# Properties

 Label 2.107.abh_sb Base Field $\F_{107}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{107}$ Dimension: $2$ L-polynomial: $1 - 33 x + 469 x^{2} - 3531 x^{3} + 11449 x^{4}$ Frobenius angles: $\pm0.0184782107058$, $\pm0.296438695563$ Angle rank: $2$ (numerical) Number field: 4.0.1890117.1 Galois group: $D_{4}$ Jacobians: 8

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 8 curves, and hence is principally polarizable:

• $y^2=40x^6+48x^5+23x^4+52x^3+33x^2+67x+16$
• $y^2=96x^6+71x^5+96x^4+51x^3+48x+26$
• $y^2=97x^6+47x^5+42x^4+82x^3+21x^2+44x+12$
• $y^2=91x^6+99x^5+101x^4+41x^3+2x^2+50x+106$
• $y^2=105x^6+97x^5+100x^4+104x^3+x^2+25x+52$
• $y^2=80x^6+61x^5+31x^4+36x^3+44x^2+99x+69$
• $y^2=91x^6+27x^5+90x^4+89x^3+44x^2+58x+5$
• $y^2=91x^6+106x^5+66x^4+91x^3+22x^2+26x+17$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 8355 129360465 1500606985365 17181445456939725 196712138388749156400 2252185309823821661433105 25785333806728116307799242785 295216369059949695931460066083125 3379932273922230878647974091324192095 38696844625731243240593577155849535379200

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 75 11299 1224945 131076427 14025303600 1500726167791 160578099725475 17181861460952323 1838459211435469125 196715135733376387414

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
 The endomorphism algebra of this simple isogeny class is 4.0.1890117.1.
All geometric endomorphisms are defined over $\F_{107}$.

## 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 2.107.bh_sb $2$ (not in LMFDB)