Hello,

I noticed something I find odd in sha().an()

sage: E=EllipticCurve([0,0,0,-3,1])
sage: E.is_minimal()
True
sage: E.rank()
1
sage: E.lseries().deriv_at1(1000)[0]
2.61683934093655
sage: E.sha().an() * E.period_lattice().basis()[0] * E.regulator()  *
E.tamagawa_product_bsd()/(E.torsion_order()**2)
1.30841967046636

so the two quantities differ by a factor of 2, whereas they should be
equal, at least in my understanding of what sha().an() is supposed to
be
doing.

Am I doing anything wrong?

Thanks,
Andrei Jorza

PS. I am running Sage Version 4.7, Release Date: 2011-05-23 on Ubuntu
11.04. The CPU is an Intel i7-960.

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