KateWishList
system:sage


<p><span style="font-size: x-large;">Reduce the points along with the curve.</span></p>

{{{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()
///
}}}

<p><span style="font-size: x-large;">Do basic things for singular Weierstrass equations.</span></p>

{{{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
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}}}

{{{id=19|
E.discriminant().factor()
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}}}

{{{id=16|
G = E.reduction(2)
///
}}}

{{{id=17|
G.cardinality()
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}}}

{{{id=18|
G.singular_point()
///
}}}

{{{id=20|
P.reduction(2)+P.reduction(2)
///
}}}

{{{id=27|
P.reduction(2).neron_component()
///
}}}

<p><span style="font-size: x-large;">Tate's Algorithm for curves over the p-adics.</span></p>

{{{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|

///
}}}