Properties

 Label 2.61.az_kq Base Field $\F_{61}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

Invariants

 Base field: $\F_{61}$ Dimension: $2$ L-polynomial: $( 1 - 14 x + 61 x^{2} )( 1 - 11 x + 61 x^{2} )$ Frobenius angles: $\pm0.146275019398$, $\pm0.251304563322$ Angle rank: $2$ (numerical) Jacobians: 10

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 10 curves, and hence is principally polarizable:

• $y^2=44x^6+52x^5+56x^4+57x^3+35x^2+34x+16$
• $y^2=7x^6+20x^5+56x^4+30x^3+35x^2+4x+21$
• $y^2=17x^6+17x^5+59x^4+3x^3+5x+19$
• $y^2=19x^6+24x^5+7x^4+30x^3+46x^2+3x+17$
• $y^2=26x^6+5x^5+10x^4+56x^3+9x^2+20x+24$
• $y^2=24x^6+60x^5+8x^4+50x^3+35x^2+26x+31$
• $y^2=52x^6+46x^5+33x^4+28x^3+13x^2+29x+11$
• $y^2=55x^6+9x^5+31x^4+2x^3+9x^2+6x+21$
• $y^2=5x^6+51x^5+22x^4+16x^3+3x^2+4$
• $y^2=13x^6+33x^5+54x^4+13x^3+7x^2+16x+23$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 2448 13581504 51634195200 191837603153664 713409532440053328 2654370081056816640000 9876835542770460249493968 36751693118511697468584459264 136753052498079096527966564524800 508858109809738883308964469679291584

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 37 3649 227482 13855249 844675177 51520784038 3142743793597 191707309147009 11694146063548642 713342911929317929

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
 The isogeny class factors as 1.61.ao $\times$ 1.61.al 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 $\F_{61}$.

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 2.61.ad_abg $2$ (not in LMFDB) 2.61.d_abg $2$ (not in LMFDB) 2.61.z_kq $2$ (not in LMFDB) 2.61.ak_eh $3$ (not in LMFDB) 2.61.c_av $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.61.ad_abg $2$ (not in LMFDB) 2.61.d_abg $2$ (not in LMFDB) 2.61.z_kq $2$ (not in LMFDB) 2.61.ak_eh $3$ (not in LMFDB) 2.61.c_av $3$ (not in LMFDB) 2.61.ay_kf $6$ (not in LMFDB) 2.61.am_fd $6$ (not in LMFDB) 2.61.ac_av $6$ (not in LMFDB) 2.61.k_eh $6$ (not in LMFDB) 2.61.m_fd $6$ (not in LMFDB) 2.61.y_kf $6$ (not in LMFDB)