Sage Reference Manual
Search.setIndex({envversion:42,terms:{bmss:[26,30],upper_triangular_matrix:34,orthogon:59,compute_wp_pari:26,parallelogram:[64,9],bound_kato:55,diedonn:47,ellipticcurve_from_cub:[13,8],four:[59,46,41,55],secondli:48,short_weierstrass_model:[30,17,59,70,26,11],grigorov:[59,20,55],scalar_multipli:31,andreytimofeev:33,sci:[59,47,55],consider:59,disappear:59,whose:[30,11,31,60,14,70,4,41,59,20,21,63,64,24,25,26,47,48,22],typeerror:[28,31,1,13,17,25,24,46,11,66],mult_by_n:45,simon_two_desc:[59,41,64,18],aug:24,"7690e1":59,sorri:34,tobia:[24,59],messi:31,under:[64,31,41,19,59,20,25,24,55,11],aux:59,spec:[62,43],"39a2":59,digit:[31,14,59,20,25,55],everi:[30,4,59,41,55,70,9,22],risk:59,"37b1":[59,61],"37b2":[13,59],"37b3":59,count_points_matrix_trac:63,arithmetic_genu:44,sage_object:[37,28,56,38,19,65,61,20,25,70,45,55,47],prime_to_2_conductor_onli:56,affect:[46,41],manin:[59,20,55],isogenies_5_1728:49,two_desc:59,schoof:4,isom1:30,isom2:30,"_ensure_ful":9,vector:[34,47,25,41,64],matric:[34,25,32,70],verif:[59,55,25],galois_represent:[59,37,41,55,61],j_invari:[13,14,4,17,59,41,24,11,49],ellan:59,repres:[0,31,13,3,56,70,4,16,59,5,61,41,25,64,44,9,22,60],vladimir:41,miller:24,naiv:[0,31,59,25,63,24],ngen:[59,42],direct:[59,47,25,8],"92b1":25,"10e":25,brill:[44,0],consequ:[13,52],second:[30,12,54,34,56,4,41,18,59,20,25,67,24,55,47,49],is_singular:[44,52,62],absprec:24,ellap:4,even:[11,31,13,14,56,4,59,41,25,63,48,47,53,22,62],usesunit:59,post_resc:[13,8],neg:[11,31,33,55,4,38,59,65,19,41,25,64,24,44,47,22],biject:[61,19],thotsaphon:9,isocls2:[59,70],steinet:59,"new":[29,28,31,13,59,52,70,11,22],symmetr:[65,34,30,61,22],s_integral_x_coords_with_abs_bounded_bi:59,ever:[59,25],"60490d1":22,"27a":59,elimin:[30,31],ell_wp:26,heegner_divisor:25,rigour:59,sha_an:59,never:[13,21],here:[4,25,8,47,12,13,14,55,24,21,30,31,34,70,38,41,19,49,56,59,61,67,65],accur:31,root_numb:59,congruence_numb:59,create_el:31,interpret:[59,56,4],cdef:21,period_lattic:[64,59,41,25,24,22],precis:[0,3,47,13,14,17,20,25,24,44,26,27,30,31,33,34,35,55,19,41,45,46,11,22,52,58,59,63,64,70],galoi:[],fraction_field:[11,12],permit:11,qp_solubl:21,fourier:[59,20],adiqu:[47,55],"837774351482055e":20,xset:59,unif:[35,42],linearli:[24,60,41],residue_field:[52,4],cps_height_bound:59,total:[24,59,35,31],unit:[11,14,59,41,25,48,47,62],highli:[62,63],plot:[0,4,59,41,25,24,44,11,9],describ:[11,31,14,56,58,59,61,55,26,47],would:[64,31,33,13,67,59,25,22,70,55,11,49,63],num_bound:34,conjugaci:[61,4],init:18,elliptic_logarithm:[24,59,64],program:[59,56,20,63],call:[28,1,4,5,6,11,12,13,14,67,17,20,21,24,25,26,30,31,33,34,35,55,41,44,46,47,66,49,37,52,56,57,59,61,62,63,64,65,69],typo:46,recommend:59,type:[],until:[59,31,4],relat:[],"4602a1":24,notic:25,warn:[13,4,59,60,65,48],berlin:[59,28],exce:[59,41],silbook:24,cremona_optimal_curv:[39,59],max_denomin:59,hold:[2,14,56,38,59,41,34,67,9],esh:[26,17],must:[28,1,3,4,6,47,13,14,17,25,22,24,55,26,29,30,31,32,33,35,41,46,11,66,49,64,56,57,58,59,63],springer:[28,60,19,59,41,24],complex_embed:[64,22],join:[13,59,22,70],insignific:25,err:[20,22],restor:[24,4],generalis:64,work:[0,3,4,25,13,14,21,55,24,44,30,31,33,19,41,45,46,11,49,64,59,61,63],zeros_in_interv:20,wors:[59,25],introduc:[24,22],rework:59,hansen:24,root:[41,30,11,31,33,60,35,4,17,58,59,20,25,70,24,55,47,22,62],pierr:[61,63,19],patriki:[59,20,55],give:[