Algorithm 2 Independent Reproduction

Builds a mirror relying only on the Python standard library, replaying squarefree, gcd, $a_p$, finite field point counts, 2-adic valuation, quadratic splitting, cubic 2-division inertness, and sign condition — deliberately not implementing the descent/isogeny/optimality/L-value parts of Algorithm 1, precisely locking the scope to the branch logic of Algorithm 2. Finite field point counts are calculated directly using the discriminant $D_x=(a_1x+a_3)^2+4(x^3+a_2x^2+a_4x+a_6)$ paired with the Legendre symbol, and the ordinary test checks $p\nmid a_p(E)$. The CLZ branch for 46a1 yields the exact same 7 twists as the official one ($1,185,265,305,745,785,905$), and the Zhai branch for 106d1 uses the cubic of the 2-torsion $x$-coordinate to determine inert primes, yielding the exact same 21 twists as the official one — both are exact list matches, not just matching counts. The document honestly marks the technical limitations of this mirror: cubic reduction modulo $p$ is only a simplified determination of inertness; formal number field computations should use full $p\mathcal O_F$ factorization or Sage's is_prime(). The reason this test can use the simplified version is that the theorem's own $(d,3N)=1$ condition has already excluded the relevant ramified bad primes — but the full production version should still use the Sage number-field backend as the authority, not this simplified mirror.