# Properties

 Label 2.61.aba_ld Base Field $\F_{61}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

# Learn more about

## Invariants

 Base field: $\F_{61}$ Dimension: $2$ L-polynomial: $1 - 26 x + 289 x^{2} - 1586 x^{3} + 3721 x^{4}$ Frobenius angles: $\pm0.125915170111$, $\pm0.234017939091$ Angle rank: $2$ (numerical) Number field: 4.0.254528.3 Galois group: $D_{4}$ Jacobians: 4

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 4 curves, and hence is principally polarizable:

• $y^2=10x^6+26x^5+20x^4+5x^3+11x^2+11x+32$
• $y^2=45x^6+52x^5+7x^4+60x^3+49x^2+9x+28$
• $y^2=23x^6+21x^5+35x^4+27x^3+32x^2+17x+54$
• $y^2=27x^6+41x^4+2x^3+55x^2+26x+9$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 2399 13489577 51567838844 191809495935353 713404598749519959 2654372735023015912208 9876838226761888029162191 36751694277761747142295787753 136753052761566100401998119463516 508858109866973019957392778594903657

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 36 3624 227190 13853220 844669336 51520835550 3142744647624 191707315193988 11694146086080174 713342912009551624

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
 The endomorphism algebra of this simple isogeny class is 4.0.254528.3.
All geometric endomorphisms are defined over $\F_{61}$.

## 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 2.61.ba_ld $2$ (not in LMFDB)