Abelian variety isogeny class 1.463.e over $\F_{463}$

• Label: 1.463.e
• Base field: $\F_{463}$
• Dimension: $1$
• $p$-rank: $1$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{463}$
Dimension:	$1$
L-polynomial:	$1 + 4 x + 463 x^{2}$
Frobenius angles:	$\pm0.529628997128$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-51}) \)
Galois group:	$C_2$
Jacobians:	$32$
Isomorphism classes:	32

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:	$1$
Slopes:	$[0, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$468$	$215280$	$99247356$	$45953668800$	$21276737698788$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$468$	$215280$	$99247356$	$45953668800$	$21276737698788$	$9851127805949040$	$4561072093620996876$	$2111776380478252051200$	$977752464194190745701108$	$452699390921255283855020400$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 32 curves (of which 0 are hyperelliptic):

• $y^2=x^3+50 x+150$
• $y^2=x^3+130 x+130$
• $y^2=x^3+239 x+239$
• $y^2=x^3+291 x+291$
• $y^2=x^3+6 x+6$
• $y^2=x^3+372 x+190$
• $y^2=x^3+394 x+394$
• $y^2=x^3+364 x+364$
• $y^2=x^3+353 x+133$
• $y^2=x^3+217 x+188$
• $y^2=x^3+222 x+203$
• $y^2=x^3+7 x+21$
• $y^2=x^3+136 x+408$
• $y^2=x^3+133 x+399$
• $y^2=x^3+146 x+438$
• $y^2=x^3+66 x+198$
• $y^2=x^3+15 x+45$
• $y^2=x^3+88 x+264$
• $y^2=x^3+410 x+410$
• $y^2=x^3+148 x+148$
• and

• $y^2=x^3+21 x+21$
• $y^2=x^3+103 x+103$
• $y^2=x^3+201 x+140$
• $y^2=x^3+113 x+339$
• $y^2=x^3+206 x+155$
• $y^2=x^3+203 x+203$
• $y^2=x^3+249 x+284$
• $y^2=x^3+232 x+233$
• $y^2=x^3+104 x+312$
• $y^2=x^3+169 x+44$
• $y^2=x^3+131 x+393$
• $y^2=x^3+207 x+207$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{463}$.

Endomorphism algebra over $\F_{463}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-51}) \).

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
1.463.ae	$2$	(not in LMFDB)