Properties

 Label 2.181.abv_biv Base Field $\F_{181}$ Dimension $2$ Ordinary No $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

Invariants

 Base field: $\F_{181}$ Dimension: $2$ L-polynomial: $1 - 47 x + 905 x^{2} - 8507 x^{3} + 32761 x^{4}$ Frobenius angles: $\pm0.0525515266489$, $\pm0.225033026600$ Angle rank: $2$ (numerical) Number field: 4.0.8177037.2 Galois group: $D_{4}$ Jacobians: 12

This isogeny class is simple and geometrically simple.

Newton polygon

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

Point counts

This isogeny class contains the Jacobians of 12 curves, and hence is principally polarizable:

• $y^2=158x^6+153x^5+61x^4+101x^3+86x^2+63x+104$
• $y^2=136x^6+62x^5+76x^4+126x^3+91x^2+120x+180$
• $y^2=92x^6+107x^5+54x^4+160x^3+121x^2+30x+7$
• $y^2=x^6+33x^5+162x^4+130x^3+23x^2+115x+161$
• $y^2=141x^6+117x^5+64x^4+81x^3+83x^2+71x+23$
• $y^2=149x^6+179x^5+130x^4+114x^3+37x^2+114x+68$
• $y^2=79x^6+106x^5+75x^4+73x^3+104x^2+139x+96$
• $y^2=140x^6+173x^5+122x^4+148x^3+5x^2+13x+82$
• $y^2=12x^6+77x^5+106x^4+170x^3+18x^2+65x$
• $y^2=111x^6+146x^5+148x^4+135x^3+59x^2+69x+72$
• $y^2=119x^6+86x^5+97x^3+120x^2+23x+82$
• $y^2=99x^6+161x^5+168x^4+20x^3+102x^2+155x+80$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 25113 1060295973 35151517455813 1151948008860622677 37738638883308874545408 1236354131781853908338566557 40504198358759399288038960007997 1326958061024072536623697374735302853 43472473116317535690473921893305252875817 1424201691967871905432422042333472488275202048

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 135 32363 5928003 1073293699 194264461290 35161827203099 6364290825493239 1151936655554708995 208500535034815720779 37738596846712369116518

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
 The endomorphism algebra of this simple isogeny class is 4.0.8177037.2.
All geometric endomorphisms are defined over $\F_{181}$.

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 2.181.bv_biv $2$ (not in LMFDB)