Properties

 Label 1.397.aba Base Field $\F_{397}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

Invariants

 Base field: $\F_{397}$ Dimension: $1$ L-polynomial: $1 - 26 x + 397 x^{2}$ Frobenius angles: $\pm0.273740693586$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-57})$$ Galois group: $C_2$ Jacobians: 12

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

 $p$-rank: $1$ Slopes: $[0, 1]$

Point counts

This isogeny class contains the Jacobians of 12 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 372 157728 62584164 24840898176 9861719479572 3915101579666976 1554295346218072452 617055253363250047488 244970935601412983747508 97253461433819099047111968

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 372 157728 62584164 24840898176 9861719479572 3915101579666976 1554295346218072452 617055253363250047488 244970935601412983747508 97253461433819099047111968

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{397}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-57})$$.
All geometric endomorphisms are defined over $\F_{397}$.

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 1.397.ba $2$ (not in LMFDB)