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See detail? Enter first and last N:
Table of curves computed from newforms via periods
(reordered to agree with Book for levels up to 1000)
(reordered to agree with LMFDB for levels over 1000)
Retrieving newform data for N = 90
Finished reading newform data for N = 90
Form number 1:
aplist = [ -1 0 1 2 6 -4 -6 -4 0 -6 -4 8 0 8 0 -6 6 2 -4 -12 ...]
aq = [ 1 1 -1 ]
ap0 = 2, dp0 = 4, np0 = 6
SFE = 1, L/P = 2/3
lplus = 1, mplus = 1
lminus = 7, mminus = 4
[(-77,2;-3,7),1,1;1]
Finding periods -- via L(f_chi) using twists by 1 and 7
[w_1,w_2] = [(1.229967685586970495175018,1.14635616957311248404033),(-1.229967685586970495175018,1.14635616957311248404033)]
tau = (-0.07028346131662992344799259,0.9975270598161003196814261) (abs(tau)=0.9999999999999999999999998)
w_R = (-2.459935371173940990350036,0) w_IR = (-1.229967685586970495175018,-1.14635616957311248404033)
c4 = -278.9999999999999999999985
c6 = -1268.999999999999999999938
After rounding, using factors 3 for c4 and 3 for c6:
ic4 = -279
ic6 = -1269
Lattice type checks OK
Real period checks OK
Imag period checks OK
Curve = [1,-1,0,6,0] N = 90
Form number 2:
aplist = [ 1 0 -1 2 -6 -4 6 -4 0 6 -4 8 0 8 0 6 -6 2 -4 12 ...]
aq = [ -1 1 1 ]
ap0 = 2, dp0 = 4, np0 = 6
SFE = 1, L/P = 2/3
lplus = 1, mplus = 1
lminus = 7, mminus = 12
[(-77,2;-3,7),1,1;1]
Finding periods -- via L(f_chi) using twists by 1 and 7
[w_1,w_2] = [(0,-1.42024434873635680197068),(1.985547129270674318649064,0.7101221743681784009853398)]
tau = (-0.5,1.398032057678869145976115) (abs(tau)=1.484753728501064551755562)
w_R = (-3.971094258541348637298128,0) w_IR = (-1.985547129270674318649064,-0.7101221743681784009853398)
c4 = 368.9999999999999999999945
c6 = -8072.999999999999999999854
After rounding, using factors 3 for c4 and 3 for c6:
ic4 = 369
ic6 = -8073
Lattice type checks OK
Real period checks OK
Imag period checks OK
Curve = [1,-1,1,-8,11] N = 90
Form number 3:
aplist = [ 1 0 1 -4 0 2 -6 -4 0 6 8 2 6 -4 0 6 0 -10 -4 0 ...]
aq = [ -1 -1 -1 ]
ap0 = -4, dp0 = 24, np0 = 12
SFE = 1, L/P = 2
lplus = 1, mplus = 1
lminus = 7, mminus = 8
[(13,1;1,7),2,2;1]
Finding periods -- via L(f_chi) using twists by 1 and 7
[w_1,w_2] = [(0.6687979972943242528826713,0.9676241148913877311526313),(-0.6687979972943242528826713,0.9676241148913877311526313)]
tau = (0.3534332136464203486286135,0.9354597604876244964377629) (abs(tau)=1)
w_R = (-1.337595994588648505765343,0) w_IR = (-0.6687979972943242528826713,-0.9676241148913877311526313)
c4 = -638.9999999999999999999905
c6 = 49598.99999999999999999972
After rounding, using factors 3 for c4 and 3 for c6:
ic4 = -639
ic6 = 49599
Lattice type checks OK
Real period checks OK
Imag period checks OK
Curve = [1,-1,1,13,-61] N = 90
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