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EdH 2021-06-05 13:12

OK! I've commented about running SIQS on lines 60 and 75. I will run those in a little while, if no one else has claimed them.

Max0526 2021-06-05 13:13

[QUOTE=bur;579995]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).[/QUOTE]

Yes, just factors the numbers from the sheet. The posted Magma script is for generating the initial records on factordb, and also for creating suitable SNFS polys.

That C127 is already factored by fivemack. I am writing a post on how to generate SNFS polys with the C139 as an example.

Max0526 2021-06-05 13:15

[QUOTE=EdH;580018]OK! I've commented about running SIQS on lines 60 and 75. I will run those in a little while, if no one else has claimed them.[/QUOTE]
Updated in the sheet, thank you!

fivemack 2021-06-05 13:18

(5,-6) finished - the C139 has a P26 by ecm

Max0526 2021-06-05 13:46

[QUOTE=fivemack;579998]I'll take the two (5,-6) ones to start with; this is a research direction I've been interested in since my PhD in early 2000s.

Could you also send me the SNFS polynomial for (3,-7) ?

I am also throwing a core-month of ECM at the (6,-7) cofactors[/QUOTE]

This is how to generate the SNFS polys from the attached Magma script, c126 / snfs144 from (3, -7) is used as an example.

Edit the script to say [3, -7][code]
m := [3, 7]; ////////////////////// edit the plot point here /////////////////////
[/code]
and uncomment the ouput for a[code]
a; " "; // uncomment this to get Y0 and Y1 for the SNFS poly, if necessary //
[/code]
Run the script in Magma Calculator ([url]http://magma.maths.usyd.edu.au/calc/[/url]).
Take the first value from the output (a-value) to produce Y0 and Y1 --> a = -Y0/Y1[code]
a = 2625497112988581533564774729619428753/581569296010330112388333512013248048
[/code]
[code]
Y0: -2625497112988581533564774729619428753
Y1: 581569296010330112388333512013248048
[/code]
Now look through the numerators at the bottom of the output and find the one that has c126 as a cofactor: [url]http://factordb.com/index.php?id=1100000002597811273[/url]
It was the second numerator from the top (ignore or comment all denominators in the output for now), generated by the second degree 4 poly on the list[code]
x^4 - 24*x^3 + 152*x^2 - 336*x + 196,
2*x^4 - 30*x^3 + 169*x^2 - 420*x + 196*2, <-- this poly
x^4 - 12*x^3 + 62*x^2 - 168*x + 196,
x^4 - 6*x^3 + 17*x^2 - 84*x + 196
[/code]
which creates the block for c0-c4[code]
c0: 392
c1: -420
c2: 169
c3: -30
c4: 2[/code]
Get these 7 lines (c0-c4, Y0, Y1) through the [url]http://cownoise.com/[/url] / Calculators / Optimal Skew to produce the values for the skew and E[code]
skew: 3.99192
# E = 2.36121084e-09
[/code]
Add the n-value (c126) at the top of the poly file. The first one is ready! (There will be a second one too, for a different a-value [Y0, Y1, rational side] but the same c0-c4 [algebraic side], will explain it in a bit, need to derive the formula first).
[code]
n: 665346346066322380069828663638962277265700573377334838072153685493190817971091678723311076185411447868488601711575118621654489
skew: 3.99192
c0: 392
c1: -420
c2: 169
c3: -30
c4: 2
Y0: -2625497112988581533564774729619428753
Y1: 581569296010330112388333512013248048
# E = 2.36121084e-09
[/code]

Max0526 2021-06-05 13:48

[QUOTE=fivemack;580021](5,-6) finished - the C139 has a P26 by ecm[/QUOTE]

Could you please post a P26 to FactorDB for this C139?
EDIT: Ignore it please, marked as done for fivemack.

EdH 2021-06-05 14:10

Line 60 is completed by SIQS and the db updated. What else may be needed?

Max0526 2021-06-05 14:11

[QUOTE=fivemack;579998]I'll take the two (5,-6) ones to start with; this is a research direction I've been interested in since my PhD in early 2000s.

Could you also send me the SNFS polynomial for (3,-7) ?

I am also throwing a core-month of ECM at the (6,-7) cofactors[/QUOTE]

The second SNFS poly is created by calculating[code]
a[SUB]2[/SUB] = 7*(a[SUB]1[/SUB]-4)/(2*a[SUB]1[/SUB]-7) = 299219928947261084011440681566436561/168572736272121754344459267878017310,
where a[SUB]1[/SUB] = 2625497112988581533564774729619428753/581569296010330112388333512013248048[/code] from the Magma script. It gives us[code]
n: 665346346066322380069828663638962277265700573377334838072153685493190817971091678723311076185411447868488601711575118621654489
skew: 3.01798 # different for a2
c0: 392
c1: -420
c2: 169
c3: -30
c4: 2
Y0: -299219928947261084011440681566436561 # for a2
Y1: 168572736272121754344459267878017310 # for a2
# E = 3.14999605e-09 # different and _better_ poly for a2 !!!
[/code]
There should be a[SUB]3[/SUB] and a[SUB]4[/SUB] values, but I didn't get to them yet. If/when I do, I'll post the additions.
Then there could be spin of course, and I am working on it too.

Max0526 2021-06-05 14:19

[QUOTE=EdH;580024]Line 60 is completed by SIQS and the db updated. What else may be needed?[/QUOTE]

I updated the sheet, thank you! Are you up for the c93 from here? [url]http://factordb.com/index.php?id=1100000002598197699[/url]

EdH 2021-06-05 14:23

[QUOTE=Max0526;580027]I updated the sheet, thank you! Are you up for the c93 from here? [URL]http://factordb.com/index.php?id=1100000002598197699[/URL][/QUOTE]
Sure! But, I might wait for the LA square root of a different project to complete. . .

Max0526 2021-06-05 14:40

[QUOTE=EdH;580028]Sure! But, I might wait for the LA square root of a different project to complete. . .[/QUOTE]

The c93 is done now.


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