Properties

Label 2.113.abi_tg
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:  $1 - 34 x + 500 x^{2} - 3842 x^{3} + 12769 x^{4}$
Frobenius angles:  $\pm0.0608513799594$, $\pm0.288168650894$
Angle rank:  $2$ (numerical)
Number field:  4.0.16430400.1
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
$A(\F_{q^r})$ 9394 161069524 2082195515554 26585131201888336 339454777675268908114 4334516670439887231859636 55347516596310011212072635394 706732547343736659709238119240704 9024267969737262773110995909201447586 115230877663070247629880793483527883745524

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 80 12614 1443068 163051590 18424245340 2081948664278 235260510341776 26584441728343294 3004041939505213904 339456739038874804214

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The endomorphism algebra of this simple isogeny class is 4.0.16430400.1.
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.bi_tg$2$(not in LMFDB)