#4606: elliptic curves -- implement gross-Zagier L-functions
-------------------------------------+-------------------------------------
Reporter: robertwb | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.7
Component: elliptic curves | Resolution:
Keywords: | Merged in:
Authors: William Stein, | Reviewers:
Robert Bradshaw, Craig Citro | Work issues:
Report Upstream: N/A | Commit:
Branch: u/chapoton/4606 | d8d92d243217643f47883f6fc9c4818efb859252
Dependencies: | Stopgaps:
-------------------------------------+-------------------------------------
Comment (by chapoton):
Now working better, but not perfectly (some problems with trivial ideal
classes)
{{{
sage: K=QuadraticField(-79)
sage: K.class_group()
Class group of order 5 with structure C5 of Number Field in a with
defining polynomial x^2 + 79
sage: A=K.class_group().gen()
sage: E=EllipticCurve('433a1')
sage: sum(E.lseries_gross_zagier(A**i)(2) for i in range(5))
0.173957331997956
sage: E.lseries()(2)*E.quadratic_twist(-79).lseries()(2)
0.327922081982688
sage: lgz=E.lseries_gross_zagier(A)
sage: lgz._dokchister.check_functional_equation()
8.32667268468867e-17
sage: lgz=E.lseries_gross_zagier(A**2)
sage: lgz._dokchister.check_functional_equation()
-2.20309881449055e-16
sage: lgz=E.lseries_gross_zagier(A**3)
sage: lgz._dokchister.check_functional_equation()
-2.20309881449055e-16
sage: lgz=E.lseries_gross_zagier(A**4)
sage: lgz._dokchister.check_functional_equation()
8.32667268468867e-17
sage: lgz=E.lseries_gross_zagier(A**5)
sage: lgz._dokchister.check_functional_equation()
-1383.90668128107
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/4606#comment:41>
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