Reduce the points along with the curve.

{{{id=1| E = EllipticCurve([1,2,3,4,0]) /// }}} {{{id=2| P = E(0,0) /// }}} {{{id=4| E.reduction(5) /// }}} {{{id=3| P.reduction(5) /// }}} {{{id=5| P.curve() /// }}}

Do basic things for singular Weierstrass equations.

{{{id=9| E = EllipticCurve([1,2,3,4,0]) /// }}} {{{id=28| F = EllipticCurve([0,0,0,0,0]) /// }}} {{{id=8| E.b_invariants() /// }}} {{{id=11| E.change_weierstrass_model([2,3,4,2]) /// }}} {{{id=12| E.division_polynomial(5,two_torsion_multiplicity=2) /// }}} {{{id=13| P = E(0,0) /// }}} {{{id=30| P.is_singular() /// }}} {{{id=14| P+P /// }}} {{{id=19| E.discriminant().factor() /// }}} {{{id=16| G = E.reduction(2) /// }}} {{{id=17| G.cardinality() /// }}} {{{id=18| G.singular_point() /// }}} {{{id=20| P.reduction(2)+P.reduction(2) /// }}} {{{id=27| P.reduction(2).neron_component() /// }}}

Tate's Algorithm for curves over the p-adics.

{{{id=21| E = EllipticCurve([1,2,3,4,0]) /// }}} {{{id=23| E.global_minimal_model() /// }}} {{{id=26| E.discriminant().factor() /// }}} {{{id=24| E.local_data(2003) /// }}} {{{id=25| /// }}}