[was@modular anti-cyclotomic_height_pairing]$ [was@modular anti-cyclotomic_height_pairing]$ Magma V2.7-1 Thu Apr 26 2001 03:37:59 on modular [Seed = 2454663411] Type ? for help. Type -D to quit. Loading startup file "/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 > Attach("anti-cyclotomic.m");SetVerbose("ac_height",1); > Attach("anti-cyclotomic.m");SetVerbose("ac_height",1);TestNontrivialityConjecture(Rank2Curve(35),3,3,8); In file "/home/was/papers/anti-cyclotomic_height_pairing/anti-cyclotomic.m", line 99, column 45: >> vprint ac_height : "pi_alphabar_v-1 = ", pi_alphabar_v-1; ^ Runtime error: Undefined reference 'pi_alphabar_v' in package "/home/was/papers/anti-cyclotomic_height_pairing/anti-cyclotomic.m" > TestNontrivialityConjecture(Rank2Curve(35),3,3,8); In file "/home/was/papers/anti-cyclotomic_height_pairing/anti-cyclotomic.m", line 100, column 45: >> vprint ac_height : "pi_alphabar_v-1 = ", pi_alphabar_v-1; ^ Runtime error: Undefined reference 'pi_alphabar_v' in package "/home/was/papers/anti-cyclotomic_height_pairing/anti-cyclotomic.m" > TestNontrivialityConjecture(Rank2Curve(35),3,3,8); In file "/home/was/papers/anti-cyclotomic_height_pairing/anti-cyclotomic.m", line 100, column 45: >> vprint ac_height : "pibar_alpha_v-1 = ", pbari_alpha_v-1; ^ Runtime error: Undefined reference 'pbari_alpha_v' in package "/home/was/papers/anti-cyclotomic_height_pairing/anti-cyclotomic.m" > TestNontrivialityConjecture(Rank2Curve(35),3,3,8); Finding acceptable K for E of conductor 1171 Trying D = -8 -8 is acceptable. Trying D = -7 Trying D = -4 Trying D = -3 Height bound (7.7261) 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, 534986635 + O(3^20) , -534986635 + O(3^20) ) 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, generated by -1/2*sqrtD + 1 Computing embeddings of canonical power of generator into Qp pi_alpha_v = -1406682737 + O(3^20) pibar_alpha_v = -520717559*3^4 + O(3^23) pi_alpha_v-1 = -156298082*3^2 + O(3^20) Valuation(pi_alpha_v-1) = 2 pibar_alpha_v-1 = -42178122280 + O(3^23) Valuation(pibar_alpha_v-1) = 0 When m = 1 hts = [* false *] H_2() NumeratorIdeal() rhotilde(I, 534986635 + O(3^20) , -534986635 + O(3^20) ) 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, generated by -152593/2*sqrtD + 255905 Computing embeddings of canonical power of generator into Qp pi_alpha_v = 94531972*3^4 + O(3^23) pibar_alpha_v = -1481252000 + O(3^20) pi_alpha_v-1 = 7657089731 + O(3^23) Valuation(pi_alpha_v-1) = 0 pibar_alpha_v-1 = -493750667*3 + O(3^20) Valuation(pibar_alpha_v-1) = 1 When m = 2 hts = [* false, false *] H_2() NumeratorIdeal() rhotilde(I, 534986635 + O(3^20) , -534986635 + O(3^20) ) 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, generated by -24350762252383107491057132047900200996629554952639/2*sqrtD - 27832994129746749885056217667545035311842495071553 Computing embeddings of canonical power of generator into Qp pi_alpha_v = 747125299 + O(3^20) pibar_alpha_v = 29336698 + O(3^20) pi_alpha_v-1 = 83013922*3^2 + O(3^20) Valuation(pi_alpha_v-1) = 2 pibar_alpha_v-1 = 3259633*3^2 + O(3^20) Valuation(pibar_alpha_v-1) = 2 Valuations ok -- now computing p-adic logarithms. lambda(pi_alpha_v) = 122570416*3^2 + O(3^20) lambda(pibar_alpha_v) = 122570416*3^2 + O(3^20) H_2() NumeratorIdeal() rhotilde(I, 