Properties

 Label 1.347.abi Base Field $\F_{347}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

Learn more about

Invariants

 Base field: $\F_{347}$ Dimension: $1$ L-polynomial: $1 - 34 x + 347 x^{2}$ Frobenius angles: $\pm0.134065237258$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-58})$$ Galois group: $C_2$ Jacobians: 2

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 2 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 314 119948 41778014 14498354656 5030921853994 1745729157853676 605767995611159086 210201493975236171648 72939918400035457463258 25310151684667810043113868

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 314 119948 41778014 14498354656 5030921853994 1745729157853676 605767995611159086 210201493975236171648 72939918400035457463258 25310151684667810043113868

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{347}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-58})$$.
All geometric endomorphisms are defined over $\F_{347}$.

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 1.347.bi $2$ (not in LMFDB)