Properties

Label 2.61.abc_me
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:  $1 - 28 x + 316 x^{2} - 1708 x^{3} + 3721 x^{4}$
Frobenius angles:  $\pm0.0517882731736$, $\pm0.201777330689$
Angle rank:  $2$ (numerical)
Number field:  4.0.35072.1
Galois group:  $D_{4}$
Jacobians:  2

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 2 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2302 13291748 51399813358 191710018256528 713358259036137982 2654354322948740827748 9876830895481746848748718 36751690580362241035969236992 136753050453397153152186677028958 508858108484243577380233065934486308

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 34 3570 226450 13846038 844614474 51520478178 3142742314858 191707295907294 11694145888702018 713342910071171890

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
The endomorphism algebra of this simple isogeny class is 4.0.35072.1.
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.
TwistExtension DegreeCommon base change
2.61.bc_me$2$(not in LMFDB)