#10236: bug in modular symbols for elliptic curves
-------------------------------+--------------------------------------------
Reporter: wuthrich | Owner: cremona
Type: defect | Status: new
Priority: major | Milestone: sage-4.6.2
Component: elliptic curves | Keywords: modular symbols
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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The following two computations should yield the same answer. First with
the modular symbols in sage
{{{
sage: E = EllipticCurve('11a1')
sage: m = E.modular_symbol()
sage: m(1/7)
7/10
sage: m(0)
1/5
}}}
and then using ec_lib :
{{{
sage: m = E.modular_symbol(use_eclib=True)
sage: m(1/7)
6/5
sage: m(0)
1/5
}}}
That the actual value of [1/7] must be 7/10 is illustrated be the
following
{{{
sage: ans = E.anlist(10^5)
sage: twopii = CC(2*pi*i)
sage: s = 0
sage: n = 1
sage: while n < 50000:
....: s += ans[n]/n*exp(twopii*n/7)
....: n += 1
sage: s.real()/E.period_lattice().basis()[0]
0.694799317284868
}}}
The fact that both values at 0 are equal show that it is unlikely that
this is a problem with the scaling of the modular symbols.
----
Here is another bug. Maybe the same, maybe different. This one looks like
being in scaling. But I am puzzled, because this example was used
originally in the design of the scaling function.
{{{
sage: E = EllipticCurve('121b1')
sage: m = E.modular_symbol()
sage: m(1/7)
2
sage: m._scaling
-2
}}}
It should in fact be [1/7]+ = 1/2.
{{{
sage: ans = E.anlist(10^5)
sage: s = 0
sage: n = 1
sage: while n < 100000:
s += ans[n]/n*exp(twopii*n/7)
n += 1
....:
sage: s.real()/E.period_lattice().basis()[0]
0.484665473298495
}}}
This was originally reported by Andrew Ohana.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10236>
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