Elliptic curve search results

Results (26 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
3192.p1	3192g1	3192.p	3192g	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7 \cdot 19 \)	\( 2^{10} \cdot 3^{7} \cdot 7^{10} \cdot 19^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1.961188581$	$1$		$5$	$94080$	$2.550579$	$13141891860831409148932/4237307541832617$	$1.03284$	$7.17138$	$[0, 1, 0, -4955392, -4246324048]$	\(y^2=x^3+x^2-4955392x-4246324048\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(-1276, 912)]$
6384.o1	6384d1	6384.o	6384d	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7 \cdot 19 \)	\( 2^{10} \cdot 3^{7} \cdot 7^{10} \cdot 19^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$188160$	$2.550579$	$13141891860831409148932/4237307541832617$	$1.03284$	$6.60403$	$[0, -1, 0, -4955392, 4246324048]$	\(y^2=x^3-x^2-4955392x+4246324048\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[ ]$
9576.f1	9576x1	9576.f	9576x	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( 2^{10} \cdot 3^{13} \cdot 7^{10} \cdot 19^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$752640$	$3.099884$	$13141891860831409148932/4237307541832617$	$1.03284$	$7.03099$	$[0, 0, 0, -44598531, 114606150766]$	\(y^2=x^3-44598531x+114606150766\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[ ]$
19152.g1	19152x1	19152.g	19152x	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( 2^{10} \cdot 3^{13} \cdot 7^{10} \cdot 19^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$3.200742333$	$1$		$5$	$1505280$	$3.099884$	$13141891860831409148932/4237307541832617$	$1.03284$	$6.53673$	$[0, 0, 0, -44598531, -114606150766]$	\(y^2=x^3-44598531x-114606150766\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(-3901, 2842)]$
22344.f1	22344d1	22344.f	22344d	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{7} \cdot 7^{16} \cdot 19^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$4515840$	$3.523533$	$13141891860831409148932/4237307541832617$	$1.03284$	$6.94376$	$[0, -1, 0, -242814224, 1456003520028]$	\(y^2=x^3-x^2-242814224x+1456003520028\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[ ]$
25536.l1	25536d1	25536.l	25536d	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19 \)	\( 2^{16} \cdot 3^{7} \cdot 7^{10} \cdot 19^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$28.24386061$	$1$		$1$	$1505280$	$2.897152$	$13141891860831409148932/4237307541832617$	$1.03284$	$6.11169$	$[0, -1, 0, -19821569, -33950770815]$	\(y^2=x^3-x^2-19821569x-33950770815\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(-36146319240767/119299, 2620260993124267616/119299)]$
25536.cg1	25536dr1	25536.cg	25536dr	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19 \)	\( 2^{16} \cdot 3^{7} \cdot 7^{10} \cdot 19^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$0.152463349$	$1$		$13$	$1505280$	$2.897152$	$13141891860831409148932/4237307541832617$	$1.03284$	$6.11169$	$[0, 1, 0, -19821569, 33950770815]$	\(y^2=x^3+x^2-19821569x+33950770815\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(2437, 11172)]$
44688.co1	44688bh1	44688.co	44688bh	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{7} \cdot 7^{16} \cdot 19^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$9031680$	$3.523533$	$13141891860831409148932/4237307541832617$	$1.03284$	$6.49426$	$[0, 1, 0, -242814224, -1456003520028]$	\(y^2=x^3+x^2-242814224x-1456003520028\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[ ]$
60648.q1	60648w1	60648.q	60648w	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( 2^{10} \cdot 3^{7} \cdot 7^{10} \cdot 19^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$44.57162070$	$1$		$1$	$33868800$	$4.022797$	$13141891860831409148932/4237307541832617$	$1.03284$	$6.85819$	$[0, -1, 0, -1788896632, 29114803265692]$	\(y^2=x^3-x^2-1788896632x+29114803265692\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(1611949548864675056718/287677121, 30675876017366573476425156950432/287677121)]$