534986635 + O(3^20) , -534986635 + O(3^20) ) 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, generated by -24350762252383107491057132047900200996629554952639/2*sqrtD - 27832994129746749885056217667545035311842495071553 Computing embeddings of canonical power of generator into Qp pi_alpha_v = 747125299 + O(3^20) pibar_alpha_v = 29336698 + O(3^20) pi_alpha_v-1 = 83013922*3^2 + O(3^20) Valuation(pi_alpha_v-1) = 2 pibar_alpha_v-1 = 3259633*3^2 + O(3^20) Valuation(pibar_alpha_v-1) = 2 Valuations ok -- now computing p-adic logarithms. lambda(pi_alpha_v) = 122570416*3^2 + O(3^20) lambda(pibar_alpha_v) = 122570416*3^2 + O(3^20) When m = 3 hts = [* false, false, O(3^14) *] Answer so far = [* <-8, [* false, false, O(3^14) *]> *] [* <-8, [* false, false, O(3^14) *]> *] > TestNontrivialityConjecture(Rank2Curve(35),3,4,8); Finding acceptable K for E of conductor 1171 Trying D = -8 -8 is acceptable. Trying D = -7 Trying D = -4 Trying D = -3 Height bound (7.7261) 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, 534986635 + O(3^20) , -534986635 + O(3^20) ) 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, generated by -1/2*sqrtD + 1 Computing embeddings of canonical power of generator into Qp pi_alpha_v = -1406682737 + O(3^20) pibar_alpha_v = -520717559*3^4 + O(3^23) pi_alpha_v-1 = -156298082*3^2 + O(3^20) Valuation(pi_alpha_v-1) = 2 pibar_alpha_v-1 = -42178122280 + O(3^23) Valuation(pibar_alpha_v-1) = 0 When m = 1 hts = [* false *] H_2() NumeratorIdeal() rhotilde(I, 534986635 + O(3^20) , -534986635 + O(3^20) ) 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, generated by -152593/2*sqrtD + 255905 Computing embeddings of canonical power of generator into Qp pi_alpha_v = 94531972*3^4 + O(3^23) pibar_alpha_v = -1481252000 + O(3^20) pi_alpha_v-1 = 7657089731 + O(3^23) Valuation(pi_alpha_v-1) = 0 pibar_alpha_v-1 = -493750667*3 + O(3^20) Valuation(pibar_alpha_v-1) = 1 When m = 2 hts = [* false, false *] H_2() NumeratorIdeal() rhotilde(I, 534986635 + O(3^20) , -534986635 + O(3^20) ) 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, generated by -24350762252383107491057132047900200996629554952639/2*sqrtD - 27832994129746749885056217667545035311842495071553 Computing embeddings of canonical power of generator into Qp pi_alpha_v = 747125299 + O(3^20) pibar_alpha_v = 29336698 + O(3^20) pi_alpha_v-1 = 83013922*3^2 + O(3^20) Valuation(pi_alpha_v-1) = 2 pibar_alpha_v-1 = 3259633*3^2 + O(3^20) Valuation(pibar_alpha_v-1) = 2 Valuations ok -- now computing p-adic logarithms. lambda(pi_alpha_v) = 122570416*3^2 + O(3^20) lambda(pibar_alpha_v) = 122570416*3^2 + O(3^20) H_2() NumeratorIdeal() rhotilde(I, 534986635 + O(3^20) , -534986635 + O(3^20) ) 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, generated by -24350762252383107491057132047900200996629554952639/2*sqrtD - 27832994129746749885056217667545035311842495071553 Computing embeddings of canonical power of generator into Qp pi_alpha_v = 747125299 + O(3^20) pibar_alpha_v = 29336698 + O(3^20) pi_alpha_v-1 = 83013922*3^2 + O(3^20) Valuation(pi_alpha_v-1) = 2 pibar_alpha_v-1 = 3259633*3^2 + O(3^20) Valuation(pibar_alpha_v-1) = 2 Valuations ok -- now computing p-adic logarithms. lambda(pi_alpha_v) = 122570416*3^2 + O(3^20) lambda(pibar_alpha_v) = 122570416*3^2 + O(3^20) When m = 3 hts = [* false, false, O(3^14) *] H_2() NumeratorIdeal() rhotilde(I, 534986635 + O(3^20) , -534986635 + O(3^20) ) 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, generated by 35461209571715970561946239670549142804714336449749315690852517107290173203859380424310798482536783904828279944784855587928396249221597803880225138537322428707372831528859537311445855017847951664420039769535325041085697374588689522120814957716655915761286170896299090583164834209896731634075735115479593199726307134794328699496706750955908301647701458008926607554172444242794559360101075333307360192658478380812078042952243933078848328025944722240792047/2*sqrtD - 29214232364130450033602446186160631795052872248971105485336882501072863324722621235740712401972091837295825885776960880938706108069104080258080823589900367879584095452140596581374973915500813891163746021785409141768433388942926502280228150757200508215563733463529469766910090334717653995750819256606940616029203988624099659246880903996695604817148593885944201124054889186060019300244626311034238693591344973387895355121108839955915280391459323742176031 Computing embeddings of canonical power of generator into Qp pi_alpha_v = 939706978 + O(3^20) pibar_alpha_v = -533291135*3^4 + O(3^23) pi_alpha_v-1 = 313235659*3 + O(3^20) Valuation(pi_alpha_v-1) = 1 pibar_alpha_v-1 = -43196581936 + O(3^23) Valuation(pibar_alpha_v-1) = 0 When m = 4 hts = [* false, false, O(3^14), false *] Answer so far = [* <-8, [* false, false, O(3^14), false *]> *] [* <-8, [* false, false, O(3^14), false *]> *] > TestNontrivialityConjecture(Rank2Curve(35),3,4,8); Finding acceptable K for E of conductor 1171 Trying D = -8 -8 is acceptable. Trying D = -7 Trying D = -4 Trying D = -3 Height bound (7.7261) 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, 534986635 + O(3^20) , -534986635 + O(3^20) ) 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 = -1406682737 + O(3^20) pibar_alpha_v = -520717559*3^4 + O(3^23) pi_alpha_v-1 = -156298082*3^2 + O(3^20) Valuation(pi_alpha_v-1) = 2 pibar_alpha_v-1 = -42178122280 + O(3^23) Valuation(pibar_alpha_v-1) = 0 When m = 1 hts = [* false *] H_2() NumeratorIdeal() rhotilde(I, 534986635 + O(3^20) , -534986635 + O(3^20) ) 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 = 94531972*3^4 + O(3^23) pibar_alpha_v = -1481252000 + O(3^20) pi_alpha_v-1 = 7657089731 + O(3^23) Valuation(pi_alpha_v-1) = 0 pibar_alpha_v-1 = -493750667*3 + O(3^20) Valuation(pibar_alpha_v-1) = 1 When m = 2 hts = [* false, false *] H_2() NumeratorIdeal() rhotilde(I, 534986635 + O(3^20) , -534986635 + O(3^20) ) 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 = 747125299 + O(3^20) pibar_alpha_v = 29336698 + O(3^20) pi_alpha_v-1 = 83013922*3^2 + O(3^20) Valuation(pi_alpha_v-1) = 2 pibar_alpha_v-1 = 3259633*3^2 + O(3^20) Valuation(pibar_alpha_v-1) = 2 Valuations ok -- now computing p-adic logarithms. lambda(pi_alpha_v) = 122570416*3^2 + O(3^20) lambda(pibar_alpha_v) = 122570416*3^2 + O(3^20) H_2() NumeratorIdeal() rhotilde(I, 534986635 + O(3^20) , -534986635 + O(3^20) ) 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 = 747125299 + O(3^20) pibar_alpha_v = 29336698 + O(3^20) pi_alpha_v-1 = 83013922*3^2 + O(3^20) Valuation(pi_alpha_v-1) = 2 pibar_alpha_v-1 = 3259633*3^2 + O(3^20) Valuation(pibar_alpha_v-1) = 