C155 polys
 

@VBCurtis
CADO can't really optimize any of your polys, sorry. I list the output here just for your reference. You can go ahead and test-sieve. Maybe you'll find a better sieving one in the CADO bunch.
[code]
Y0: -550035408931400289182387096506
Y1: 3772541237989709
c0: -832397597963911566496591389962673705
c1: 342162987196316628514235085798
c2: -5150338662671966117819625
c3: 11595913923336328588
c4: 6624649288340
c5: 265200
skew: 1785621.22864
# lognorm 48.55, E 41.26, alpha -7.29 (proj -2.70), 3 real roots
# MurphyE = 3.09749183e-12
[/code]
[code]
Y0: -918495892344930208874266009177
Y1: 2549566030265807
c0: -11780797099833345872548067569902584640
c1: -31120993232550559446390375883056
c2: 14936750165662565025684636
c3: 9348457521246097948
c4: -976434433819
c5: 20424
skew: 6083953.82854
# lognorm 48.43, E 41.50, alpha -6.94 (proj -1.11), 5 real roots
# MurphyE = 3.06015493e-12
[/code]
[code]
Y0: -581069316484212954617286438865
Y1: 3495047121029561
c0: -561326274760973322024682734754064664
c1: 5164901371305751014512245479508
c2: -2937022526495692702957782
c3: -7326841004667715167
c4: 706980166748
c5: 201552
skew: 2013554.79439
# lognorm 47.70, E 41.36, alpha -6.34 (proj -1.63), 5 real roots
# MurphyE = 3.05165690e-12
[/code]
[code]
Y0: -399866113230837003717886899914
Y1: 1122590280894899
c0: 518790490718821545376566834110874729
c1: 1085530911524300734741511234826
c2: -9058539782056951440723617
c3: 4236745463868270266
c4: 12644954058988
c5: 1306032
skew: 988568.71234
# lognorm 48.21, E 41.36, alpha -6.85 (proj -1.96), 3 real roots
# MurphyE = 2.98930194e-12
[/code]

Thanks Max! I appreciate your time. I've been test-sieving the 3.10 for parameters, and confusing myself (lots of settings seem to produce similar timings, including 13e/31LP). I'll compare these four and then test for settings again.

C155 poly
 

@VBCurtis
I can also continue my CADO run past a standard prescribed limit and (hopefully) get you a poly with the E > 3.103e-12. I think there is enough space for improvement. Let me know.

Naw, this isn't a big enough job to spend more cycles on poly select. Thanks, though!
Edit: I finally thought to compare sieve times to the SNFS poly for this number, and it's 20-30% faster. Whoops! Dunno why my notes had this as a GNFS candidate.
Edit2: I should finish test-sieving before posting; the SNFS poly is way faster at small Q, slower at large Q. The GNFS is competitive after all, gotta do some parameter tweaking to see if SNFS can be made the winner.

C157 poly, could it be improved?

[CODE]# norm 3.634689e-15 alpha -8.130689 e 2.145e-12 rroots 5
n: 2153646797243598406022781698871921179468736333856465460905533539179197067080286019717757270291317968880659999793269997464862726882530680275363360113121869979
skew: 4136524.86
c0: 38183868219853541865705925791334065840
c1: 551587635274133890657872371831148
c2: -246906223399614490859771480
c3: -64134178097710951129
c4: 12746613352440
c5: 1576368
Y0: -1064395440425155733396732383817
Y1: 558292606562844097
rlim: 35200000
alim: 35200000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6
type: gnfs[/CODE]

C157 poly
 

@unconnected
I'll CADO it and let you know later today.

C157 poly
 

@unconnected
CADO produces nothing better. Its pick just FYI (might sieve better):
[code]
Y0: -1064395061264640034487103814946
Y1: 558292606562844097
c0: 281758656292635602645290902781804696245
c1: 145123545456157447958732226605265
c2: -337362047392207821363903701
c3: -22236320844340903129
c4: 18099509815560
c5: 1576368
skew: 4054530.09879
# lognorm 50.87, E 42.73, alpha -8.13 (proj -1.89), 5 real roots
# MurphyE = 2.14140620e-12
[/code]Also, 2.141e-12 seems to be a bit low for C157. I started a CADO run and will post my best poly tomorrow.

C157 poly
 

@unconnected
This one seems to be a much better poly:
[code]
Y0: -3412887084652747994920013434801
Y1: 726799483512671712557
c0: -155739768072620872585403642819221342740
c1: 105731537875959470823347887885348
c2: 16051986632892334694632495
c3: -2782308567581898834
c4: -134653299134
c5: 4680
skew: 11561243.62085
# lognorm 47.75, E 41.44, alpha -6.31 (proj -1.64), 5 real roots
# MurphyE = 2.41811536e-12
[/code]

C161 poly
 

@unconnected
Sorry, I forgot that I extended the CADO run past its regular time and found a better poly:
[code]
n: 35097073616687632557752801198533520945254874632510346030786883919679811022567348870834681872114366711474697302202057340103253717267147506425581175254494314589829
skew: 1332658.97356
c0: -767582233216309473318502622003853805
c1: 2599999618240688534281558074558
c2: 2386357136502882543721094
c3: -11540743461082593189
c4: -1602756954640
c5: 1043700
Y0: -11095433717730497171177235063900
Y1: 934179615219147727771
# lognorm 47.95, E 42.50, alpha -5.45 (proj -1.99), 3 real roots
# MurphyE = 1.29505988e-12
[/code]

c157 poly
 

The last one is clearly winner, thanks!

C161 from 3613045528091^17-1
 

Can any of these polys be improved?

[CODE]N: 18240051261562921058567070311861891715172678007177798917429354382357183300885632657444483979332189347244110527138705974473160994107001905334487636771142410048269
# 3613045528091^17-1 - C161
R0: -11569763219615258807229377328496
R1: 1457789863829927
A0: -138784982551807568987379122073936193125
A1: 69624897411842882523815023692815
A2: 127037715715746868633596635
A3: 2611630321401617357
A4: -4610400041514
A5: 87984
skew 5367311.02, size 1.032e-15, alpha -5.994, combined = 1.144e-12 rroots = 5[/CODE]

[CODE]R0: -7315658960766022049026997110086
R1: 300755933324077
A0: -1681804806422343535898862414903118078345
A1: 4044121456548186940964861376739429
A2: 170820988658065775328775695
A3: -287271342078511683013
A4: -4079653365014
A5: 870480
skew 7711953.66, size 1.046e-15, alpha -7.809, combined = 1.146e-12 rroots = 5[/CODE]

[CODE]R0: -6987156922492347492992085104602
R1: 1377547375433647
A0: -465455346359262550329910809670477095735
A1: 73044220337119752380630101270869
A2: 311885311446221017809968261
A3: 19974851616189828055
A4: -27334438923334
A5: 1095276
skew 3622479.48, size 1.102e-15, alpha -6.932, combined = 1.168e-12 rroots = 5[/CODE]