Properties

 Label 2.73.abg_pl Base Field $\F_{73}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

Learn more about

Invariants

 Base field: $\F_{73}$ Dimension: $2$ L-polynomial: $( 1 - 17 x + 73 x^{2} )( 1 - 15 x + 73 x^{2} )$ Frobenius angles: $\pm0.0323195869136$, $\pm0.159004799845$ Angle rank: $2$ (numerical) Jacobians: 1

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 1 curves, and hence is principally polarizable:

• $y^2=20x^6+26x^5+68x^4+66x^3+68x^2+26x+20$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 3363 27236937 150837168384 806307493291209 4297611830675103123 22902068002443410866176 122045027238992274935655651 650377878381822048892404086025 3465863710242070217007992518492416 18469587757765250116119549627771142377

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 42 5108 387738 28392868 2073064842 151334358158 11047399713882 806460090113476 58871586516205194 4297625826359864468

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
 The isogeny class factors as 1.73.ar $\times$ 1.73.ap 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 $\F_{73}$.

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 2.73.ac_aef $2$ (not in LMFDB) 2.73.c_aef $2$ (not in LMFDB) 2.73.bg_pl $2$ (not in LMFDB) 2.73.ai_bp $3$ (not in LMFDB) 2.73.af_ae $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.73.ac_aef $2$ (not in LMFDB) 2.73.c_aef $2$ (not in LMFDB) 2.73.bg_pl $2$ (not in LMFDB) 2.73.ai_bp $3$ (not in LMFDB) 2.73.af_ae $3$ (not in LMFDB) 2.73.az_lk $6$ (not in LMFDB) 2.73.aw_jr $6$ (not in LMFDB) 2.73.f_ae $6$ (not in LMFDB) 2.73.i_bp $6$ (not in LMFDB) 2.73.w_jr $6$ (not in LMFDB) 2.73.z_lk $6$ (not in LMFDB)