# Properties

 Label 2.41.as_fy 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: $( 1 - 12 x + 41 x^{2} )( 1 - 6 x + 41 x^{2} )$ Frobenius angles: $\pm0.113551764296$, $\pm0.344786929280$ Angle rank: $2$ (numerical) Jacobians: 46

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 46 curves, and hence is principally polarizable:

• $y^2=8x^6+33x^5+15x^4+6x^3+15x^2+33x+8$
• $y^2=14x^6+25x^5+7x^4+25x^3+24x^2+28x+6$
• $y^2=35x^6+23x^5+38x^4+21x^3+38x^2+23x+35$
• $y^2=3x^6+5x^5+20x^3+11x^2+25x+19$
• $y^2=35x^6+38x^5+12x^4+7x^3+39x^2+25x+12$
• $y^2=34x^6+32x^5+15x^4+4x^3+15x^2+32x+34$
• $y^2=30x^5+24x^4+26x^3+9x^2+18x+29$
• $y^2=14x^6+20x^5+4x^4+30x^3+19x^2+28x+3$
• $y^2=16x^6+35x^5+5x^4+19x^3+5x^2+12x+25$
• $y^2=31x^6+19x^5+32x^4+33x^3+39x^2+11x+2$
• $y^2=7x^6+40x^5+16x^4+11x^3+16x^2+40x+7$
• $y^2=22x^6+38x^5+25x^4+35x^3+25x^2+36x+15$
• $y^2=9x^6+17x^5+20x^4+20x^3+17x^2+30x+37$
• $y^2=3x^6+7x^5+28x^4+21x^3+28x^2+7x+3$
• $y^2=22x^6+31x^5+31x^4+19x^3+12x^2+23x+14$
• $y^2=3x^6+x^5+27x^4+14x^3+24x^2+18x+7$
• $y^2=8x^6+12x^5+29x^4+3x^3+29x^2+29x+19$
• $y^2=9x^6+16x^4+23x^3+8x^2+37$
• $y^2=37x^6+6x^5+33x^4+21x^3+2x^2+22x+13$
• $y^2=6x^6+25x^5+19x^4+7x^3+29x^2+18x+38$
• and 26 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 1080 2799360 4768719480 7987089162240 13421572979067000 22563203849571168000 37929318476855600472120 63759106916838493051944960 107178954017719783117741454520 180167786296072881445675492704000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 24 1666 69192 2826526 115846824 4750043938 194754742584 7984934747326 327382004801592 13422659558959426

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{41}$
 The isogeny class factors as 1.41.am $\times$ 1.41.ag 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.ag_k $2$ (not in LMFDB) 2.41.g_k $2$ (not in LMFDB) 2.41.s_fy $2$ (not in LMFDB)