ASKSAGE: Sage Q&A Forum - Individual question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 08 Jan 2020 20:44:48 -0600Is it error in Sage or mwrankhttps://ask.sagemath.org/question/49431/is-it-error-in-sage-or-mwrank/Sage is unable to compute generators of this elliptic curve:
E=EllipticCurve([0,0,0,-3904/3,-144025/27])
E.gens()
The curve has quite small point (-1373/300, 22927/1000).
Is it error in Sage or in mwrank algorithm?
**EDIT:**
Another example:
E=EllipticCurve([0,0,0,-106/3, -911/27])
E.gens()
It has small point: (-7/3, -6).
Sage is terrible.Tue, 07 Jan 2020 15:41:06 -0600https://ask.sagemath.org/question/49431/is-it-error-in-sage-or-mwrank/Comment by nbruin for <p>Sage is unable to compute generators of this elliptic curve:</p>
<pre><code>E=EllipticCurve([0,0,0,-3904/3,-144025/27])
E.gens()
</code></pre>
<p>The curve has quite small point (-1373/300, 22927/1000).</p>
<p>Is it error in Sage or in mwrank algorithm?</p>
<p><strong>EDIT:</strong>
Another example:</p>
<pre><code>E=EllipticCurve([0,0,0,-106/3, -911/27])
E.gens()
</code></pre>
<p>It has small point: (-7/3, -6).</p>
<p>Sage is terrible.</p>
https://ask.sagemath.org/question/49431/is-it-error-in-sage-or-mwrank/?comment=49459#post-id-49459The more diplomatic ,specific, and constructive version of your "sage is terrible" would be: "It looks like there are many opportunities to make "E.gets()" succeed on a lot more elliptic crurves."
It does look like a lot of the higher descent techniques (and 3-descent) that are available in magma, aren't available in sage. It's hard to find someone motivated to do the hard work again -- the first time (for the implementation in magma) the author got a nice paper out of it. That's hard to replicate for the person who'd implement these routines in sage.Wed, 08 Jan 2020 20:44:48 -0600https://ask.sagemath.org/question/49431/is-it-error-in-sage-or-mwrank/?comment=49459#post-id-49459Answer by nbruin for <p>Sage is unable to compute generators of this elliptic curve:</p>
<pre><code>E=EllipticCurve([0,0,0,-3904/3,-144025/27])
E.gens()
</code></pre>
<p>The curve has quite small point (-1373/300, 22927/1000).</p>
<p>Is it error in Sage or in mwrank algorithm?</p>
<p><strong>EDIT:</strong>
Another example:</p>
<pre><code>E=EllipticCurve([0,0,0,-106/3, -911/27])
E.gens()
</code></pre>
<p>It has small point: (-7/3, -6).</p>
<p>Sage is terrible.</p>
https://ask.sagemath.org/question/49431/is-it-error-in-sage-or-mwrank/?answer=49433#post-id-49433The reason why this curve is a little problematic is because it has nontrivial Sha[2]. It would be fairly straightforward to get `E.gens()` to work: this is a rank 1 elliptic curve and enough of BSD is proved that this can be proven analytically. Sage knows how to do that too:
sage: E.rank(only_use_mwrank=False,proof=True)
1
So the only thing to do is to prove that the point you found isn't divisible by any $n>1$. It is a little surprising that `E.gens` doesn't seem to have obvious options to help it discover this. The basic elements for implementing this are available.Tue, 07 Jan 2020 22:56:38 -0600https://ask.sagemath.org/question/49431/is-it-error-in-sage-or-mwrank/?answer=49433#post-id-49433Comment by azerbajdzan for <p>The reason why this curve is a little problematic is because it has nontrivial Sha[2]. It would be fairly straightforward to get <code>E.gens()</code> to work: this is a rank 1 elliptic curve and enough of BSD is proved that this can be proven analytically. Sage knows how to do that too:</p>
<pre><code>sage: E.rank(only_use_mwrank=False,proof=True)
1
</code></pre>
<p>So the only thing to do is to prove that the point you found isn't divisible by any $n>1$. It is a little surprising that <code>E.gens</code> doesn't seem to have obvious options to help it discover this. The basic elements for implementing this are available.</p>
https://ask.sagemath.org/question/49431/is-it-error-in-sage-or-mwrank/?comment=49456#post-id-49456@nbruin: I just found even easier case of elliptic curve that Sage is unable to compute its generators. See edit of my question.Wed, 08 Jan 2020 18:29:40 -0600https://ask.sagemath.org/question/49431/is-it-error-in-sage-or-mwrank/?comment=49456#post-id-49456