# Properties

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

## Invariants

 Base field: $\F_{61}$ Dimension: $2$ L-polynomial: $( 1 - 15 x + 61 x^{2} )^{2}$ Frobenius angles: $\pm0.0900194921159$, $\pm0.0900194921159$ Angle rank: $1$ (numerical) Jacobians: 1

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 1 curves, and hence is principally polarizable:

• $y^2=29x^6+26x^5+50x^4+46x^3+6x^2+40x+26$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 2209 13097161 51235227904 191619651155625 713327584011549529 2654354854115086667776 9876841392793072459507729 36751700628427917473879855625 136753057025814888000782067437824 508858111912130669426735905295937241

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 32 3516 225722 13839508 844578152 51520488486 3142745655032 191707348320868 11694146450728322 713342914876556556

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
 The isogeny class factors as 1.61.ap 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-19})$$$)$
All geometric endomorphisms are defined over $\F_{61}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.61.a_adz $2$ (not in LMFDB) 2.61.be_nj $2$ (not in LMFDB) 2.61.p_gi $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.61.a_adz $2$ (not in LMFDB) 2.61.be_nj $2$ (not in LMFDB) 2.61.p_gi $3$ (not in LMFDB) 2.61.a_dz $4$ (not in LMFDB) 2.61.ap_gi $6$ (not in LMFDB)