Properties

Label 2.113.abj_uj
Base Field $\F_{113}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{113}$
Dimension:  $2$
L-polynomial:  $1 - 35 x + 529 x^{2} - 3955 x^{3} + 12769 x^{4}$
Frobenius angles:  $\pm0.137664879391$, $\pm0.235612203595$
Angle rank:  $2$ (numerical)
Number field:  4.0.2758925.3
Galois group:  $D_{4}$
Jacobians:  18

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 18 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9309 160943301 2083115228661 26589198285335781 339463767954118059264 4334529842175871071532341 55347529374318298318208500821 706732552804952654710197679217925 9024267963106071302294653949277045549 115230877646497266095321406081964749213696

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 79 12603 1443703 163076531 18424733294 2081954990907 235260564656063 26584441933772323 3004041937297790839 339456738990052731678

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The endomorphism algebra of this simple isogeny class is 4.0.2758925.3.
All geometric endomorphisms are defined over $\F_{113}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.113.bj_uj$2$(not in LMFDB)