Properties

 Label 1.397.am 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: $1 - 12 x + 397 x^{2}$ Frobenius angles: $\pm0.402635731257$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-1})$$ Galois group: $C_2$ Jacobians: 11

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 11 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 386 158260 62583338 24840489600 9861710686466 3915101601104980 1554295350724299338 617055253442518694400 244970935601150591766146 97253461433786059144765300

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 386 158260 62583338 24840489600 9861710686466 3915101601104980 1554295350724299338 617055253442518694400 244970935601150591766146 97253461433786059144765300

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{397}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-1})$$.
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.m $2$ (not in LMFDB) 1.397.abm $4$ (not in LMFDB) 1.397.bm $4$ (not in LMFDB)