Properties

 Label 2.83.abh_qv Base Field $\F_{83}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

Invariants

 Base field: $\F_{83}$ Dimension: $2$ L-polynomial: $1 - 33 x + 437 x^{2} - 2739 x^{3} + 6889 x^{4}$ Frobenius angles: $\pm0.0821076990436$, $\pm0.180078914894$ Angle rank: $2$ (numerical) Number field: 4.0.51525.2 Galois group: $D_{4}$ Jacobians: 4

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 4 curves, and hence is principally polarizable:

• $y^2=32x^6+60x^5+43x^4+81x^3+61x^2+18x+78$
• $y^2=34x^6+33x^5+42x^4+33x^3+25x^2+17x+22$
• $y^2=58x^6+41x^5+10x^4+6x^3+42x^2+42x+73$
• $y^2=8x^6+82x^5+65x^4+51x^3+61x^2+40x+22$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 4555 46000945 326431847605 2252373940644525 15516374481032902000 106890361098075995548705 736365522272100916162333105 5072820439732946811101747049525 34946659089926511028740376087580455 240747534127427914826869600343301088000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 51 6675 570897 47460043 3939125256 326941454175 27136060532667 2252292294643843 186940255537323621 15516041187486819750

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
 The endomorphism algebra of this simple isogeny class is 4.0.51525.2.
All geometric endomorphisms are defined over $\F_{83}$.

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 2.83.bh_qv $2$ (not in LMFDB)