Properties

Label 2.113.abl_vt
Base Field $\F_{113}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{113}$
Dimension:  $2$
L-polynomial:  $1 - 37 x + 565 x^{2} - 4181 x^{3} + 12769 x^{4}$
Frobenius angles:  $\pm0.0958952581556$, $\pm0.212472008282$
Angle rank:  $2$ (numerical)
Number field:  4.0.1164917.2
Galois group:  $D_{4}$
Jacobians:  18

This isogeny class is simple and geometrically simple.

Newton polygon

$p$-rank:  $1$
Slopes:  $[0, 1/2, 1/2, 1]$

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
$A(\F_{q^r})$ 9117 160030701 2081259110493 26586662263297461 339461322782047472592 4334528413923021250525917 55347529452542401822728035877 706732554040567788993606236828133 9024267964612568669938333784086791381 115230877648077837219268421333060384034816

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 77 12531 1442417 163060979 18424600582 2081954304891 235260564988561 26584441980251203 3004041937799280965 339456738994708910046

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The endomorphism algebra of this simple isogeny class is 4.0.1164917.2.
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.bl_vt$2$(not in LMFDB)