# Properties

 Label 2.137.abq_bbi 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: $1 - 42 x + 710 x^{2} - 5754 x^{3} + 18769 x^{4}$ Frobenius angles: $\pm0.0387594407114$, $\pm0.204006140474$ Angle rank: $2$ (numerical) Number field: 4.0.39600.1 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:

• $y^2=42x^5+34x^4+58x^3+85x^2+127x+108$
• $y^2=44x^6+52x^5+69x^4+37x^3+82x^2+51x+88$
• $y^2=108x^6+67x^5+121x^4+18x^3+117x^2+23x+108$
• $y^2=114x^6+19x^5+111x^4+121x^3+109x^2+26x$
• $y^2=86x^6+20x^5+116x^4+95x^3+95x^2+120x+98$
• $y^2=43x^6+105x^5+81x^4+76x^3+19x^2+10x+34$
• $y^2=29x^6+51x^5+127x^4+76x^3+94x^2+56x+71$
• $y^2=3x^6+95x^5+7x^4+65x^3+91x^2+78x+117$
• $y^2=21x^6+63x^5+128x^4+14x^3+80x^2+61x+71$
• $y^2=46x^6+93x^5+123x^4+18x^3+65x^2+58x+63$
• $y^2=124x^6+39x^5+81x^4+33x^3+114x^2+11x+9$
• $y^2=98x^6+4x^5+59x^4+30x^3+92x^2+68x+106$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 13684 345876784 6606998222836 124097319488330496 2329197815680791488884 43716643676903369178871216 820517650277001837983016620404 15400296137895869596701921316614144 289048159609537543091930575351321032244 5425144910903940809160689567253233459253424

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 96 18426 2569464 352273630 48261802536 6611856341082 905824280205360 124097929287834814 17001416394624755088 2329194047434250395386

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
 The endomorphism algebra of this simple isogeny class is 4.0.39600.1.
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.bq_bbi $2$ (not in LMFDB)