# Properties

 Label 2.113.abj_tz 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: $1 - 35 x + 519 x^{2} - 3955 x^{3} + 12769 x^{4}$ Frobenius angles: $\pm0.0338691187123$, $\pm0.273965054653$ Angle rank: $2$ (numerical) Number field: 4.0.3721925.1 Galois group: $C_4$ Jacobians: 10

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 10 curves, and hence is principally polarizable:

• $y^2=16x^6+105x^5+12x^4+x^3+64x^2+76x+74$
• $y^2=89x^6+56x^5+57x^4+91x^3+67x^2+46x+11$
• $y^2=89x^6+14x^5+101x^4+7x^3+14x^2+87x+66$
• $y^2=60x^6+7x^5+41x^4+78x^3+111x^2+37x+40$
• $y^2=40x^6+10x^5+89x^4+104x^3+90x^2+8x+64$
• $y^2=81x^6+64x^5+39x^4+49x^3+64x^2+11x+79$
• $y^2=37x^6+83x^5+55x^4+112x^3+66x^2+66x+57$
• $y^2=5x^6+83x^5+12x^4+62x^3+13x^2+40x+65$
• $y^2=89x^6+63x^5+9x^4+45x^3+53x^2+15x+95$
• $y^2=64x^6+100x^5+19x^4+92x^3+40x^2+90x+65$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 9299 160677421 2081596484051 26584625768358821 339454417535489545264 4334515652801270765071621 55347513182994454725101116811 706732539822785125234621810213925 9024267958055401135225644097329609539 115230877649715360789030727424741616061696

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 79 12583 1442653 163048491 18424225794 2081948175487 235260495833113 26584441445435283 3004041935616499339 339456738999532863678

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
 The endomorphism algebra of this simple isogeny class is 4.0.3721925.1.
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.bj_tz $2$ (not in LMFDB)