# Properties

 Label 2.113.abl_vu 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: $( 1 - 20 x + 113 x^{2} )( 1 - 17 x + 113 x^{2} )$ Frobenius angles: $\pm0.110150159186$, $\pm0.205038125192$ Angle rank: $2$ (numerical) Jacobians: 4

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 4 curves, and hence is principally polarizable:

• $y^2=47x^6+111x^5+32x^4+36x^3+81x^2+33x+55$
• $y^2=108x^6+20x^5+101x^4+55x^3+30x^2+57x+47$
• $y^2=16x^6+51x^5+77x^4+84x^3+100x^2+10x+66$
• $y^2=26x^6+69x^5+88x^4+36x^3+25x^2+49x+30$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 9118 160057372 2081419729144 26587186403114944 339462519183652738798 4334530513379495713263616 55347532353172396016025559966 706732557053439966264107101843200 9024267966369572655428891749569593656 115230877646759520939012157403185911949852

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 77 12533 1442528 163064193 18424665517 2081955313298 235260577317997 26584442093583361 3004041938384160944 339456738990825303893

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
 The isogeny class factors as 1.113.au $\times$ 1.113.ar and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.
 Twist Extension Degree Common base change 2.113.ad_aek $2$ (not in LMFDB) 2.113.d_aek $2$ (not in LMFDB) 2.113.bl_vu $2$ (not in LMFDB)