# Properties

 Label 2.41.av_hi Base Field $\F_{41}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{41}$ Dimension: $2$ L-polynomial: $( 1 - 12 x + 41 x^{2} )( 1 - 9 x + 41 x^{2} )$ Frobenius angles: $\pm0.113551764296$, $\pm0.251940962052$ Angle rank: $2$ (numerical) Jacobians: 6

This isogeny class is not 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 6 curves, and hence is principally polarizable:

• $y^2=11x^6+30x^5+13x^4+16x^3+19x^2+15x+29$
• $y^2=35x^6+40x^5+36x^4+9x^3+15x^2+22$
• $y^2=13x^6+34x^5+30x^4+36x^3+14x^2+35x+1$
• $y^2=22x^6+15x^5+11x^4+35x^3+38x^2+30x+40$
• $y^2=11x^6+18x^5+11x^4+3x^3+36x^2+4x+14$
• $y^2=35x^6+31x^5+4x^4+35x^3+3x^2+2x+37$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 990 2726460 4758831000 7993064629440 13424895517794750 22563819472715136000 37929237987933420172110 63759029113231317298287360 107178934881384557380968471000 180167785978512555597338603941500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 21 1621 69048 2828641 115875501 4750173538 194754329301 7984925003521 327381946348968 13422659535300901

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{41}$
 The isogeny class factors as 1.41.am $\times$ 1.41.aj and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{41}$.

## 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 2.41.ad_aba $2$ (not in LMFDB) 2.41.d_aba $2$ (not in LMFDB) 2.41.v_hi $2$ (not in LMFDB)