# Properties

 Label 2.61.aba_lb 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: $( 1 - 15 x + 61 x^{2} )( 1 - 11 x + 61 x^{2} )$ Frobenius angles: $\pm0.0900194921159$, $\pm0.251304563322$ 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:

• $y^2=27x^6+2x^5+52x^4+53x^3+3x^2+7x+60$
• $y^2=x^6+24x^5+53x^4+22x^3+25x^2+49x+24$
• $y^2=45x^6+22x^5+23x^4+23x^3+11x^2+56x+15$
• $y^2=35x^6+23x^5+39x^4+22x^3+13x^2+54x+21$
• $y^2=38x^6+40x^5+12x^4+23x^3+49x^2+40x+23$
• $y^2=5x^6+54x^5+31x^4+29x^3+30x+24$
• $y^2=51x^6+29x^5+19x^4+23x^3+46x^2+22x+50$
• $y^2=32x^6+42x^5+39x^4+38x^3+45x^2+57x+30$
• $y^2=44x^6+45x^5+35x^4+17x^3+58x^2+6x+57$
• $y^2=40x^6+13x^5+11x^4+54x^3+45x^2+33x+54$
• $y^2=24x^6+41x^5+52x^4+35x^3+58x^2+52x+28$
• $y^2=53x^6+33x^5+43x^4+13x^3+55x^2+24x+11$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 2397 13473537 51532201728 191766494252025 713369242431934077 2654351339185173196800 9876828861175819282487877 36751691936687469312987333225 136753053211936915846625854879488 508858110815275790850534678501921537

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 36 3620 227034 13850116 844627476 51520420262 3142741667556 191707302982276 11694146124592674 713342913338930180

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
 The isogeny class factors as 1.61.ap $\times$ 1.61.al 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 is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.61.ae_abr $2$ (not in LMFDB) 2.61.e_abr $2$ (not in LMFDB) 2.61.ba_lb $2$ (not in LMFDB)