#9322: bug in simon_two_descent for elliptic curves
-------------------------------+--------------------------------------------
Reporter: cremona | Owner: AlexGhitza
Type: defect | Status: needs_work
Priority: major | Milestone: sage-4.7
Component: elliptic curves | Keywords: Simon
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
-------------------------------+--------------------------------------------
Changes (by cremona):
* status: needs_info => needs_work
* upstream: Not yet reported upstream; Will do shortly. => N/A
Comment:
Running under gp directly:
{{{
? K = bnfinit(y^2 - y - 232);
? a = Mod(y,K.pol);
? bnfellrank(K, [-a + 2,3*a + 18,9*a + 209,175*a + 2581,-55*a + 852])
courbe elliptique : Y^2 = x^3 + Mod(9*y + 308, y^2 - y - 232)*x^2 +
Mod(1200*y + 27936, y^2 - y - 232)*x + Mod(57968*y + 1054096, y^2 - y -
232)
points triviaux sur la courbe = [[1, 1, 0]]
#S(E/K)[2] = 4
#E(K)/2E(K) >= 2
#III(E/K)[2] <= 2
rang(E/K) >= 1
III devrait etre un carre, donc
#E(K)/2E(K) = 4
#III(E/K)[2] = 1
rang(E/K) = 2
listpointsmwr = [[Mod(-35/4*y - 186, y^2 - y - 232), Mod(-21/8*y - 37, y^2
- y - 232)]]
%71 = [2, 2, [[Mod(-35/16*y - 93/2, y^2 - y - 232), Mod(-1727/64*y -
2531/8, y^2 - y - 232)]]]
}}}
we get instant success. Also with the gp2c-compiled version. So it is
*not* an upstream problem,and one which should be solvable within Sage.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9322#comment:4>
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