Hi Enrique,
> On Wed, 29 Nov 2006 09:57:06 -0800, Enrique Acosta
> <[EMAIL PROTECTED]> wrote:
> > I tried it both on my computer and on the online SAGE notebook (the
> > worksheet called 0 is unlocked), and it crashes on both.
On the SAGE command line E.rank() doesn't crash, it just raises a
NotImplementedError exception --- not sure why.
Hope the following helps. All computations were run on sage.math
Ifti.
ps: You have a curve with rank >= 8!
pps: two_descent_simon is da bomb!
====
sage: E = EllipticCurve([0, -285193/512, 0, 10272094875/131072,
-115889280609375/268435456])
sage: EM = E.minimal_model()
sage: time EM.two_descent_simon()
CPU times: user 0.02 s, sys: 0.00 s, total: 0.02 s
Wall time: 426.37
(8,
8,
[(-1215132 : 10275255000 : 1),
(2024405508/3481 : 1399019017725000/205379 : 1),
(110215236/25 : 157858782984/125 : 1),
(-42363243528/18769 : 29469850310821680/2571353 : 1),
(177996328/121 : 5817722755600/1331 : 1),
(80882233177/17689 : 5728840955768125/2352637 : 1),
(2169480 : 1534252752 : 1),
(-2550336 : 11672417520 : 1)])
>From two_descent's documentation:
"...
NOTE: The points are not translated back to self only because I haven't written
code to do this yet.
..."
======================================
The two_descent method invokes mwrank.
On the original model two_descent terminates but I'm not sure what to make of
the output.
sage: time E.two_descent()
Basic pair: I=76257, J=-34430400
disc=588325044426372
2-adic index bound = 2
2-adic index = 2
Two (I,J) pairs
Looking for quartics with I = 76257, J = -34430400
Looking for Type 2 quartics:
Trying positive a from 1 up to 79 (square a first...)
Trying positive a from 1 up to 79 (...then non-square a)
Trying negative a from -1 down to -21
Finished looking for Type 2 quartics.
Looking for Type 1 quartics:
Trying positive a from 1 up to 100 (square a first...)
Trying positive a from 1 up to 100 (...then non-square a)
Finished looking for Type 1 quartics.
Looking for quartics with I = 1220112, J = -2203545600
Looking for Type 2 quartics:
Trying positive a from 1 up to 317 (square a first...)
Trying positive a from 1 up to 317 (...then non-square a)
(89,-140,-978,2100,-579) --nontrivial...locally soluble...(x:y:z) = (-49
: 18283 : 10)
Point = [5519704840404938:-114647772666259630:6111423471187]
height = 26.249770150564216044299105711607770697196854030312
Doubling global 2-adic index to 2
global 2-adic index is equal to local index
so we abort the search for large quartics
Rank of B=im(eps) increases to 1
Exiting search for large quartics after finding enough globally soluble ones.
Looking for Type 1 quartics:
Trying positive a from 1 up to 403 (square a first...)
Trying positive a from 1 up to 403 (...then non-square a)
Finished looking for Type 1 quartics.
Mordell rank contribution from B=im(eps) = 1
Selmer rank contribution from B=im(eps) = 1
Sha rank contribution from B=im(eps) = 0
Mordell rank contribution from A=ker(eps) = 0
Selmer rank contribution from A=ker(eps) = 0
Sha rank contribution from A=ker(eps) = 0
CPU times: user 1.91 s, sys: 0.00 s, total: 1.91 s
Wall time: 1.91
======================================
Two_descent on the minimal model hasn't completed as yet.
sage: EM.two_descent()
Basic pair: I=78809911996, J=-38197235343608588
disc=498925368345172860180530043750000
2-adic index bound = 2
After 2-adic refinement (case 1); 2-adic index = 2
2-adic index = 2
Two (I,J) pairs
Looking for quartics with I = 78809911996, J = -38197235343608588
Looking for Type 2 quartics:
Trying positive a from 1 up to 82645 (square a first...)
(1,0,-3610947932,118112251884750,-1086578740733763719) --nontrivial...(x:y:z) =
(1 : 1 : 0)
Point = [2407298621:118112251884750:1]
height = 16.321496267498527535905399749860055852097312312975
Rank of B=im(eps) increases to 1
(1,0,-574346060,7492444623342,-27489443152300967) --nontrivial...(x:y:z) =
(1 : 1 : 0)
Point = [382897373:7492444623342:1]
height = 16.041343458676659090742200454054250418256469900583
Rank of B=im(eps) increases to 2
(1,0,-4470236,5137208370,-1658683331975) --nontrivial...(x:y:z) = (1 : 1
: 0)
Point = [2980157:5137208370:1]
height = 11.196782508525490806554970385438002826340043215484
Rank of B=im(eps) increases to 3
(1,0,-957080,494380698,-69766017867) --nontrivial...(x:y:z) = (1 : 1 : 0)
Point = [638053:494380698:1]
height = 12.718590453229143759444773755133553887696114482461
Rank of B=im(eps) increases to 4
(1,-1,-1509851,998153865,-183652882650) --nontrivial...(x:y:z) = (1 : 1 : 0)
Point = [8052538:7979191515:8]
height = 12.261589901149609917240226853306431110996268789891
Rank of B=im(eps) increases to 5
=================================
On Magma Rank(E) and TwoDescent(E) are still running and haven't printed
anything on screen.
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