Properties

 Label 2.41.aw_hu 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: $( 1 - 12 x + 41 x^{2} )( 1 - 10 x + 41 x^{2} )$ Frobenius angles: $\pm0.113551764296$, $\pm0.214776712523$ Angle rank: $2$ (numerical) Jacobians: 8

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 8 curves, and hence is principally polarizable:

• $y^2=34x^6+7x^5+9x^4+x^3+33x^2+3x+30$
• $y^2=19x^6+6x^5+35x^4+25x^3+35x^2+6x+19$
• $y^2=13x^6+23x^5+11x^4+28x^3+24x^2+18x+35$
• $y^2=13x^6+36x^5+32x^4+26x^3+32x^2+36x+13$
• $y^2=12x^6+27x^5+29x^4+15x^3+14x^2+6x+6$
• $y^2=7x^6+22x^5+5x^4+9x^3+5x^2+22x+7$
• $y^2=28x^6+15x^5+25x^4+40x^3+25x^2+15x+28$
• $y^2=26x^6+22x^5+39x^4+14x^3+39x^2+22x+26$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 960 2695680 4748667840 7992152064000 13425613738584000 22564246912784478720 37929362755568712853440 63759045617100820905984000 107178931200881801984319898560 180167783007937079057781079872000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 20 1602 68900 2828318 115881700 4750263522 194754969940 7984927070398 327381935106740 13422659313990402

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{41}$
 The isogeny class factors as 1.41.am $\times$ 1.41.ak 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 are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.41.ac_abm $2$ (not in LMFDB) 2.41.c_abm $2$ (not in LMFDB) 2.41.w_hu $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.41.ac_abm $2$ (not in LMFDB) 2.41.c_abm $2$ (not in LMFDB) 2.41.w_hu $2$ (not in LMFDB) 2.41.au_gw $4$ (not in LMFDB) 2.41.ae_ao $4$ (not in LMFDB) 2.41.e_ao $4$ (not in LMFDB) 2.41.u_gw $4$ (not in LMFDB)