# Properties

 Label 2.139.abp_bau 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: $( 1 - 22 x + 139 x^{2} )( 1 - 19 x + 139 x^{2} )$ Frobenius angles: $\pm0.117174211439$, $\pm0.201746658314$ Angle rank: $2$ (numerical) Jacobians: 12

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 12 curves, and hence is principally polarizable:

• $y^2=20x^6+90x^5+76x^4+2x^3+95x^2+66x+128$
• $y^2=74x^6+13x^5+124x^4+3x^3+124x^2+44x+26$
• $y^2=63x^6+74x^5+93x^4+109x^3+57x^2+111x+72$
• $y^2=78x^6+81x^5+16x^4+133x^3+80x^2+62x+75$
• $y^2=25x^6+68x^5+64x^4+79x^3+39x^2+22x+72$
• $y^2=5x^6+123x^5+118x^4+66x^3+119x^2+18x+100$
• $y^2=91x^6+113x^5+106x^4+37x^3+43x^2+19x+2$
• $y^2=94x^6+104x^5+124x^4+93x^3+78x^2+4x+43$
• $y^2=111x^6+121x^5+114x^4+127x^3+94x^2+35x+94$
• $y^2=108x^6+64x^5+85x^4+35x^3+41x^2+122x+131$
• $y^2=10x^6+18x^5+59x^4+98x^3+111x^2+x+76$
• $y^2=20x^6+17x^5+75x^4+71x^3+11x^2+31x+50$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 14278 367772724 7211452111864 139364104961648160 2692482135346412639098 52020922682124690210012096 1005095281582266730038402829258 19419444630918487938498711760448640 375203088472309216431017324620185208024 7249298871845690387189460158870626553418804

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 99 19033 2685210 373329001 51889421529 7212556850866 1002544439162211 139353667682240401 19370159743729368750 2692452204182354269753

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
 The isogeny class factors as 1.139.aw $\times$ 1.139.at 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 $\F_{139}$.

## 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.ad_afk $2$ (not in LMFDB) 2.139.d_afk $2$ (not in LMFDB) 2.139.bp_bau $2$ (not in LMFDB)