Properties

 Label 1.337.ax Base Field $\F_{337}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

Invariants

 Base field: $\F_{337}$ Dimension: $1$ L-polynomial: $1 - 23 x + 337 x^{2}$ Frobenius angles: $\pm0.284509337221$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-91})$$ Galois group: $C_2$ Jacobians: 10

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 10 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 315 113715 38283840 12898123875 4346599290075 1464803575845120 493638819276370635 166356282552832519875 56062067226017575786560 18892916655145415998953075

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 315 113715 38283840 12898123875 4346599290075 1464803575845120 493638819276370635 166356282552832519875 56062067226017575786560 18892916655145415998953075

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{337}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-91})$$.
All geometric endomorphisms are defined over $\F_{337}$.

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 1.337.x $2$ (not in LMFDB)