67032.ck1	67032cf1	67032.ck	67032cf	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 7^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{13} \cdot 7^{16} \cdot 19^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$49$	$7$	$1$	$36126720$	$4.072838$	$13141891860831409148932/4237307541832617$	$1.03284$	$6.85046$	$[0, 0, 0, -2185328019, -39309909712738]$	\(y^2=x^3-2185328019x-39309909712738\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[ ]$
76608.eb1	76608bf1	76608.eb	76608bf	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( 2^{16} \cdot 3^{13} \cdot 7^{10} \cdot 19^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$4$	$2$	$1$	$12042240$	$3.446457$	$13141891860831409148932/4237307541832617$	$1.03284$	$6.10078$	$[0, 0, 0, -178394124, 916849206128]$	\(y^2=x^3-178394124x+916849206128\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[ ]$
76608.ff1	76608fn1	76608.ff	76608fn	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 7 \cdot 19 \)	\( 2^{16} \cdot 3^{13} \cdot 7^{10} \cdot 19^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1.845469085$	$1$		$3$	$12042240$	$3.446457$	$13141891860831409148932/4237307541832617$	$1.03284$	$6.10078$	$[0, 0, 0, -178394124, -916849206128]$	\(y^2=x^3-178394124x-916849206128\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(109994, 36197280)]$
79800.o1	79800bj1	79800.o	79800bj	$2$	$2$	\( 2^{3} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{10} \cdot 3^{7} \cdot 5^{6} \cdot 7^{10} \cdot 19^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$12042240$	$3.355297$	$13141891860831409148932/4237307541832617$	$1.03284$	$5.98180$	$[0, -1, 0, -123884808, -530542736388]$	\(y^2=x^3-x^2-123884808x-530542736388\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[ ]$
121296.dj1	121296bn1	121296.dj	121296bn	$2$	$2$	\( 2^{4} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( 2^{10} \cdot 3^{7} \cdot 7^{10} \cdot 19^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$67737600$	$4.022797$	$13141891860831409148932/4237307541832617$	$1.03284$	$6.45210$	$[0, 1, 0, -1788896632, -29114803265692]$	\(y^2=x^3+x^2-1788896632x-29114803265692\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[ ]$
134064.eo1	134064ew1	134064.eo	134064ew	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 7^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{13} \cdot 7^{16} \cdot 19^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$72253440$	$4.072838$	$13141891860831409148932/4237307541832617$	$1.03284$	$6.44827$	$[0, 0, 0, -2185328019, 39309909712738]$	\(y^2=x^3-2185328019x+39309909712738\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[ ]$
159600.fl1	159600gc1	159600.fl	159600gc	$2$	$2$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{10} \cdot 3^{7} \cdot 5^{6} \cdot 7^{10} \cdot 19^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$24084480$	$3.355297$	$13141891860831409148932/4237307541832617$	$1.03284$	$5.63571$	$[0, 1, 0, -123884808, 530542736388]$	\(y^2=x^3+x^2-123884808x+530542736388\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[ ]$
178752.dv1	178752et1	178752.dv	178752et	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( 2^{16} \cdot 3^{7} \cdot 7^{16} \cdot 19^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$49.75336035$	$1$		$1$	$72253440$	$3.870106$	$13141891860831409148932/4237307541832617$	$1.03284$	$6.09372$	$[0, -1, 0, -971256897, -11647056903327]$	\(y^2=x^3-x^2-971256897x-11647056903327\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(107442725548368459323581/1716113199, 6138286213795994381930855950269536/1716113199)]$
178752.jw1	178752ho1	178752.jw	178752ho	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7^{2} \cdot 19 \)	\( 2^{16} \cdot 3^{7} \cdot 7^{16} \cdot 19^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$72253440$	$3.870106$	$13141891860831409148932/4237307541832617$	$1.03284$	$6.09372$	$[0, 1, 0, -971256897, 11647056903327]$	\(y^2=x^3+x^2-971256897x+11647056903327\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[ ]$
