Properties

Label 2.113.abi_td
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:  $1 - 34 x + 497 x^{2} - 3842 x^{3} + 12769 x^{4}$
Frobenius angles:  $\pm0.0129716274501$, $\pm0.295145069788$
Angle rank:  $2$ (numerical)
Number field:  4.0.13888.1
Galois group:  $D_{4}$
Jacobians:  6

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 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9391 160989913 2081753042812 26583844632986809 339452221851545632351 4334512753243155823843216 55347511478752908560333821903 706732540804895663541403895314473 9024267960357933615312565984074965116 115230877648112880642639724865091355964713

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 80 12608 1442762 163043700 18424106620 2081946782774 235260488589052 26584441482378340 3004041936382977482 339456738994812143888

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The endomorphism algebra of this simple isogeny class is 4.0.13888.1.
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_td$2$(not in LMFDB)