# Properties

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

## 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:

• $y^2=75x^6+7x^5+107x^4+109x^3+37x^2+81x+48$

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

 $r$ 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.
 Twist Extension Degree Common 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.
 Twist Extension Degree Common 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)