Properties

Label 2.113.abk_ve
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:  $( 1 - 18 x + 113 x^{2} )^{2}$
Frobenius angles:  $\pm0.178616545187$, $\pm0.178616545187$
Angle rank:  $1$ (numerical)
Jacobians:  46

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 46 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9216 160579584 2082733876224 26589638502383616 339466183491188745216 4334534812822949426774016 55347535662524742615108166656 706732556518712387337796498489344 9024267958264608008618500785583727616 115230877627652515305272763087380269645824

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 78 12574 1443438 163079230 18424864398 2081957378398 235260591384750 26584442073469054 3004041935686141134 339456738934538291614

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The isogeny class factors as 1.113.as 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-2}) \)$)$
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.a_adu$2$(not in LMFDB)
2.113.bk_ve$2$(not in LMFDB)
2.113.s_id$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.113.a_adu$2$(not in LMFDB)
2.113.bk_ve$2$(not in LMFDB)
2.113.s_id$3$(not in LMFDB)
2.113.a_du$4$(not in LMFDB)
2.113.as_id$6$(not in LMFDB)
2.113.aq_ey$8$(not in LMFDB)
2.113.q_ey$8$(not in LMFDB)