Magma V2.7-1 Fri Apr 27 2001 22:04:26 on modular [Seed = 2041229250] Type ? for help. Type -D to quit. Loading startup file "/home/was/modsym/init.m" Loading "/home/was/modsym/init-magma.m" C IndexGamma0 R ellap idxG0 CS MS S factormod modcharpoly DC ND Tn factorpadic padiccharpoly ES NS Z fcp qexp F Q charpoly fn x Finding acceptable K for E of conductor 389 Height bound (8.7373) on point search is too large -- reducing to 0.5000 This means that the computed group may only generate a group of finite index in the actual group. H_2() NumeratorIdeal() rhotilde(I, 4776992648266327621 + O(3^40) , -4776992648266327620 + O(3^40) ) Time: 4.209 Computing class number h Class number h = 1 Raising ideal to the power h Finding generator for the principal ideal I^h I^h is principal. Computing embeddings of canonical power of generator into Qp pi_alpha_v = 1 - q^3 - q^4 - q^5 + q^6 - q^7 - q^8 - q^11 + q^12 + q^15 - q^16 + q^18 + q^19 + q^20 + q^21 + q^22 + q^23 + q^25 - q^26 + q^27 - q^28 + q^30 - q^31 + q^32 - q^34 + q^35 - q^36 - q^37 + q^38 - q^39 + q^40 + q^41 - q^43 + q^45 + q^46 + q^47 + q^48 + O(q^49) pibar_alpha_v = 1 - q^3 - q^4 - q^5 + q^6 - q^7 - q^8 - q^9 + q^10 - q^13 - q^14 + q^15 + q^16 - q^18 + q^20 - q^21 - q^22 + q^24 - q^29 + q^30 - q^33 - q^34 + q^35 - q^36 - q^37 + q^39 - q^40 - q^41 - q^42 - q^43 - q^45 + q^46 - q^48 + O(q^49) pi_alpha_v-1 = -q^3 - q^4 - q^5 + q^6 - q^7 - q^8 - q^11 + q^12 + q^15 - q^16 + q^18 + q^19 + q^20 + q^21 + q^22 + q^23 + q^25 - q^26 + q^27 - q^28 + q^30 - q^31 + q^32 - q^34 + q^35 - q^36 - q^37 + q^38 - q^39 + q^40 + q^41 - q^43 + q^45 + q^46 + q^47 + q^48 + O(q^49) Valuation(pi_alpha_v-1) = 3 pibar_alpha_v-1 = -q^3 - q^4 - q^5 + q^6 - q^7 - q^8 - q^9 + q^10 - q^13 - q^14 + q^15 + q^16 - q^18 + q^20 - q^21 - q^22 + q^24 - q^29 + q^30 - q^33 - q^34 + q^35 - q^36 - q^37 + q^39 - q^40 - q^41 - q^42 - q^43 - q^45 + q^46 - q^48 + O(q^49) Valuation(pibar_alpha_v-1) = 3 Valuations ok -- now computing p-adic logarithms. lambda(pi_alpha_v) = -q^3 - q^4 - q^5 - q^6 - q^8 - q^9 - q^11 + q^12 - q^14 - q^15 - q^16 + q^18 - q^19 + q^20 - q^22 - q^23 - q^25 + q^26 - q^27 - q^29 - q^31 + q^32 + q^34 - q^36 + q^38 - q^39 + q^40 - q^41 - q^42 + q^43 - q^44 + q^45 - q^46 - q^47 + q^48 + O(q^49) lambda(pibar_alpha_v) = -q^3 - q^4 - q^5 - q^6 - q^8 + q^9 - q^12 - q^13 - q^14 + q^17 - q^18 + q^20 + q^26 + q^29 + q^30 + q^31 + q^32 - q^33 - q^34 - q^35 - q^37 - q^39 + q^40 + q^41 + q^42 + q^43 - q^44 - q^45 + q^46 + q^48 + O(q^49) H_2() NumeratorIdeal() rhotilde(I, 4776992648266327621 + O(3^40) , -4776992648266327620 + O(3^40) ) Time: 5.050 Computing class number h Class number h = 1 Raising ideal to the power h Finding generator for the principal ideal I^h I^h is principal. Computing embeddings of canonical power of generator into Qp pi_alpha_v = 1 - q^9 + q^10 + q^11 + q^14 + q^15 - q^16 - q^21 - q^22 - q^24 - q^25 + q^27 + q^28 - q^29 - q^30 - q^31 + q^35 - q^37 + q^38 - q^39 + q^42 - q^43 + q^44 + q^45 + q^46 - q^47 + q^48 + O(q^49) pibar_alpha_v = 1 + q^9 - q^10 + q^12 - q^13 - q^15 - q^16 + q^17 - q^18 - q^22 - q^23 + q^27 - q^28 - q^29 + q^32 + q^33 + q^34 + q^36 - q^37 - q^38 + q^39 + q^40 - q^41 - q^42 - q^44 - q^47 + q^48 + O(q^49) pi_alpha_v-1 = -q^9 + q^10 + q^11 + q^14 + q^15 - q^16 - q^21 - q^22 - q^24 - q^25 + q^27 + q^28 - q^29 - q^30 - q^31 + q^35 - q^37 + q^38 - q^39 + q^42 - q^43 + q^44 + q^45 + q^46 - q^47 + q^48 + O(q^49) Valuation(pi_alpha_v-1) = 9 pibar_alpha_v-1 = q^9 - q^10 + q^12 - q^13 - q^15 - q^16 + q^17 - q^18 - q^22 - q^23 + q^27 - q^28 - q^29 + q^32 + q^33 + q^34 + q^36 - q^37 - q^38 + q^39 + q^40 - q^41 - q^42 - q^44 - q^47 + q^48 + O(q^49) Valuation(pibar_alpha_v-1) = 9 Valuations ok -- now computing p-adic logarithms. lambda(pi_alpha_v) = -q^9 + q^10 + q^11 + q^14 + q^15 - q^16 + q^18 - q^19 + q^20 + q^21 - q^22 - q^23 + q^24 - q^26 - q^28 + q^30 + q^32 - q^34 - q^37 - q^39 - q^40 + q^41 - q^44 + q^47 + q^48 + O(q^49) lambda(pibar_alpha_v) = q^9 - q^10 + q^12 - q^13 - q^15 - q^16 + q^17 - q^19 - q^21 + q^22 + q^23 + q^24 - q^25 - q^26 + q^27 + q^28 - q^29 + q^31 - q^35 - q^36 + q^37 - q^39 - q^40 - q^41 + q^42 - q^43 + q^44 + q^46 - q^48 + O(q^49) Height bound (9.6232) on point search is too large -- reducing to 0.5000 This means that the computed group may only generate a group of finite index in the actual group. H_2() NumeratorIdeal() rhotilde(I, 809754760839083609 + O(3^40) , -809754760839083609 + O(3^40) ) Time: 12.459 Computing class number h Class number h = 2 Raising ideal to the power h Finding generator for the principal ideal I^h I^h is principal. Computing embeddings of canonical power of generator into Qp pi_alpha_v = 1 + q^3 - q^6 + q^7 + q^8 - q^11 - q^13 - q^14 - q^15 - q^17 + q^19 - q^20 - q^23 - q^26 - q^27 - q^28 - q^29 - q^31 + q^34 - q^35 + q^36 + q^37 + q^38 + q^39 + q^40 - q^41 + q^42 - q^43 - q^46 + O(q^49) pibar_alpha_v = 1 + q^3 - q^6 + q^7 + q^8 - q^9 - q^11 - q^13 - q^14 - q^15 + q^16 + q^18 + q^22 - q^23 + q^25 + q^26 - q^28 - q^30 + q^31 - q^33 + q^34 + q^35 - q^36 - q^37 + q^39 - q^40 + q^42 - q^43 + q^44 - q^45 - q^47 + O(q^49) pi_alpha_v-1 = q^3 - q^6 + q^7 + q^8 - q^11 - q^13 - q^14 - q^15 - q^17 + q^19 - q^20 - q^23 - q^26 - q^27 - q^28 - q^29 - q^31 + q^34 - q^35 + q^36 + q^37 + q^38 + q^39 + q^40 - q^41 + q^42 - q^43 - q^46 + O(q^49) Valuation(pi_alpha_v-1) = 3 pibar_alpha_v-1 = q^3 - q^6 + q^7 + q^8 - q^9 - q^11 - q^13 - q^14 - q^15 + q^16 + q^18 + q^22 - q^23 + q^25 + q^26 - q^28 - q^30 + q^31 - q^33 + q^34 + q^35 - q^36 - q^37 + q^39 - q^40 + q^42 - q^43 + q^44 - q^45 - q^47 + O(q^49) Valuation(pibar_alpha_v-1) = 3 Valuations ok -- now computing p-adic logarithms. lambda(pi_alpha_v) = q^3 - q^7 + q^8 + q^10 - q^11 + q^13 - q^14 - q^15 + q^16 + q^18 - q^19 + q^21 - q^22 - q^23 + q^24 - q^25 - q^27 - q^28 + q^29 + q^30 - q^31 + q^32 + q^33 - q^34 - q^35 - q^36 - q^37 - q^38 + q^39 + q^40 + q^44 - q^47 - q^48 + O(q^49) lambda(pibar_alpha_v) = q^3 - q^7 + q^8 - q^9 + q^10 - q^11 + q^12 + q^13 - q^14 - q^16 + q^18 + q^19 - q^21 + q^22 + q^23 - q^24 - q^25 + q^26 + q^27 + q^30 + q^31 + q^32 + q^33 + q^36 - q^37 + q^38 - q^39 + q^40 - q^44 + q^46 + q^47 + O(q^49) H_2() NumeratorIdeal() rhotilde(I, 809754760839083609 + O(3^40) , -809754760839083609 + O(3^40) ) Time: 13.099 Computing class number h Class number h = 2 Raising ideal to the power h Finding generator for the principal ideal I^h