#19276: precision problem computing heights on elliptic curves
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Reporter: cremona | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.9
Component: elliptic curves | Keywords: height precision
Merged in: | Authors: John Cremona
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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Computing heights of points over number fields (this does not effect
things over Q): in the expression (from Silverman's paper) for the number
of terms needed for the requested precision for local height at an
archimedean place v, there is log(max(1,1/|D|_v)) where D is the
discriminant and v the valuation. Over Q D is integral so this term is
always 0. Over number fields, |D|_v can be extremely small for some v,
indistinguishable from 0 to moderate precision.
Example (from an LMFDB curve):
{{{
sage: K.<a> = NumberField(x^2-x-104)
sage: E = EllipticCurve([1, a - 1, 1, -816765673272*a - 7931030674178,
1478955604013312315*a + 14361086227143654561])
sage: P = E(5393511/49*a + 52372721/49 , -33896210324/343*a -
329141996591/343 )
sage: P.height()
}}}
I have a fix and am testing now.
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Ticket URL: <http://trac.sagemath.org/ticket/19276>
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