Elliptic curves over $\Q$ of conductor 90972

Results (28 matches)

 

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
90972.a1	90972e2	90972.a	90972e	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( 2^{8} \cdot 3^{8} \cdot 7 \cdot 19^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$84$	$12$	$0$	$1$	$1$		$1$	$663552$	$1.697538$	$20720464/63$	$0.91015$	$4.08555$	$[0, 0, 0, -118047, -15569930]$	\(y^2=x^3-118047x-15569930\)	2.3.0.a.1, 12.6.0.c.1, 28.6.0.a.1, 84.12.0.?	$[]$
90972.a2	90972e1	90972.a	90972e	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 2^{4} \cdot 3^{7} \cdot 7^{2} \cdot 19^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$84$	$12$	$0$	$1$	$1$		$1$	$331776$	$1.350965$	$-16384/147$	$1.05520$	$3.46273$	$[0, 0, 0, -4332, -445835]$	\(y^2=x^3-4332x-445835\)	2.3.0.a.1, 6.6.0.a.1, 28.6.0.b.1, 84.12.0.?	$[]$
90972.b1	90972d2	90972.b	90972d	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( 2^{8} \cdot 3^{28} \cdot 7^{4} \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$228$	$12$	$0$	$1$	$1$		$1$	$48660480$	$4.083237$	$2702232642991073488/1431572558302971$	$1.03024$	$6.32704$	$[0, 0, 0, -598635831, -1639269654370]$	\(y^2=x^3-598635831x-1639269654370\)	2.3.0.a.1, 12.6.0.c.1, 76.6.0.?, 228.12.0.?	$[]$
90972.b2	90972d1	90972.b	90972d	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 2^{4} \cdot 3^{17} \cdot 7^{8} \cdot 19^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$228$	$12$	$0$	$1$	$1$		$1$	$24330240$	$3.736660$	$582498235727347712/368659410191667$	$1.09701$	$5.94983$	$[0, 0, 0, 142444824, -200239238491]$	\(y^2=x^3+142444824x-200239238491\)	2.3.0.a.1, 6.6.0.a.1, 76.6.0.?, 228.12.0.?	$[]$
90972.c1	90972j1	90972.c	90972j	$1$	$1$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 2^{8} \cdot 3^{7} \cdot 7^{5} \cdot 19^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$84$	$2$	$0$	$0.111866100$	$1$		$10$	$172800$	$1.195154$	$-2395702096/50421$	$0.88109$	$3.47323$	$[0, 0, 0, -11343, 473366]$	\(y^2=x^3-11343x+473366\)	84.2.0.?	$[(55, 126)]$
90972.d1	90972f1	90972.d	90972f	$1$	$1$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 2^{8} \cdot 3^{7} \cdot 7^{5} \cdot 19^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$84$	$2$	$0$	$1$	$1$		$0$	$3283200$	$2.667374$	$-2395702096/50421$	$0.88109$	$5.02045$	$[0, 0, 0, -4094823, -3246817394]$	\(y^2=x^3-4094823x-3246817394\)	84.2.0.?	$[]$
90972.e1	90972b2	90972.e	90972b	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( 2^{8} \cdot 3^{20} \cdot 7 \cdot 19^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$84$	$12$	$0$	$1$	$1$		$1$	$7741440$	$3.224796$	$895043160898000/12086562663$	$0.95781$	$5.62530$	$[0, 0, 0, -41419335, -101397132002]$	\(y^2=x^3-41419335x-101397132002\)	2.3.0.a.1, 12.6.0.c.1, 28.6.0.a.1, 84.12.0.?	$[]$
90972.e2	90972b1	90972.e	90972b	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 2^{4} \cdot 3^{13} \cdot 7^{2} \cdot 19^{10} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$84$	$12$	$0$	$1$	$1$		$1$	$3870720$	$2.878223$	$-10061824000/13965589323$	$1.09010$	$5.06607$	$[0, 0, 0, -368220, -4212722351]$	\(y^2=x^3-368220x-4212722351\)	2.3.0.a.1, 6.6.0.a.1, 28.6.0.b.1, 84.12.0.?	$[]$
