Properties

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

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Invariants

Base field:  $\F_{61}$
Dimension:  $2$
L-polynomial:  $1 - 23 x + 240 x^{2} - 1403 x^{3} + 3721 x^{4}$
Frobenius angles:  $\pm0.0670806493623$, $\pm0.335333706816$
Angle rank:  $2$ (numerical)
Number field:  4.0.1598508.2
Galois group:  $D_{4}$
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2536 13663968 51561860704 191688035816832 713292776461893256 2654318549208695334912 9876826327937573587297864 36751697348483655285774263808 136753056175367779080861619284064 508858110771447441494460621759438048

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 39 3673 227166 13844449 844536939 51519783814 3142740861495 191707331211745 11694146378004150 713342913277489393

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
The endomorphism algebra of this simple isogeny class is 4.0.1598508.2.
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.x_jg$2$(not in LMFDB)