# Properties

 Label 2.107.abi_tj 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: $( 1 - 17 x + 107 x^{2} )^{2}$ Frobenius angles: $\pm0.193011390838$, $\pm0.193011390838$ Angle rank: $1$ (numerical) Jacobians: 21

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 21 curves, and hence is principally polarizable:

• $y^2=58x^6+50x^5+23x^4+15x^3+23x^2+50x+58$
• $y^2=95x^6+45x^5+90x^4+76x^3+90x^2+45x+95$
• $y^2=45x^6+17x^5+45x^4+80x^3+55x^2+72x+66$
• $y^2=43x^6+50x^5+103x^4+71x^3+10x^2+23x+54$
• $y^2=82x^6+50x^5+55x^4+48x^3+62x^2+91x+36$
• $y^2=95x^6+90x^5+8x^4+32x^3+8x^2+90x+95$
• $y^2=37x^6+18x^5+54x^4+19x^3+54x^2+18x+37$
• $y^2=25x^6+103x^5+56x^4+99x^3+102x^2+77x+45$
• $y^2=10x^6+97x^5+9x^4+61x^3+9x^2+97x+10$
• $y^2=77x^6+68x^5+94x^4+6x^3+94x^2+68x+77$
• $y^2=83x^6+13x^5+79x^4+87x^3+26x^2+83x+63$
• $y^2=81x^6+101x^5+55x^4+13x^3+73x^2+106x+5$
• $y^2=70x^6+27x^5+52x^4+72x^3+97x^2+4x+87$
• $y^2=104x^6+85x^5+104x^4+58x^3+104x^2+85x+104$
• $y^2=63x^6+105x^5+95x^4+81x^3+95x^2+105x+63$
• $y^2=13x^6+51x^5+95x^4+77x^3+95x^2+51x+13$
• $y^2=35x^6+99x^5+78x^4+68x^3+78x^2+99x+35$
• $y^2=5x^6+6x^5+61x^4+50x^3+61x^2+6x+5$
• $y^2=28x^6+73x^5+81x^4+46x^3+81x^2+73x+28$
• $y^2=75x^6+11x^5+23x^4+40x^3+42x^2+34x+9$
• $y^2=103x^6+30x^5+8x^4+84x^3+63x^2+47x+55$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 8281 129390625 1502065945744 17186390634765625 196721739951669013081 2252198054565040036000000 25785345172578550339972705969 295216373612665823448502353515625 3379932268973325549429141508622202256 38696844614090589496713891203503312890625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 74 11300 1226132 131114148 14025988174 1500734660150 160578170506282 17181861725924548 1838459208743592524 196715135674201206500

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
 The isogeny class factors as 1.107.ar 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-139})$$$)$
All geometric endomorphisms are defined over $\F_{107}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.107.a_acx $2$ (not in LMFDB) 2.107.bi_tj $2$ (not in LMFDB) 2.107.r_ha $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.107.a_acx $2$ (not in LMFDB) 2.107.bi_tj $2$ (not in LMFDB) 2.107.r_ha $3$ (not in LMFDB) 2.107.a_cx $4$ (not in LMFDB) 2.107.ar_ha $6$ (not in LMFDB)