90972.f1	90972a2	90972.f	90972a	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( 2^{8} \cdot 3^{8} \cdot 7^{3} \cdot 19^{10} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$84$	$12$	$0$	$1$	$1$		$1$	$4976640$	$2.840508$	$1367595682000/402300927$	$0.92192$	$5.05745$	$[0, 0, 0, -4770615, -2812231154]$	\(y^2=x^3-4770615x-2812231154\)	2.3.0.a.1, 12.6.0.c.1, 28.6.0.a.1, 84.12.0.?	$[]$
90972.f2	90972a1	90972.f	90972a	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 2^{4} \cdot 3^{7} \cdot 7^{6} \cdot 19^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$84$	$12$	$0$	$1$	$1$		$1$	$2488320$	$2.493935$	$103737344000/127413867$	$0.97321$	$4.59889$	$[0, 0, 0, 801420, -292556927]$	\(y^2=x^3+801420x-292556927\)	2.3.0.a.1, 6.6.0.a.1, 28.6.0.b.1, 84.12.0.?	$[]$
90972.g1	90972i4	90972.g	90972i	$4$	$6$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( 2^{8} \cdot 3^{8} \cdot 7^{3} \cdot 19^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$1596$	$96$	$1$	$6.836520336$	$1$		$1$	$1990656$	$2.436333$	$2640279346000/3087$	$1.02245$	$5.11507$	$[0, 0, 0, -5940255, -5572567114]$	\(y^2=x^3-5940255x-5572567114\)	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.j.1, 28.6.0.a.1, $\ldots$	$[(12065/2, 502873/2)]$
90972.g2	90972i3	90972.g	90972i	$4$	$6$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 2^{4} \cdot 3^{7} \cdot 7^{6} \cdot 19^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$1596$	$96$	$1$	$3.418260168$	$1$		$3$	$995328$	$2.089760$	$-10061824000/352947$	$1.07286$	$4.38960$	$[0, 0, 0, -368220, -88570267]$	\(y^2=x^3-368220x-88570267\)	2.3.0.a.1, 3.4.0.a.1, 6.24.0.b.1, 28.6.0.b.1, 57.8.0-3.a.1.1, $\ldots$	$[(1387, 45486)]$
90972.g3	90972i2	90972.g	90972i	$4$	$6$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( 2^{8} \cdot 3^{12} \cdot 7 \cdot 19^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$1596$	$96$	$1$	$2.278840112$	$1$		$7$	$663552$	$1.887028$	$9826000/5103$	$0.97243$	$4.02021$	$[0, 0, 0, -92055, -3443218]$	\(y^2=x^3-92055x-3443218\)	2.3.0.a.1, 3.4.0.a.1, 6.12.0.a.1, 12.24.0.j.1, 28.6.0.a.1, $\ldots$	$[(323, 722)]$
90972.g4	90972i1	90972.g	90972i	$4$	$6$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 2^{4} \cdot 3^{9} \cdot 7^{2} \cdot 19^{6} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.3.0.1, 3.4.0.1	2B, 3B	$1596$	$96$	$1$	$1.139420056$	$1$		$9$	$331776$	$1.540455$	$2048000/1323$	$1.10843$	$3.64006$	$[0, 0, 0, 21660, -418399]$	\(y^2=x^3+21660x-418399\)	2.3.0.a.1, 3.4.0.a.1, 6.24.0.b.1, 28.6.0.b.1, 57.8.0-3.a.1.2, $\ldots$	$[(190, 3249)]$
90972.h1	90972c2	90972.h	90972c	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( 2^{8} \cdot 3^{8} \cdot 7^{2} \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$228$	$12$	$0$	$1$	$1$		$1$	$2211840$	$2.639694$	$52852623679312/8379$	$0.93884$	$5.37751$	$[0, 0, 0, -16129119, -24932396410]$	\(y^2=x^3-16129119x-24932396410\)	2.3.0.a.1, 12.6.0.c.1, 76.6.0.?, 228.12.0.?	$[]$
