# Properties

 Label 2.107.abi_tf 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: $( 1 - 19 x + 107 x^{2} )( 1 - 15 x + 107 x^{2} )$ Frobenius angles: $\pm0.129482033963$, $\pm0.241815531636$ Angle rank: $2$ (numerical) Jacobians: 24

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 24 curves, and hence is principally polarizable:

• $y^2=x^6+78x^5+14x^4+24x^3+14x^2+78x+1$
• $y^2=82x^6+78x^5+48x^4+87x^3+92x^2+89x+4$
• $y^2=89x^6+84x^5+86x^4+83x^3+86x^2+84x+89$
• $y^2=79x^6+13x^5+85x^4+56x^3+85x^2+13x+79$
• $y^2=38x^6+83x^5+92x^4+52x^3+89x^2+93x+45$
• $y^2=17x^6+64x^5+94x^4+33x^3+53x^2+48x+56$
• $y^2=60x^6+96x^5+101x^4+106x^3+92x^2+37x+82$
• $y^2=64x^6+91x^5+60x^4+51x^3+98x^2+94x+63$
• $y^2=83x^6+72x^5+98x^4+11x^3+45x^2+52x+81$
• $y^2=61x^6+64x^5+56x^4+53x^3+56x^2+64x+61$
• $y^2=87x^6+69x^5+94x^4+44x^3+94x^2+69x+87$
• $y^2=17x^6+42x^5+3x^4+34x^3+55x^2+81x+63$
• $y^2=30x^6+22x^5+16x^4+44x^3+81x^2+33x+100$
• $y^2=5x^6+18x^5+40x^4+74x^3+40x^2+18x+5$
• $y^2=91x^6+45x^5+96x^4+93x^3+81x^2+17x+46$
• $y^2=9x^6+73x^5+13x^4+50x^3+13x^2+73x+9$
• $y^2=66x^6+99x^5+6x^4+60x^3+38x^2+102x+72$
• $y^2=93x^6+78x^5+10x^4+77x^3+10x^2+78x+93$
• $y^2=46x^6+18x^5+96x^4+7x^3+96x^2+18x+46$
• $y^2=x^6+52x^5+42x^4+20x^3+103x^2+29x+17$
• $y^2=82x^6+67x^5+24x^4+41x^3+24x^2+67x+82$
• $y^2=12x^6+105x^5+104x^4+6x^3+104x^2+105x+12$
• $y^2=79x^6+90x^5+105x^4+39x^3+52x^2+70x+91$
• $y^2=73x^6+101x^5+80x^4+65x^3+80x^2+101x+73$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 8277 129295017 1501564737456 17185016651539689 196719250667275990077 2252194964065070623984896 25785343080852433730061534309 295216374922951237108434786134025 3379932275820634270367058092356553904 38696844626774200475460261397404101793177

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 74 11292 1225724 131103668 14025810694 1500732600822 160578157480066 17181861802184356 1838459212468074788 196715135738678253132

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
 The isogeny class factors as 1.107.at $\times$ 1.107.ap 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.ae_act $2$ (not in LMFDB) 2.107.e_act $2$ (not in LMFDB) 2.107.bi_tf $2$ (not in LMFDB)