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-   -   Factoring for a publication (https://www.mersenneforum.org/showthread.php?t=26875)

 Max0526 2021-06-05 01:21

Factoring for a publication

Our respected colleagues have submitted a paper on elliptic curves: [url]https://web.math.pmf.unizg.hr/~duje/pdf/DKP-Z8Z2Z6.pdf[/url] (the uncorrected version on arXiv : [url]https://arxiv.org/abs/2105.06215[/url])
The authors experienced factoring bottleneck while building the three plots on p. 17-19: "The bottleneck of the root number computation is the factorization of the discriminant".
I volunteered to help and had a lot of success improving plot 2. Now I am working on adding points to plot 3.
I summarized my efforts so far and all the necessary information in the sheet: [url]https://tinyurl.com/x5fcvknc[/url]

Does anybody have spare cycles to help me and speed up the process?

The discriminants can be easily generated by Magma Calculator ([url]http://magma.maths.usyd.edu.au/calc/[/url]) by the script: [url]https://tinyurl.com/ytjr542p[/url]. [C]https://docs.google.com/document/d/16hnhZ6NlpQ8qFvieiDXthikh3nNakH8BHXgMG8eblBc/edit[/C]
The output also includes a number of SNFS cofactors.
The factors can be submitted directly to FactorDB (direct links are provided in the sheet), I am retrieving them from there to add to the Magma code to recreate the updated plot.

The general ideas are:
1) to extend an existing Figure 3 plot (p. 19), ideally keeping it roughly rectangular, and focusing on a half-plot for x >= 1, the left half-plot is built using the existing symmetry;
2) to reach ~250 plot points at the end (157 points now);
3) to use ECM, SIQS, etc. (yafu's sequence of test works really well so far) rather than NFS;
4) to factor everything up to SNFS 170;
5) to avoid GNFS (if the Magma code is not descriptive enough, I'll help you create some good SNFS poly(s) for a composite, the discriminants have many suitable cofactors to play with).

So far I finished the layout for stage 6 (x = 6 or y = 6 or y = -6), and spiral out clockwise in the consecutive stages.

You should be able to comment directly in the sheet. You are welcome to add any ideas to the thread or send me a PM.

Thank you so much in advance! Promise to always try spinning your GNFS polys. :-)

 wombatman 2021-06-05 03:52

I can do the c97 in (1,-7), [STRIKE]the c94 in (7, -7)[/STRIKE], the c116 in (7, -4). Probably others depending on what's still available once I finish these.

 Max0526 2021-06-05 04:25

[QUOTE=wombatman;579982]I can do the c97 in (1,-7), [STRIKE]the c94 in (7, -7)[/STRIKE], the c116 in (7, -4). Probably others depending on what's still available once I finish these.[/QUOTE]
Thank you! I updated the sheet.

 LaurV 2021-06-05 04:52

I took the first non-green for a spin (line 28 in the excel sheet). The [U]three[/U] composites will be done today.
Edit: I said three :razz:

 Max0526 2021-06-05 05:19

[QUOTE=LaurV;579984]I took the first non-green for a spin (line 28 in the excel sheet). The three composites will be done today.[/QUOTE]

Thank you! c90 is already done. I updated the sheet.

 wombatman 2021-06-05 05:20

Doing the C111 in (7,7).

 Max0526 2021-06-05 05:36

[QUOTE=wombatman;579986]Doing the C111 in (7,7).[/QUOTE]

Thank you! Updated.

 LaurV 2021-06-05 06:33

Edit2: the 117 seems to be already a prime, so only 2 to factor for me. Almost done.
Edit3: ecm hit for 119. So the most difficult proved to be the c113 :lol:
C'mon man, give us some serious work to do.. :razz:

 LaurV 2021-06-05 07:16

Took lines 61 and 62 in the excel sheet.

 bur 2021-06-05 07:30

I'd gladly do some factoring, but admittedly I'm not 100% clear on what to do...

Do I just factor the numbers from your sheet? What about the magma script, is it used on the prime factors after factorization?