Factoring for a publication

[Max0526]

Our respected colleagues have submitted a paper on elliptic curves: https://web.math.pmf.unizg.hr/~duje/pdf/DKP-Z8Z2Z6.pdf (the uncorrected version on arXiv : https://arxiv.org/abs/2105.06215)
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: https://tinyurl.com/x5fcvknc
Mod untiny url https://docs.google.com/spreadsheets/d/1G-FaJRjNMf9blg45skDnryMiZ1bHkHvMvirERPrz9Jc/edit#gid=0

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

The discriminants can be easily generated by Magma Calculator (http://magma.maths.usyd.edu.au/calc/) by the script: https://tinyurl.com/ytjr542p. https://docs.google.com/document/d/16hnhZ6NlpQ8qFvieiDXthikh3nNakH8BHXgMG8eblBc/edit
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]

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

[Max0526]

Originally Posted by wombatman

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

Thank you! I updated the sheet.

[LaurV]

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

[Max0526]

Originally Posted by LaurV

I took the first non-green for a spin (line 28 in the excel sheet). The three composites will be done today.

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

[wombatman]

Doing the C111 in (7,7).

[Max0526]

Originally Posted by wombatman

Doing the C111 in (7,7).

Thank you! Updated.

[LaurV]

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
C'mon man, give us some serious work to do..

[LaurV]

Took lines 61 and 62 in the excel sheet.

[bur]

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?


I could start with the C127 & C139 (5,-6).

[LaurV]

Took lines 63 and 64 in the excel sheet.