Frobenius angles: $\pm0.0512302470248$, $\pm0.267624205263$ Angle rank: $2$ (numerical) Number field: 4.0.14321592.1 Galois group: $D_{4}$ Jacobians: 12

This isogeny class is simple and geometrically 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 12 curves, and hence is principally polarizable:

• $y^2=16x^6+111x^5+129x^4+133x^3+68x^2+42x+125$
• $y^2=124x^6+42x^5+69x^4+75x^3+67x^2+72x+26$
• $y^2=59x^6+120x^5+10x^4+4x^3+135x^2+5x+86$
• $y^2=61x^6+53x^5+42x^4+73x^3+24x^2+65x+83$
• $y^2=64x^6+97x^5+53x^4+131x^3+126x^2+79x+46$
• $y^2=95x^6+2x^5+31x^4+14x^3+127x^2+68x+133$
• $y^2=84x^6+44x^5+30x^4+4x^2+99x+12$
• $y^2=89x^6+115x^5+73x^4+30x^3+22x^2+61x+95$
• $y^2=33x^6+22x^5+53x^4+11x^3+7x^2+84x+97$
• $y^2=114x^6+71x^5+101x^4+25x^3+33x^2+120x+76$
• $y^2=120x^6+99x^5+60x^4+41x^3+120x^2+121x+123$
• $y^2=134x^6+67x^5+55x^4+5x^3+2x^2+34x+75$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 14506 368829556 7211918601832 139356201880518048 2692447325174472076966 52020834364737421315889344 1005095124858502421737943123638 19419444442267330846062043979620992 375203088377945894339435326435240409608 7249298872042682638569157054840574533816756

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 101 19089 2685386 373307833 51888750671 7212544605906 1002544282836197 139353666328482289 19370159738857786718 2692452204255518893089

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
 The endomorphism algebra of this simple isogeny class is 4.0.14321592.1.
All geometric endomorphisms are defined over $\F_{139}$.

## 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 2.139.bn_yu $2$ (not in LMFDB)