# Properties

 Label 2.107.abi_ta 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: $( 1 - 20 x + 107 x^{2} )( 1 - 14 x + 107 x^{2} )$ Frobenius angles: $\pm0.0823304377774$, $\pm0.263402699857$ Angle rank: $2$ (numerical) Jacobians: 20

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 20 curves, and hence is principally polarizable:

• $y^2=106x^6+39x^5+12x^4+51x^3+39x^2+4x+71$
• $y^2=65x^6+64x^5+83x^4+96x^3+101x^2+50x+58$
• $y^2=77x^6+32x^5+95x^4+26x^3+71x^2+76x+82$
• $y^2=32x^6+81x^4+53x^3+47x^2+96x+94$
• $y^2=38x^6+13x^5+73x^4+83x^3+92x^2+26x+94$
• $y^2=51x^6+3x^5+82x^4+28x^3+82x^2+3x+51$
• $y^2=100x^6+17x^5+31x^4+51x^3+21x^2+48x+57$
• $y^2=34x^6+102x^5+20x^4+34x^3+78x^2+47x+29$
• $y^2=24x^6+91x^5+67x^4+81x^3+29x^2+80x+10$
• $y^2=16x^6+35x^5+73x^4+6x^3+78x^2+18x+95$
• $y^2=36x^6+30x^5+64x^4+74x^3+52x^2+82x+105$
• $y^2=94x^6+88x^5+76x^4+52x^3+76x^2+88x+94$
• $y^2=48x^6+8x^5+62x^4+61x^3+48x^2+6x+94$
• $y^2=96x^6+62x^5+44x^4+51x^3+99x^2+60x+22$
• $y^2=71x^6+76x^5+40x^4+83x^3+72x^2+72x+70$
• $y^2=91x^6+22x^5+4x^4+39x^3+79x^2+67x+97$
• $y^2=20x^6+51x^5+86x^4+85x^3+32x^2+97x$
• $y^2=78x^6+62x^5+82x^4+30x^3+37x^2+6x+102$
• $y^2=94x^6+80x^5+32x^4+80x^3+45x^2+41x+86$
• $y^2=105x^6+42x^5+81x^4+60x^3+41x^2+25x+75$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 8272 129175552 1500938294416 17183287418159104 196716031782848094352 2252190600390749948317696 25785338878827623582466059344 295216372758458844710307731865600 3379932277185452691706594731269500624 38696844631806666330693711679133023178752

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 74 11282 1225214 131090478 14025581194 1500729693122 160578131311966 17181861676208926 1838459213210445578 196715135764260757682

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
 The isogeny class factors as 1.107.au $\times$ 1.107.ao 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 $\F_{107}$.

## 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.ag_aco $2$ (not in LMFDB) 2.107.g_aco $2$ (not in LMFDB) 2.107.bi_ta $2$ (not in LMFDB)