# Properties

 Label 2.61.abb_lq 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: $( 1 - 15 x + 61 x^{2} )( 1 - 12 x + 61 x^{2} )$ Frobenius angles: $\pm0.0900194921159$, $\pm0.221142061624$ Angle rank: $2$ (numerical) Jacobians: 5

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 5 curves, and hence is principally polarizable:

• $y^2=16x^6+22x^5+3x^4+43x^3+21x^2+50x+43$
• $y^2=29x^6+21x^5+35x^4+47x^3+12x^2+12x+37$
• $y^2=38x^6+43x^5+3x^4+2x^3+8x^2+36x+56$
• $y^2=43x^6+34x^5+21x^4+49x^2+34x+24$
• $y^2=21x^6+37x^5+21x^4+57x^3+9x^2+41x+41$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 2350 13390300 51483762400 191759808240000 713381657019583750 2654364018363346643200 9876835289341756339168150 36751693269957700872277440000 136753052405163214028601309253600 508858109817094550832148042994357500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 35 3597 226820 13849633 844642175 51520666362 3142743712955 191707309936993 11694146055603140 713342911939629477

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
 The isogeny class factors as 1.61.ap $\times$ 1.61.am 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 $\F_{61}$.

## 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.ad_acg $2$ (not in LMFDB) 2.61.d_acg $2$ (not in LMFDB) 2.61.bb_lq $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.61.ad_acg $2$ (not in LMFDB) 2.61.d_acg $2$ (not in LMFDB) 2.61.bb_lq $2$ (not in LMFDB) 2.61.az_km $4$ (not in LMFDB) 2.61.af_abc $4$ (not in LMFDB) 2.61.f_abc $4$ (not in LMFDB) 2.61.z_km $4$ (not in LMFDB)