#14476: non-integral models can cause a bug in local_data for elliptic curves
over
number fields
-----------------------------------+----------------------------------------
Reporter: wuthrich | Owner: cremona
Type: defect | Status: new
Priority: major | Milestone: sage-5.10
Component: elliptic curves | Resolution:
Keywords: local_data | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
-----------------------------------+----------------------------------------
Comment (by cremona):
The reason is this:
{{{
sage: E.is_global_integral_model()
False
}}}
and if one replaces E by a global integral model then all is well:
{{{
sage: E1 = E.global_integral_model()
sage: E1.local_data()
[Local data at Fractional ideal (g^3 - g^2 - 2*g - 1):
Reduction type: bad split multiplicative
Local minimal model: Elliptic Curve defined by y^2 + (g^3+g)*x*y + g*y =
x^3 + (-g^2+1)*x^2 + (126914883*g^3-73346242*g^2-411702677*g-300687331)*x
+ (-1068031359960*g^3+617234077764*g^2+3464617746565*g+2530385673583) over
Number Field in g with defining polynomial t^4 - t^3 - 3*t^2 - t + 1
Minimal discriminant valuation: 11
Conductor exponent: 1
Kodaira Symbol: I11
Tamagawa Number: 11,
Local data at Fractional ideal (-g^2 + g + 1):
Reduction type: bad split multiplicative
Local minimal model: Elliptic Curve defined by y^2 + (g^3+g)*x*y + g*y =
x^3 + (-g^2+1)*x^2 + (126914883*g^3-73346242*g^2-411702677*g-300687331)*x
+ (-1068031359960*g^3+617234077764*g^2+3464617746565*g+2530385673583) over
Number Field in g with defining polynomial t^4 - t^3 - 3*t^2 - t + 1
Minimal discriminant valuation: 11
Conductor exponent: 1
Kodaira Symbol: I11
Tamagawa Number: 11,
Local data at Fractional ideal (g^2 - g - 2):
Reduction type: bad split multiplicative
Local minimal model: Elliptic Curve defined by y^2 + (g^3+g)*x*y + g*y =
x^3 + (-g^2+1)*x^2 + (126914883*g^3-73346242*g^2-411702677*g-300687331)*x
+ (-1068031359960*g^3+617234077764*g^2+3464617746565*g+2530385673583) over
Number Field in g with defining polynomial t^4 - t^3 - 3*t^2 - t + 1
Minimal discriminant valuation: 11
Conductor exponent: 1
Kodaira Symbol: I11
Tamagawa Number: 11,
Local data at Fractional ideal (3*g^3 - 12*g - 4):
Reduction type: bad non-split multiplicative
Local minimal model: Elliptic Curve defined by y^2 + (g^3+g)*x*y + g*y =
x^3 + (-g^2+1)*x^2 + (126914883*g^3-73346242*g^2-411702677*g-300687331)*x
+ (-1068031359960*g^3+617234077764*g^2+3464617746565*g+2530385673583) over
Number Field in g with defining polynomial t^4 - t^3 - 3*t^2 - t + 1
Minimal discriminant valuation: 1
Conductor exponent: 1
Kodaira Symbol: I1
Tamagawa Number: 1]
}}}
Of course it would be possible to have local_data() do this. At the very
least, local data should give a more polite message.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14476#comment:1>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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