181944.k1	181944bl1	181944.k	181944bl	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( 2^{10} \cdot 3^{13} \cdot 7^{10} \cdot 19^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$123.0678774$	$1$		$1$	$270950400$	$4.572105$	$13141891860831409148932/4237307541832617$	$1.03284$	$6.78035$	$[0, 0, 0, -16100069691, -786083588103994]$	\(y^2=x^3-16100069691x-786083588103994\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(-52349475079543077515042197444732721219050169209851222505/26834846199102997921979377, 7485731553020220096118521945299972122854961790893667853091987750987805825196441392/26834846199102997921979377)]$
239400.ep1	239400ep1	239400.ep	239400ep	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{10} \cdot 3^{13} \cdot 5^{6} \cdot 7^{10} \cdot 19^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$96337920$	$3.904602$	$13141891860831409148932/4237307541832617$	$1.03284$	$5.98341$	$[0, 0, 0, -1114963275, 14325768845750]$	\(y^2=x^3-1114963275x+14325768845750\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[ ]$
363888.n1	363888n1	363888.n	363888n	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( 2^{10} \cdot 3^{13} \cdot 7^{10} \cdot 19^{9} \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$2.547567791$	$1$		$17$	$541900800$	$4.572105$	$13141891860831409148932/4237307541832617$	$1.03284$	$6.41331$	$[0, 0, 0, -16100069691, 786083588103994]$	\(y^2=x^3-16100069691x+786083588103994\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(77045, 1728468), (74315, 166698)]$
386232.cc1	386232cc1	386232.cc	386232cc	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7 \cdot 11^{2} \cdot 19 \)	\( 2^{10} \cdot 3^{7} \cdot 7^{10} \cdot 11^{6} \cdot 19^{3} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$2.787421663$	$1$		$5$	$101606400$	$3.749527$	$13141891860831409148932/4237307541832617$	$1.03284$	$5.61628$	$[0, 1, 0, -599602472, 5649458898048]$	\(y^2=x^3+x^2-599602472x+5649458898048\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(13552, 112896)]$
424536.cs1	424536cs1	424536.cs	424536cs	$2$	$2$	\( 2^{3} \cdot 3 \cdot 7^{2} \cdot 19^{2} \)	\( 2^{10} \cdot 3^{7} \cdot 7^{16} \cdot 19^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$10.42184510$	$1$		$1$	$1625702400$	$4.995750$	$13141891860831409148932/4237307541832617$	$1.03284$	$6.72933$	$[0, 1, 0, -87655934984, -9986202208262400]$	\(y^2=x^3+x^2-87655934984x-9986202208262400\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(-378158072/47, 172164302064/47)]$
478800.f1	478800f1	478800.f	478800f	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{10} \cdot 3^{13} \cdot 5^{6} \cdot 7^{10} \cdot 19^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$192675840$	$3.904602$	$13141891860831409148932/4237307541832617$	$1.03284$	$5.66631$	$[0, 0, 0, -1114963275, -14325768845750]$	\(y^2=x^3-1114963275x-14325768845750\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[ ]$
485184.s1	485184s1	485184.s	485184s	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( 2^{16} \cdot 3^{7} \cdot 7^{10} \cdot 19^{9} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$1$	$1$		$1$	$541900800$	$4.369370$	$13141891860831409148932/4237307541832617$	$1.03284$	$6.08657$	$[0, -1, 0, -7155586529, -232911270539007]$	\(y^2=x^3-x^2-7155586529x-232911270539007\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[ ]$
485184.fo1	485184fo1	485184.fo	485184fo	$2$	$2$	\( 2^{6} \cdot 3 \cdot 7 \cdot 19^{2} \)	\( 2^{16} \cdot 3^{7} \cdot 7^{10} \cdot 19^{9} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$3192$	$12$	$0$	$4.143565411$	$1$		$5$	$541900800$	$4.369370$	$13141891860831409148932/4237307541832617$	$1.03284$	$6.08657$	$[0, 1, 0, -7155586529, 232911270539007]$	\(y^2=x^3+x^2-7155586529x+232911270539007\)	2.3.0.a.1, 56.6.0.c.1, 114.6.0.?, 3192.12.0.?	$[(36619, 4470624)]$

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