0,3,4,13,14,17,25,49,24,55,30,32,33,34,35,70,38,41,47,22,59,61,63,67,65],gebel:59,cartan:61,want:[13,31,56,25,59],boothbi:45,keep:[31,9],unsign:21,"53a1":55,new_point:41,recov:[4,63],isomorphism_to:[24,30,11],end:[24,20,31],eng:33,ordinari:[31,14,56,4,59,61,55,47],hom:[24,34,11,67],classifi:5,revisit:[24,14,59],two_selmer_bound:55,how:[30,28,31,56,4,19,59,64,25,24,22],division_polynomi:[30,17,59,41,11,49],affinecurve_gener:0,min_psi:59,answer:[0,31,33,14,59,65,61,25,67,45,47],verifi:[0,31,13,14,59,25,45,55,11,9,69],ring_class_field:25,teichm:35,updat:58,"42767548272846e17":59,"059997738340522e":20,psi2:49,wp_c:22,after:[64,31,14,56,17,59,41,63,8,65,22],secondlim:59,befor:[12,67,59,20,55,63,45,49],wrong:[13,34,55,33],adic:[],has_additive_reduct:[28,41],heegner_conductor:25,law:45,i_2:56,demonstr:[2,28,60,59,25,24,21],i_0:56,ellipticcurve_number_field:[59,41],attempt:[59,22],third:[30,41],interpol:[59,14,35,47],classmethod:22,think:59,"36a1":59,"36a2":59,"36a3":59,"36a4":59,incorpor:31,ueberschiebung:[],morain:[26,30],unramifi:[56,25,61],order:[0,4,47,13,17,20,55,39,25,48,30,32,33,34,24,41,42,44,11,22,54,56,59,60,61,70],oper:[31,60,65,17,5,25,24,11],composit:[30,52,13,4,41,24],is_squar:[21,49],bad_prim:[59,41],becaus:[52,31,54,34,35,4,59,25,63,65,55,11],"990l1":59,non_surject:[59,37,41,55,61],padic_squar:21,keyboard:21,steinwuthrich:59,is_perfect_pow:17,vari:[59,37,41,31,61],is_quartic_twist:17,imb:63,fit:[59,4],"37a":[11,3,64,59,45,61,20,25,14,24,55,47,22],fix:[30,64,13,14,35,4,17,18,59,45,61,41,25,24,44,26,11,53,65],"37b":[64,14,59,61,20,25,47],leprevost:35,modp_dual_elliptic_curve_factor:25,better:[31,14,59,34,65,22],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xmap2:30,xmap1:30,gens_certain:59,phi_ker_poli:30,lang:60,agm:64,uller:35,"1450c1":49,algorithm:[],monic:[30,31,60,58,17,25],descend_to:17,confirm:25,"128b1":[13,48],"128b2":[13,48],discrimin:[28,33,14,56,55,41,59,20,21,11,64,24,25,70,47,22,62],get_pre_isomorph:30,len_:59,ellwp:26,oop:[59,14],code:[30,28,31,33,14,56,38,17,58,59,45,41,25,37,24,42,26,11,46,49],partial:[59,17],edg:[59,41,25,70],cdf:[3,64,9,22],p07:59,p_list:30,edu:[59,5,46,38],compact:59,"s\u00e9r":[47,55],privat:[24,4],simon:[],dieudonn:47,elsewher:59,lawsonwuthrich:59,send:[30,13,3,67,59,25,34,8,65,69],carefulli:[59,48],switch_sign:30,weierstrassisomorph:[30,11,16],adjoin:[11,17],test_mu:22,opposit:[9,8],sens:[30,31,14,35,41,59,20,25,45,26],pgl_2:61,"54658247036311e":20,fly:49,"3364c1":55,"121b2":[13,48],ellipticcurve_from_weierstrass_polynomi:13,isogenies_prime_degre:[30,17,59,41,70,49],hamish:45,padiclseriesordinari:[59,14,47],uniquefactori:13,"55318e":20,galois_group_over_quadratic_field:25,commutativealgebrael:31,bernardi:[47,55],volum:[59,46,64],implicitli:30,x_onli:11,relev:[59,48,63,69],conjug:[64,25],tri:[24,54,46,31,59],analytic_rank_upper_bound:59,meant:62,image_class:61,eta:[24,47],michael:[24,59],newform:59,"try":[30,64,31,14,55,4,17,59,41,21,37,25,48,22],read_cach:[54,34,12,67],appar:59,mpz_t:21,ellipticcurvepoint_number_field:24,defining_polynomi:[2,52,12,13,3,67,59,54,6,34,8,69],pleas:4,impli:[59,55,31],smaller:[60,41,59,61,20,25,63,24],set_post_isomorph:30,hyperellipticcurve_finite_field:[68,4,63],elist:[13,48],natur:[29,34,59,61,11,9],"0x0":41,compute_isogeny_stark:30,max_it:22,"990a1":59,blanklin:[56,41],show_graph:59,optimal_embed:25,"64a4":[13,48],velu:[30,17],odd