Abelian variety isogeny class 2.137.abn_yq over $\F_{137}$

• Label: 2.137.abn_yq
• Base field: $\F_{137}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{137}$
Dimension:	$2$
L-polynomial:	$1 - 39 x + 640 x^{2} - 5343 x^{3} + 18769 x^{4}$
Frobenius angles:	$\pm0.0341358853414$, $\pm0.265546250536$
Angle rank:	$2$ (numerical)
Number field:	4.0.1533528.4
Galois group:	$D_{4}$
Jacobians:	$24$

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

$p$-rank:	$2$
Slopes:	$[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$14028$	$347782176$	$6610650166512$	$124098875979071616$	$2329186742728070020908$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$99$	$18529$	$2570886$	$352278049$	$48261573099$	$6611850650734$	$905824207948563$	$124097928855447553$	$17001416398082163030$	$2329194047562543026929$

Jacobians and polarizations

This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=54x^6+84x^5+116x^4+90x^3+70x^2+76x+107$
• $y^2=15x^6+71x^5+75x^4+133x^3+18x^2+118x+87$
• $y^2=113x^6+22x^5+25x^4+38x^3+64x^2+13x+41$
• $y^2=110x^6+132x^5+104x^4+120x^3+116x^2+134x+65$
• $y^2=4x^6+84x^5+87x^4+131x^3+34x^2+126x+132$
• $y^2=43x^6+4x^5+125x^4+128x^3+35x^2+x+125$
• $y^2=114x^6+58x^5+11x^4+114x^3+128x^2+121x+50$
• $y^2=40x^6+40x^5+102x^4+54x^3+102x^2+79x+119$
• $y^2=31x^6+21x^5+60x^4+120x^3+37x^2+38x+104$
• $y^2=57x^6+102x^5+70x^4+36x^3+116x^2+131x+116$
• $y^2=45x^6+124x^5+112x^4+66x^3+19x^2+128x+73$
• $y^2=13x^6+132x^5+20x^4+21x^3+105x^2+15x+120$
• $y^2=4x^6+5x^5+58x^4+82x^3+98x^2+88x+5$
• $y^2=44x^6+95x^5+48x^4+93x^3+17x^2+132x+27$
• $y^2=94x^6+95x^5+117x^4+16x^3+120x^2+111x+41$
• $y^2=71x^6+32x^5+76x^4+70x^3+110x^2+80x+129$
• $y^2=131x^6+56x^5+30x^4+59x^3+98x^2+76x+32$
• $y^2=124x^6+133x^5+58x^4+128x^3+102x^2+68x+32$
• $y^2=123x^6+3x^5+124x^4+25x^3+114x^2+121x+12$
• $y^2=92x^6+125x^5+88x^4+87x^3+79x^2+6x+54$
• $y^2=111x^6+131x^5+49x^4+20x^3+33x^2+23x+23$
• $y^2=115x^6+70x^5+48x^4+64x^3+77x^2+90x+5$
• $y^2=48x^6+70x^5+75x^4+113x^3+120x^2+97x+83$
• $y^2=34x^6+63x^5+58x^4+106x^3+132x^2+93x+79$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{137}$.

Endomorphism algebra over $\F_{137}$

The endomorphism algebra of this simple isogeny class is 4.0.1533528.4.

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.bn_yq	$2$	(not in LMFDB)