# Properties

 Label 2.137.abn_yy Base Field $\F_{137}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{137}$ Dimension: $2$ L-polynomial: $( 1 - 22 x + 137 x^{2} )( 1 - 17 x + 137 x^{2} )$ Frobenius angles: $\pm0.111017258455$, $\pm0.241282780251$ Angle rank: $2$ (numerical) Jacobians: 28

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 28 curves, and hence is principally polarizable:

• $y^2=54x^6+70x^5+112x^4+91x^3+47x^2+99x+44$
• $y^2=106x^6+98x^5+9x^4+70x^3+37x^2+43x+134$
• $y^2=39x^6+128x^5+17x^4+104x^3+128x^2+11x+13$
• $y^2=68x^6+55x^5+44x^4+117x^3+10x^2+120x+124$
• $y^2=57x^6+110x^5+109x^4+107x^3+75x^2+99x+36$
• $y^2=112x^6+34x^5+45x^4+15x^3+71x^2+15x+113$
• $y^2=126x^6+73x^5+6x^4+11x^3+129x^2+39x+51$
• $y^2=81x^6+55x^5+84x^4+15x^3+127x^2+129x+110$
• $y^2=14x^6+72x^5+11x^4+42x^3+42x^2+75x+23$
• $y^2=131x^6+93x^5+116x^4+129x^3+55x^2+97x+111$
• $y^2=66x^6+98x^5+106x^4+60x^3+49x^2+7x+92$
• $y^2=87x^6+109x^5+21x^4+38x^3+119x^2+109x+10$
• $y^2=88x^6+91x^5+48x^4+125x^3+98x^2+78x+37$
• $y^2=71x^6+135x^5+37x^4+105x^3+84x^2+135x+125$
• $y^2=112x^6+10x^5+70x^4+25x^3+72x^2+85x+45$
• $y^2=54x^6+32x^5+84x^4+29x^3+37x^2+62x$
• $y^2=110x^6+61x^5+113x^4+111x^3+72x+132$
• $y^2=84x^6+87x^5+31x^4+86x^3+104x^2+116x+80$
• $y^2=x^6+16x^5+82x^4+36x^3+129x^2+61x+84$
• $y^2=58x^6+38x^5+93x^4+73x^3+123x^2+30x+23$
• $y^2=57x^6+61x^5+67x^4+126x^3+9x^2+83x+31$
• $y^2=117x^6+19x^5+134x^4+17x^3+132x^2+54x+75$
• $y^2=51x^6+5x^5+58x^4+127x^3+58x^2+23x+38$
• $y^2=101x^6+63x^5+48x^4+47x^3+97x^2+115x+18$
• $y^2=101x^6+9x^5+101x^4+65x^3+135x^2+4x+62$
• $y^2=83x^6+97x^5+114x^4+79x^3+14x^2+62x+58$
• $y^2=102x^6+119x^5+49x^4+75x^3+x^2+125x+39$
• $y^2=80x^6+121x^5+19x^4+68x^3+101x^2+127x+34$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 14036 348092800 6613061456144 124108763247040000 2329214599507414458356 43716665590119660045107200 820517685137746174907301395444 15400296219009643949969287223040000 289048159815531421831448249677398338576 5425144911355422887767742670736080004720000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 99 18545 2571822 352306113 48262150299 6611859655310 905824318690467 124097929941461953 17001416406741032574 2329194047628086576225

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
 The isogeny class factors as 1.137.aw $\times$ 1.137.ar 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 $\F_{137}$.

## 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 2.137.af_adw $2$ (not in LMFDB) 2.137.f_adw $2$ (not in LMFDB) 2.137.bn_yy $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.137.af_adw $2$ (not in LMFDB) 2.137.f_adw $2$ (not in LMFDB) 2.137.bn_yy $2$ (not in LMFDB) 2.137.az_pu $4$ (not in LMFDB) 2.137.aj_fi $4$ (not in LMFDB) 2.137.j_fi $4$ (not in LMFDB) 2.137.z_pu $4$ (not in LMFDB)