# Properties

 Label 2.113.abn_xg 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: $( 1 - 21 x + 113 x^{2} )( 1 - 18 x + 113 x^{2} )$ Frobenius angles: $\pm0.0498602789898$, $\pm0.178616545187$ Angle rank: $2$ (numerical) Jacobians: 7

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 7 curves, and hence is principally polarizable:

• $y^2=84x^6+27x^5+31x^4+60x^3+105x^2+111x+17$
• $y^2=83x^6+18x^5+112x^4+29x^3+61x^2+42x+80$
• $y^2=70x^6+24x^5+23x^4+54x^3+76x^2+21x+54$
• $y^2=12x^6+109x^5+95x^4+72x^3+90x^2+3x+96$
• $y^2=83x^6+40x^5+92x^4+26x^3+78x^2+59x$
• $y^2=76x^6+42x^5+33x^4+107x^3+71x^2+32x+25$
• $y^2=58x^6+92x^5+58x^4+3x^3+81x^2+64x+85$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 8928 159096960 2079252955008 26583666961420800 339457916682754407648 4334525412248450170920960 55347527268266932222499849184 706732551891434700776371275417600 9024267960046823190201538832157916032 115230877637388224888831714218660042396800

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 75 12457 1441026 163042609 18424415715 2081952863134 235260555704067 26584441899409441 3004041936279413538 339456738963218557657

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
 The isogeny class factors as 1.113.av $\times$ 1.113.as 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_afw $2$ (not in LMFDB) 2.113.d_afw $2$ (not in LMFDB) 2.113.bn_xg $2$ (not in LMFDB)