︠ac1b2306-8551-4ba5-8931-1f40ce698854s︠
E = EllipticCurve('389a')
E
︡9ebc438b-0359-474e-8664-937964e6f931︡︡{"stdout":"Elliptic Curve defined by y^2 + y = x^3 + x^2 - 2*x over Rational Field\n","done":false}︡{"done":true}
︠6f06021b-a161-4e88-a63f-7ab39e00662es︠
R = E.coordinate_ring(); R
︡5eb01382-78c9-4036-9e6b-1e902a9c3ba9︡︡{"stdout":"Quotient of Multivariate Polynomial Ring in x, y, z over Rational Field by the ideal (-x^3 - x^2*z + y^2*z + 2*x*z^2 + y*z^2)\n","done":false}︡{"done":true}
︠8e361dda-f734-47ed-9ec6-bf7492e0d0b9s︠
S = PolynomialRing(E.base_field(), 'a,b,c')
︡a0b05605-12fa-41ad-8060-07f0120445e4︡︡{"done":true}
︠03699106-bfb5-47c1-a9ae-4501fe1d969bs︠
p = R.cover_ring().hom(S.gens())(R.defining_ideal().gens()[0])
p
︡23dc88ce-0184-4c83-b9c8-af0e06f49599︡︡{"stdout":"-a^3 - a^2*c + b^2*c + 2*a*c^2 + b*c^2\n","done":false}︡{"done":true}
︠c55054d9-57c2-4b70-8b7e-4f00fe714892s︠
S.quotient(p)
︡0613aa29-886c-4983-9c6d-86cb4e65360c︡︡{"stdout":"Quotient of Multivariate Polynomial Ring in a, b, c over Rational Field by the ideal (-a^3 - a^2*c + b^2*c + 2*a*c^2 + b*c^2)\n","done":false}︡{"done":true}
︠4d0cb2d5-e19f-4603-90fd-f74011fc9bce︠











Collaborative Calculation and Data Science

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