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Curves over p-adic Fields

The functions in this section are for elliptic curves defined over p-adic fields. They provide an interface to the same code for Tate's algorithm that is used for curves over number fields.

Subsections

Local Invariants

Conductor(E) : CrvEll -> FldPadElt
The conductor of the elliptic curve E defined over a p-adic field.
LocalInformation(E) : CrvEll, RngOrdIdl -> Tup, CrvEll
Implements Tate's algorithm for the elliptic curve E over a p-adic field. This intrinsic computes local reduction data at the prime ideal P, and a local minimal model. The model is not required to be integral on input. Output is < P, vp(d), fp, cp, K, s > and Emin where P is the uniformizer of the ground field, vp(d) is the valuation of the local minimal discriminant, fp is the valuation of the conductor, cp is the Tamagawa number, K is the Kodaira Symbol, and s is false if the curve has non-split multiplicative reduction and true otherwise. Emin is an integral minimal model of E.
RootNumber(E) : CrvEll -> RngIntElt
The local root number of the elliptic curve E (defined over a p-adic field).
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Version: V2.19 of Wed Apr 24 15:09:57 EST 2013