#10152 closed defect (duplicate)
bug in integral_points (for elliptic curves over Q)
Reported by: | John Cremona | Owned by: | John Cremona |
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Priority: | major | Milestone: | sage-duplicate/invalid/wontfix |
Component: | elliptic curves | Keywords: | integral points sd32 |
Cc: | gaganskehon, Jamie Weigandt | Merged in: | |
Authors: | Reviewers: | William Stein | |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
sage: E = EllipticCurve('2082a1') sage: [P[0] for P in E.integral_points()] [-11, -2, 4, 13]
but
sage: E.lift_x(507525709) (507525709 : 11433453531221 : 1)
so we miss one point. Note that this point is 13*P where P is the generator, and our code computes the bound to be 12.
John Cannon is sending me a complete list of integral points for all curves in the Cremona database, computed using Magma, using some recent enhancements. Previously I had checked that Sage and Magma agreed to conductor 10000, so their enhancements must also fix bugs.
Magma V2.15-15 Thu Oct 21 2010 20:56:33 on John-laptop [Seed = 2704111428] Type ? for help. Type <Ctrl>-D to quit. Loading startup file "/home/john/magma/Startup/startup.m" > E:=EllipticCurve([1,0,1,-118,584]); > IntegralPoints(E); [ (13 : 29 : 1), (4 : 11 : 1), (-11 : 29 : 1), (-2 : -28 : 1), (507525709 : -11433961056931 : 1) ] [ [ <(13 : 29 : 1), 1> ], [ <(13 : 29 : 1), 2> ], [ <(13 : 29 : 1), 3> ], [ <(13 : 29 : 1), 4> ], [ <(13 : 29 : 1), 13> ] ] 19
Change History (10)
comment:1 Changed 12 years ago by
comment:2 Changed 12 years ago by
Here is a list of curves and integral x-coordinates not found by Sage, as provided by John Cannon. It is not necessarily complete, but is a minimal set of test cases for any patch fixing this.
Curve Points found by Magma not in JC tables -------------------------- 2082a1 507525709 6104b1 23036693 8470g1 1681690 8470g2 18888968 13578j1 106398748 16560w2 102492113 23808e1 22259471153 35739g1 148611521 36094c1 1733011457 36600bd1 880839998 38646bd1 633070349 38752c1 71243131 39270x2 15427732395 39330bu2 28736032507 39715e1 367032124 43050c2 127290394 43770f1 247 44282b1 704349106 48294d1 26406701298449 51414v1 649726 51825h1 29581907 52200e1 62128741241070 56355b4 9817312168 56392b1 49071409 60610w2 81996154 60648bm2 63137880 Curves missing around here 63099e1 37015368 65481c2 21083414 Curves missing around here 75730a1 3786617429 76128p1 50684407 78078by1 1361015 5344835475 83490r2 87561186 90870a2 72592777212 95337a1 167959 100096h1 3318161 101320f2 14134787 103520a1 94894808 108990cb2 71041501977 109330k2 377482949 109968f1 135059618524 110976h2 116239257 113706i1 1945 9319420657 114240ev1 938125 115920bb2 184673663 116088n1 1374364421 116511b1 1375325 124110y1 37815783 129420b1 1172841435
comment:3 Changed 12 years ago by
Cc: | gaganskehon added |
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comment:4 Changed 12 years ago by
Cc: | Jamie Weigandt added |
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comment:5 Changed 12 years ago by
See #10973. The patch there finds the missing integral points mentioned here.
comment:7 Changed 11 years ago by
Resolution: | → duplicate |
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Status: | new → closed |
comment:8 Changed 11 years ago by
Work issues: | → sd32 |
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comment:9 Changed 11 years ago by
Milestone: | sage-4.7.2 → sage-duplicate/invalid/wontfix |
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comment:10 Changed 11 years ago by
Keywords: | sd32 added |
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Reviewers: | → William Stein |
Work issues: | sd32 |
More data points: with E=2082a1 and using the S_integral_points function, with S=[2] or S=[3] the coefficient bound used is 11, while with S=[2,3] it is 13 and the extra integral point is found! Clearly, a priori, enlarging S should not ever reduce this bound, so something is wrong there. This shows that both integral_points() and S_integral_points() need fixing.