# Properties

 Label 2.113.abm_wl 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: $( 1 - 21 x + 113 x^{2} )( 1 - 17 x + 113 x^{2} )$ Frobenius angles: $\pm0.0498602789898$, $\pm0.205038125192$ Angle rank: $2$ (numerical) Jacobians: 6

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 6 curves, and hence is principally polarizable:

• $y^2=9x^6+66x^5+6x^4+33x^3+7x^2+13x+66$
• $y^2=68x^6+14x^5+52x^4+98x^3+30x^2+7x+37$
• $y^2=24x^6+111x^5+28x^4+107x^3+106x^2+26x+92$
• $y^2=53x^6+19x^5+45x^4+79x^3+6x^2+19x+29$
• $y^2=25x^6+77x^5+93x^4+77x^3+96x^2+61x+15$
• $y^2=79x^6+87x^5+76x^4+5x^3+37x^2+87x+34$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 9021 159536385 2080088593488 26584585616734425 339458180535141361221 4334524059813697535016960 55347523627759087962830460117 706732546273360427175587303877225 9024267954290481694632254660550387792 115230877634826652792380154325682492517425

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 76 12492 1441606 163048244 18424430036 2081952213534 235260540229700 26584441688080036 3004041934363214758 339456738955672464732

## Decomposition and endomorphism algebra

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