

<p>The following code reduces an elliptic curve defined over Qp or Zp to the residue field. Currently it doesn't work for extensions of p-adics due to a coercion problem in p-adics.</p>

{{{id=1|
def pAdic_reduction(self):
    OK = E.base_ring().integer_ring()
    Fv = OK.residue_field()
    return self.change_ring(Fv)
///
}}}

{{{id=3|
F = pAdicField(5); E = EllipticCurve(F,[1,2,3,4,5]);
pAdic_reduction(E)
///
Elliptic Curve defined by y^2 + x*y + 3*y = x^3 + 4*x over Finite Field of size 5
}}}

{{{id=6|
EEE = EllipticCurve([1,2,3,4,5]); EEE
///
Elliptic Curve defined by y^2 + x*y + 3*y = x^3 + 2*x^2 + 4*x + 5 over Rational Field
}}}

{{{id=5|
EEE = EllipticCurve([1,2,3,4,5]); EEE
///
Elliptic Curve defined by y^2 + x*y + 3*y = x^3 + 2*x^2 + 4*x + 5 over Rational Field
}}}

{{{id=12|

///
}}}