Properties

Label 2.113.abk_va
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:  $( 1 - 20 x + 113 x^{2} )( 1 - 16 x + 113 x^{2} )$
Frobenius angles:  $\pm0.110150159186$, $\pm0.228810695365$
Angle rank:  $2$ (numerical)
Jacobians:  36

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 36 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9212 160473040 2082108851228 26587686780928000 339462031324100340572 4334528345891382494499280 55347528629347858138866470588 706732553283519274288526131200000 9024267965344594308033001649810310332 115230877651386491245580173612768806005200

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 78 12566 1443006 163067262 18424639038 2081954272214 235260561489486 26584441951774078 3004041938042961198 339456739004455819286

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The isogeny class factors as 1.113.au $\times$ 1.113.aq 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 $\F_{113}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.113.ae_adq$2$(not in LMFDB)
2.113.e_adq$2$(not in LMFDB)
2.113.bk_va$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.113.ae_adq$2$(not in LMFDB)
2.113.e_adq$2$(not in LMFDB)
2.113.bk_va$2$(not in LMFDB)
2.113.abi_tm$4$(not in LMFDB)
2.113.ag_acc$4$(not in LMFDB)
2.113.g_acc$4$(not in LMFDB)
2.113.bi_tm$4$(not in LMFDB)