I want to know the same math code of
selmer_generators(S, m, proof=True)
in this page,
doc.sagemath.org/html/en/reference/polynomial_rings/sage/rings/polynomial/polynomial_quotient_ring.html#sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_generic.selmer_generators
I especially want the case $E:y^2=x^3+17x$,$K=\Bbb{Q}(\sqrt{-19})$ and $S=Ω_∞\cup \{b\in Ω_f \mid v(2)\neq 0 , v(17)\neq 0 \}$, where $Ω_∞$ is infinite places of $K$ and $\{b\in Ω_f \mid v(2)\neq 0 , v(17)\neq 0 \}$ is finite places of $K$. I’m having difficulty how to input the information of $S$.
Could you tell me the code I should input?
Theoritically, this question is related to this Mathoverfrow question, mathoverflow.net/questions/446409/ks-2-b-in-k-times-k-times2-mid-vb%e2%89%a10-bmod2-forall-v-notin-s#comment1153119_446409.
Thank you in advance.
P.S
The following code didn’t work.
K. = QuadraticField(-19)
sage: R. = K[]
sage: D. = R.quotient(x)
sage: D.selmer_generators([K.ideal(2), K.ideal(17)], 2)
Where did I go wrong ?
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