2 Valuations ok -- now computing p-adic logarithms. lambda(pi_alpha_v) = 122570416*3^2 + O(3^20) lambda(pibar_alpha_v) = 122570416*3^2 + O(3^20) When m = 3 hts = [* false, false, O(3^14) *] H_2() NumeratorIdeal() rhotilde(I, 534986635 + O(3^20) , -534986635 + O(3^20) ) 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 = 939706978 + O(3^20) pibar_alpha_v = -533291135*3^4 + O(3^23) pi_alpha_v-1 = 313235659*3 + O(3^20) Valuation(pi_alpha_v-1) = 1 pibar_alpha_v-1 = -43196581936 + O(3^23) Valuation(pibar_alpha_v-1) = 0 When m = 4 hts = [* false, false, O(3^14), false *] Answer so far = [* <-8, [* false, false, O(3^14), false *]> *] [* <-8, [* false, false, O(3^14), false *]> *] > TestNontrivialityConjecture(Rank2Curve(35),3,4,8); Finding acceptable K for E of conductor 1171 Trying D = -8 -8 is acceptable. Trying D = -7 Trying D = -4 Trying D = -3 Height bound (7.7261) 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, 534986635 + O(3^20) , -534986635 + O(3^20) ) 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 = -1406682737 + O(3^20) pibar_alpha_v = -520717559*3^4 + O(3^23) pi_alpha_v-1 = -156298082*3^2 + O(3^20) Valuation(pi_alpha_v-1) = 2 pibar_alpha_v-1 = -42178122280 + O(3^23) Valuation(pibar_alpha_v-1) = 0 doing something mysterious? When m = 1 hts = [* false *] H_2() NumeratorIdeal() rhotilde(I, 534986635 + O(3^20) , -534986635 + O(3^20) ) 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 = 94531972*3^4 + O(3^23) pibar_alpha_v = -1481252000 + O(3^20) pi_alpha_v-1 = 7657089731 + O(3^23) Valuation(pi_alpha_v-1) = 0 pibar_alpha_v-1 = -493750667*3 + O(3^20) Valuation(pibar_alpha_v-1) = 1 doing something mysterious? When m = 2 hts = [* false, false *] H_2() NumeratorIdeal() rhotilde(I, 534986635 + O(3^20) , -534986635 + O(3^20) ) 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 = 747125299 + O(3^20) pibar_alpha_v = 29336698 + O(3^20) pi_alpha_v-1 = 83013922*3^2 + O(3^20) Valuation(pi_alpha_v-1) = 2 pibar_alpha_v-1 = 3259633*3^2 + O(3^20) Valuation(pibar_alpha_v-1) = 2 doing something mysterious? done. Valuations ok -- now computing p-adic logarithms. lambda(pi_alpha_v) = 122570416*3^2 + O(3^20) lambda(pibar_alpha_v) = 122570416*3^2 + O(3^20) H_2() NumeratorIdeal() rhotilde(I, 534986635 + O(3^20) , -534986635 + O(3^20) ) 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 = 747125299 + O(3^20) pibar_alpha_v = 29336698 + O(3^20) pi_alpha_v-1 = 83013922*3^2 + O(3^20) Valuation(pi_alpha_v-1) = 2 pibar_alpha_v-1 = 3259633*3^2 + O(3^20) Valuation(pibar_alpha_v-1) = 2 doing something mysterious? done. Valuations ok -- now computing p-adic logarithms. lambda(pi_alpha_v) = 122570416*3^2 + O(3^20) lambda(pibar_alpha_v) = 122570416*3^2 + O(3^20) When m = 3 hts = [* false, false, O(3^14) *] H_2() NumeratorIdeal() rhotilde(I, 534986635 + O(3^20) , -534986635 + O(3^20) ) 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 = 939706978 + O(3^20) pibar_alpha_v = -533291135*3^4 + O(3^23) pi_alpha_v-1 = 313235659*3 + O(3^20) Valuation(pi_alpha_v-1) = 1 pibar_alpha_v-1 = -43196581936 + O(3^23) Valuation(pibar_alpha_v-1) = 0 doing something mysterious? [Interrupt twice in half a second; exiting] Total time: 18.539 seconds [was@modular anti-cyclotomic_height_pairing]$ exit exit Process magma finished