#19276: precision problem computing heights on elliptic curves
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       Reporter:         |        Owner:
  cremona                |       Status:  needs_review
           Type:         |    Milestone:  sage-6.9
  defect                 |   Resolution:
       Priority:  major  |    Merged in:
      Component:         |    Reviewers:
  elliptic curves        |  Work issues:
       Keywords:         |       Commit:
  height precision       |  3ea3fc73d85a9b50fb618f63c345bce415cf7e1a
        Authors:  John   |     Stopgaps:
  Cremona                |
Report Upstream:  N/A    |
         Branch:         |
  u/cremona/19276        |
   Dependencies:         |
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Comment (by jdemeyer):

 Instead of embedding into `RR`, embedding in `AAbar` and then coercing to
 `RR` just works:
 {{{
 sage: K.<a> = NumberField(x^2-x-104)
 sage: E = EllipticCurve([1, a - 1, 1, -816765673272*a - 7931030674178,
 1478955604013312315*a + 14361086227143654561])
 sage: D = E.discriminant()
 sage: AAbar = AlgebraicRealField()
 sage: phi = K.embeddings(AAbar)[0]
 sage: RR(phi(D))
 -4.32015718504111e-35
 }}}

 Using this looks like the right fix to me.

--
Ticket URL: <http://trac.sagemath.org/ticket/19276#comment:12>
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