Abelian variety isogeny class 2.149.abp_bbl over $\F_{149}$

• Label: 2.149.abp_bbl
• Base field: $\F_{149}$
• 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:	$\F_{149}$
Dimension:	$2$
L-polynomial:	$1 - 41 x + 713 x^{2} - 6109 x^{3} + 22201 x^{4}$
Frobenius angles:	$\pm0.116678124869$, $\pm0.232039777634$
Angle rank:	$2$ (numerical)
Number field:	4.0.8928045.2
Galois group:	$D_{4}$
Jacobians:	$34$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$16765$	$487274725$	$10944021617305$	$242954079080495125$	$5393445839783145365200$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$109$	$21947$	$3308401$	$492923043$	$73440390914$	$10942532673707$	$1630436498408141$	$242935032826379203$	$36197319879932052889$	$5393400662112036526502$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 34 curves (of which all are hyperelliptic):

• $y^2=51 x^6+76 x^5+102 x^4+102 x^3+141 x^2+103 x+14$
• $y^2=132 x^6+130 x^5+17 x^3+84 x^2+39 x+90$
• $y^2=96 x^6+41 x^5+18 x^4+42 x^3+104 x^2+92 x+128$
• $y^2=12 x^6+77 x^5+55 x^4+119 x^3+52 x^2+81$
• $y^2=83 x^6+86 x^5+129 x^4+41 x^3+64 x^2+115 x+145$
• $y^2=30 x^6+71 x^5+26 x^4+50 x^3+95 x^2+76 x+51$
• $y^2=41 x^6+97 x^5+127 x^4+138 x^3+133 x^2+66 x+78$
• $y^2=138 x^6+145 x^5+102 x^4+108 x^3+70 x^2+11 x+40$
• $y^2=96 x^6+4 x^5+89 x^4+16 x^3+131 x^2+55 x+49$
• $y^2=14 x^6+111 x^5+53 x^4+89 x^3+37 x^2+24 x+52$
• $y^2=79 x^6+121 x^5+29 x^4+71 x^3+20 x^2+145 x+141$
• $y^2=62 x^6+71 x^5+66 x^4+102 x^3+47 x^2+72 x+41$
• $y^2=59 x^6+46 x^5+96 x^4+90 x^3+146 x^2+86 x$
• $y^2=19 x^6+60 x^5+31 x^4+82 x^3+144 x^2+119 x+68$
• $y^2=40 x^6+124 x^5+4 x^4+31 x^3+87 x^2+22 x+130$
• $y^2=75 x^6+8 x^5+13 x^4+103 x^3+54 x^2+102 x+35$
• $y^2=137 x^6+133 x^5+76 x^4+141 x^3+86 x^2+37 x+52$
• $y^2=70 x^6+76 x^5+47 x^4+10 x^3+41 x^2+8 x+75$
• $y^2=20 x^6+131 x^5+77 x^4+69 x^3+38 x^2+113 x+11$
• $y^2=95 x^6+42 x^5+52 x^4+38 x^3+86 x^2+124 x+44$
• and

• $y^2=21 x^6+113 x^5+49 x^4+124 x^3+50 x^2+61 x+32$
• $y^2=6 x^6+57 x^5+55 x^4+130 x^3+18 x^2+67 x+141$
• $y^2=81 x^6+27 x^5+120 x^4+52 x^3+107 x^2+128 x+57$
• $y^2=118 x^6+33 x^5+37 x^4+49 x^3+86 x^2+48 x+143$
• $y^2=47 x^6+50 x^5+108 x^4+40 x^3+134 x^2+103 x+84$
• $y^2=63 x^6+41 x^5+73 x^4+68 x^3+86 x^2+128 x+50$
• $y^2=142 x^6+101 x^5+75 x^4+19 x^3+58 x^2+72 x+69$
• $y^2=27 x^6+79 x^5+124 x^4+98 x^3+142 x^2+80 x+122$
• $y^2=123 x^6+36 x^4+88 x^3+133 x^2+108 x+36$
• $y^2=27 x^6+101 x^5+97 x^4+11 x^3+9 x^2+69 x+4$
• $y^2=2 x^6+44 x^5+120 x^4+119 x^3+47 x^2+111 x+97$
• $y^2=134 x^6+56 x^5+95 x^4+10 x^3+9 x^2+136 x+67$
• $y^2=7 x^6+96 x^5+139 x^4+84 x^3+85 x^2+37 x+18$
• $y^2=66 x^6+57 x^5+96 x^4+6 x^3+55 x^2+64 x+101$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{149}$.

Endomorphism algebra over $\F_{149}$

The endomorphism algebra of this simple isogeny class is 4.0.8928045.2.

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
2.149.bp_bbl	$2$	(not in LMFDB)