# Properties

 Label 2.113.abl_vv Base field $\F_{113}$ Dimension $2$ $p$-rank $2$ Ordinary Yes Supersingular No Simple Yes Geometrically simple Yes Primitive Yes Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{113}$ Dimension: $2$ L-polynomial: $1 - 37 x + 567 x^{2} - 4181 x^{3} + 12769 x^{4}$ Frobenius angles: $\pm0.125932323751$, $\pm0.195315764367$ Angle rank: $2$ (numerical) Number field: 4.0.251525.1 Galois group: $D_{4}$ Jacobians: 11

This isogeny class is simple and geometrically 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 11 curves, and hence is principally polarizable:

• $y^2=22x^6+41x^5+47x^4+71x^3+19x^2+5x+10$
• $y^2=83x^6+45x^5+12x^4+94x^3+22x^2+20x+2$
• $y^2=108x^6+103x^5+93x^4+63x^3+44x^2+97x+59$
• $y^2=107x^6+22x^5+45x^4+72x^3+86x^2+95x+73$
• $y^2=20x^6+24x^5+2x^4+99x^3+101x+52$
• $y^2=36x^6+62x^5+36x^4+110x^3+12x^2+106x+40$
• $y^2=50x^6+29x^5+107x^4+65x^3+16x+70$
• $y^2=58x^6+31x^5+40x^4+70x^3+88x^2+93x+43$
• $y^2=94x^6+67x^5+101x^4+107x^3+29x^2+102x+41$
• $y^2=110x^6+103x^5+89x^4+105x^3+32x^2+71x+109$
• $y^2=59x^6+89x^5+61x^4+39x^3+89x^2+24x+48$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 9119 160084045 2081580351191 26587709893247525 339463708769380319344 4334532575673493601124805 55347535113292175299156359551 706732559654515008153553485743525 9024267967138072773892549595512288799 115230877643442455480000794885904731168000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 77 12535 1442639 163067403 18424730082 2081956303855 235260589050179 26584442191425363 3004041938639982977 339456738981053615550

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
 The endomorphism algebra of this simple isogeny class is 4.0.251525.1.
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.bl_vv $2$ (not in LMFDB)