# Properties

 Label 2.137.abq_bbl 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: $1 - 42 x + 713 x^{2} - 5754 x^{3} + 18769 x^{4}$ Frobenius angles: $\pm0.0931478584563$, $\pm0.184503139221$ Angle rank: $2$ (numerical) Number field: 4.0.479808.2 Galois group: $D_{4}$ Jacobians: 8

This isogeny class is simple and geometrically 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:

• $y^2=63x^6+109x^5+69x^4+56x^3+55x^2+59x+114$
• $y^2=106x^6+108x^5+5x^4+56x^3+80x^2+4x+80$
• $y^2=7x^6+82x^5+97x^4+41x^3+116x^2+28x+99$
• $y^2=66x^6+71x^5+76x^4+49x^3+35x^2+55x+26$
• $y^2=12x^6+56x^5+24x^4+11x^3+105x^2+98x+48$
• $y^2=125x^6+3x^5+42x^4+57x^3+72x^2+46x+124$
• $y^2=123x^6+10x^5+5x^4+127x^3+127x^2+31x+82$
• $y^2=118x^6+124x^5+130x^4+32x^3+79x^2+66x+92$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 13687 345993673 6607972406812 124101769395764889 2329212349354414145287 43716681432499936510270096 820517732220779645642672984071 15400296289724485385115161369609193 289048159850417540615711168388585923548 5425144911225669194566207389440905852605913

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 96 18432 2569842 352286260 48262103676 6611862051366 905824370668572 124097930511292900 17001416408792986242 2329194047572379026512

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
 The endomorphism algebra of this simple isogeny class is 4.0.479808.2.
All geometric endomorphisms are defined over $\F_{137}$.

## 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 2.137.bq_bbl $2$ (not in LMFDB)