:[30,52,14,35,58,41,59,20,25,63,55,53,56,49],"64a3":[13,48],"64a2":[13,48],compat:[37,31,56,59,61,41,25],index:[10,28,33,56,59,41,25,70,55],is_quarticcurv:15,compar:[0,31,14,59,61,65,47,22],ramanujan:31,slight:45,urst:[11,16],find:[0,4,47,12,13,67,17,25,24,55,48,2,30,31,33,34,35,41,11,52,59,60,61],access:[30,28],experiment:48,tate_pair:24,superingular:47,left_ord:25,fill_isogeny_matrix:30,deduc:[24,41,22],can:[28,4,5,47,13,14,17,66,20,25,49,24,55,26,30,31,33,34,70,19,41,11,48,22,52,56,59,61,62,63,64,65,69],max_pow_i:31,"ast\u00e9risqu":[59,55],"enum":[44,0],led:[59,14],chose:25,iteritem:25,got:[59,14,25],endian:[30,17],len:[30,0,12,33,13,34,4,59,41,21,63,44,24,25,48,11,49],semist:[61,20],closur:[56,19,59,6,41,63,46],"n\u00e9ron":24,let:[28,31,14,56,45,19,59,5,61,64,21,24,26,46],"648a1":61,vertic:[59,70],sinc:[28,31,33,13,17,59,41,25,63,70,24,55,11,22],l_invari:[59,19],convert:[59,5,56,11],convers:[59,38],"67090854562318e6":22,genu:[],genr:[5,46,56],herrmann:59,nontors:59,converg:[59,14],rdf:29,"794a1":24,earli:25,typic:28,coercibl:[56,31],abcd:64,see:[28,4,6,0,8,11,12,13,14,17,20,25,22,39,55,26,30,31,34,70,37,19,24,41,46,47,49,51,64,54,56,59,60,61,62,67,65,69],clark:[45,52],appli:[30,31,12,60,14,67,59,5,41,25,8,11],approxim:[30,64,33,3,59,20,25,14,47,9,22],jacobian_generic_with_categori:1,"boolean":[12,13,14,70,4,59,61,41,22,67,24,44,46,11,9,49],w1w2:64,"990h3":59,rank_bound:[59,41],riemann_roch_basi:[44,0],emod:4,k96:30,"990h4":59,cha:59,hasse_invari:17,from:[28,1,3,4,5,6,8,9,12,13,14,15,16,17,20,21,22,24,25,26,29,30,31,32,33,34,35,55,19,40,41,42,45,46,11,48,49,52,56,58,59,61,63,64,65,67,69,70],zip:64,projectiveconic_rational_field:67,doubl:[29,64,33,56,59,45,62,24],check_prim:28,next:[64,13,14,4,59,60,25,24,44],websit:56,few:[59,34,20,25,55],nonneg_region:22,hyperellipticcurve_from_invari:46,isogenies_prime_degree_genus_plus_0_j1728:49,simpler:41,commut:[13,31],pencil:[56,28],projectivecurve_finite_field:[54,44],babi:4,lim3:[59,64,41,22,18],zimmer:59,lim1:[59,41,64,18],is_ident:16,qflllgram:41,castiglioncello:[5,46],tamagawa:[28,59,47,41],iii:[56,4,38,41,55,47],balakrishnan:[59,14,35,52,31],account:[41,4,49],q_expans:[59,3],retriev:31,affinecurve_finite_field:0,alia:[47,31],"389a":[11,13,14,4,41,59,20,25,64,24,55,47,22],isogeny_graph:59,cambridg:[24,65],is_cm_j_invari:33,reduce_neg_y_fast:31,counterexampl:[59,61],squarefre:[20,25,17],ellipticcurve_from_plane_curv:13,proof:[28,31,33,13,55,4,41,59,20,21,24,25,48,22],control:[13,59,28,25,41],tau:[3,64,25,22],complex_intersection_is_empti:22,high:[39,31,21],tab:[59,55],locu:32,xmin:[59,11],max_prim:59,uncondition:59,bigf2:54,tamagawa_number_old:59,surfac:[],gcd:[24,30,25,17],sit:25,halv:9,six:41,cardin:[24,44,25,4,63],ellipticcurvecanonicalheight:[41,22],periodlattic:64,instead:[64,31,13,14,56,45,4,41,18,59,39,61,20,55,63,70,24,22],kolyvagin_cyclic_subid:25,sil:41,everywher:[41,22],map_to_complex_numb:[3,25],frac:[11,17],ta2:41,singular:[62,28,54,34,56,59,6,0,63,44,52],hyperellipticjacobian_gener:[2,1],womack:59,inst:59,color_by_label:41,domain_gen:25,redund:[59,14],isogenies_13_0:49,coeffient:[26,63],"2x2":[64,31],essenti:59,villega:56,seriou:4,"492262044273650e":20,correspond:[30,11,31,34,56,38,19,59,20,25,70,44,46,47,49],element:[28,1,4,47,13,14,17,55,49,24,25,48,30,31,33,19,41,44,11,22,52,56,59,60,61,63,64],iss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