# Properties

 Label 2.137.abq_bbm 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: $( 1 - 22 x + 137 x^{2} )( 1 - 20 x + 137 x^{2} )$ Frobenius angles: $\pm0.111017258455$, $\pm0.173950867407$ Angle rank: $2$ (numerical) Jacobians: 8

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 8 curves, and hence is principally polarizable:

• $y^2=48x^6+28x^5+64x^4+3x^3+7x^2+39x+33$
• $y^2=91x^6+23x^5+89x^4+30x^3+89x^2+23x+91$
• $y^2=136x^6+20x^5+51x^4+30x^3+51x^2+20x+136$
• $y^2=92x^6+81x^5+2x^4+31x^3+2x^2+81x+92$
• $y^2=30x^6+69x^5+57x^4+127x^3+79x^2+129x+63$
• $y^2=52x^6+82x^5+31x^4+44x^3+114x^2+43x+66$
• $y^2=131x^6+119x^5+62x^4+3x^3+62x^2+119x+131$
• $y^2=28x^6+68x^5+106x^4+56x^3+54x^2+93x+30$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 13688 346032640 6608297143352 124103249888051200 2329217153377091196728 43716693710857697597217280 820517757907671806068415624312 15400296333554233556514706882560000 289048159907190344829510762934876984568 5425144911262577773947614111142999329651200

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 96 18434 2569968 352290462 48262203216 6611863908386 905824399026048 124097930864479678 17001416412132284736 2329194047588225099714

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
 The isogeny class factors as 1.137.aw $\times$ 1.137.au 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.ac_agk $2$ (not in LMFDB) 2.137.c_agk $2$ (not in LMFDB) 2.137.bq_bbm $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.137.ac_agk $2$ (not in LMFDB) 2.137.c_agk $2$ (not in LMFDB) 2.137.bq_bbm $2$ (not in LMFDB) 2.137.abc_qs $4$ (not in LMFDB) 2.137.am_ek $4$ (not in LMFDB) 2.137.m_ek $4$ (not in LMFDB) 2.137.bc_qs $4$ (not in LMFDB)