Properties

Label 2.113.abq_zr
Base Field $\F_{113}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{113}$
Dimension:  $2$
L-polynomial:  $( 1 - 21 x + 113 x^{2} )^{2}$
Frobenius angles:  $\pm0.0498602789898$, $\pm0.0498602789898$
Angle rank:  $1$ (numerical)
Jacobians:  1

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 1 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8649 157628025 2075777851536 26577696761555625 339449650075636504569 4334516011694338524057600 55347518874010394941030878201 706732547264157044511694930055625 9024267961829038372136549024080043664 115230877647123934473213223010237074025625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 72 12340 1438614 163005988 18423967032 2081948347870 235260520023384 26584441725349828 3004041936872685942 339456738991898823700

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The isogeny class factors as 1.113.av 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-11}) \)$)$
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_aih$2$(not in LMFDB)
2.113.bq_zr$2$(not in LMFDB)
2.113.v_mq$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.113.a_aih$2$(not in LMFDB)
2.113.bq_zr$2$(not in LMFDB)
2.113.v_mq$3$(not in LMFDB)
2.113.a_ih$4$(not in LMFDB)
2.113.av_mq$6$(not in LMFDB)