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It is a consequence of the generalized Sato-Tate conjecture, that given a non-CM elliptic curve over $\mathbb Q$, any element of $Gal(\bar{\mathbb Q}/\mathbb Q)$, and a real number $\in[−1,1]$, one can construct an ultrafilter on the primes such that Frobenius converges to that element and the angle of Frobenius converges to that real number.

Thus any attempt to answer this question must somehow make use of the transcendentals. I have no idea how one might do that.

EDIT: By ACL's answer to my question, the nonstandard angle of Frobenius is totally independent from all first-order statements about the nonstandard elliptic curve.

It is a consequence of the generalized Sato–Tate conjecture, that given a non-CM elliptic curve over $\mathbb Q$, any element of $\operatorname{Gal}(\bar{\mathbb Q}/\mathbb Q)$, and a real number $\in[−1,1]$, one can construct an ultrafilter on the primes such that Frobenius converges to that element and the angle of Frobenius converges to that real number.

Thus any attempt to answer this question must somehow make use of the transcendentals. I have no idea how one might do that.

EDIT: By ACL's answer to my question, the nonstandard angle of Frobenius is totally independent from all first-order statements about the nonstandard elliptic curve.

It is a consequence of the generalized Sato-Tate conjecture, that given a non-CM elliptic curve over $\mathbb Q$, any element of $Gal(\bar{\mathbb Q}/\mathbb Q)$, and a real number $\in[−1,1]$, one can construct an ultrafilter on the primes such that Frobenius converges to that element and the angle of Frobenius converges to that real number.

Thus any attempt to answer this question must somehow make use of the transcendentals. I have no idea how one might do that.

EDIT: By ACL's answer to my question, the nonstandard angle of Frobenius is totally independent from all first-order statements about the nonstandard elliptic curve.

It is a consequence of the generalized Sato-Tate conjecture, that given a non-CM elliptic curve over $\mathbb Q$, any element of $Gal(\bar{\mathbb Q}/\mathbb Q)$, and a real number $\in[−1,1]$, one can construct an ultrafilter on the primes such that Frobenius converges to that element and the angle of Frobenius converges to that real number.

Thus any attempt to answer this question must somehow make use of the transcendentals. I have no idea how one might do that.

EDIT: By ACL's answer to my question, the nonstandard angle of Frobenius is totally independent from all first-order statements about the nonstandard elliptic curve.

It is a consequence of the generalized Sato-Tate conjecture, that given a non-CM elliptic curve over $\mathbb Q$, any element of $Gal(\bar{\mathbb Q}/\mathbb Q)$, and a real number $\in[−1,1]$, one can construct an ultrafilter on the primes such that Frobenius converges to that element and the angle of Frobenius converges to that real number.

Thus any attempt to answer this question must somehow make use of the transcendentals. I have no idea how one might do that.

(I had a different answer earlier, but this comment is a better one.)

It is a consequence of the generalized Sato-Tate conjecture, that given a non-CM elliptic curve over $\mathbb Q$, any element of $Gal(\bar{\mathbb Q}/\mathbb Q)$, and a real number $\in[−1,1]$, one can construct an ultrafilter on the primes such that Frobenius converges to that element and the angle of Frobenius converges to that real number.

Thus any attempt to answer this question must somehow make use of the transcendentals. I have no idea how one might do that.

EDIT: By ACL's answer to my question, the nonstandard angle of Frobenius is totally independent from all first-order statements about the nonstandard elliptic curve.