90972.h2	90972c1	90972.h	90972c	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 2^{4} \cdot 3^{7} \cdot 7^{4} \cdot 19^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$228$	$12$	$0$	$1$	$1$		$1$	$1105920$	$2.293121$	$-204589760512/2600283$	$1.04305$	$4.65015$	$[0, 0, 0, -1005024, -392039863]$	\(y^2=x^3-1005024x-392039863\)	2.3.0.a.1, 6.6.0.a.1, 76.6.0.?, 228.12.0.?	$[]$
90972.i1	90972l2	90972.i	90972l	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( 2^{8} \cdot 3^{6} \cdot 7 \cdot 19^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$532$	$12$	$0$	$4.549945427$	$1$		$3$	$691200$	$1.853148$	$12869712/2527$	$1.01837$	$4.04385$	$[0, 0, 0, -100719, 10000422]$	\(y^2=x^3-100719x+10000422\)	2.3.0.a.1, 28.6.0.a.1, 76.6.0.?, 532.12.0.?	$[(66, 1908)]$
90972.i2	90972l1	90972.i	90972l	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 2^{4} \cdot 3^{6} \cdot 7^{2} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$532$	$12$	$0$	$9.099890855$	$1$		$1$	$345600$	$1.506575$	$442368/931$	$0.82449$	$3.59075$	$[0, 0, 0, 12996, 925965]$	\(y^2=x^3+12996x+925965\)	2.3.0.a.1, 28.6.0.b.1, 38.6.0.b.1, 532.12.0.?	$[(21633/8, 3393855/8)]$
90972.j1	90972k2	90972.j	90972k	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( 2^{8} \cdot 3^{16} \cdot 7^{2} \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$228$	$12$	$0$	$2.366670298$	$1$		$5$	$5529600$	$2.884102$	$50338425969232/54974619$	$0.93852$	$5.37324$	$[0, 0, 0, -15869199, 24309187670]$	\(y^2=x^3-15869199x+24309187670\)	2.3.0.a.1, 12.6.0.c.1, 76.6.0.?, 228.12.0.?	$[(55, 153090)]$
90972.j2	90972k1	90972.j	90972k	$2$	$2$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 2^{4} \cdot 3^{11} \cdot 7^{4} \cdot 19^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$228$	$12$	$0$	$1.183335149$	$1$		$7$	$2764800$	$2.537529$	$-83369132032/210622923$	$1.04089$	$4.71676$	$[0, 0, 0, -745104, 573432977]$	\(y^2=x^3-745104x+573432977\)	2.3.0.a.1, 6.6.0.a.1, 76.6.0.?, 228.12.0.?	$[(76, 22743)]$
90972.k1	90972h2	90972.k	90972h	$2$	$3$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 2^{8} \cdot 3^{9} \cdot 7^{3} \cdot 19^{4} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.1	3B.1.1	$84$	$16$	$0$	$1$	$1$		$2$	$1679616$	$2.234310$	$-203262147053008/9261$	$1.01037$	$4.97973$	$[0, 0, 0, -3548991, 2573389222]$	\(y^2=x^3-3548991x+2573389222\)	3.8.0-3.a.1.2, 84.16.0.?	$[]$
90972.k2	90972h1	90972.k	90972h	$2$	$3$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 2^{8} \cdot 3^{15} \cdot 7 \cdot 19^{4} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.8.0.2	3B.1.2	$84$	$16$	$0$	$1$	$1$		$0$	$559872$	$1.685005$	$-292571728/137781$	$0.91375$	$3.85383$	$[0, 0, 0, -40071, 4157998]$	\(y^2=x^3-40071x+4157998\)	3.8.0-3.a.1.1, 84.16.0.?	$[]$
90972.l1	90972n2	90972.l	90972n	$2$	$3$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 2^{8} \cdot 3^{9} \cdot 7^{3} \cdot 19^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1596$	$16$	$0$	$58.48433533$	$1$		$0$	$31912704$	$3.706532$	$-203262147053008/9261$	$1.01037$	$6.52695$	$[0, 0, 0, -1281185751, -17650876673698]$	\(y^2=x^3-1281185751x-17650876673698\)	3.4.0.a.1, 57.8.0-3.a.1.1, 84.8.0.?, 1596.16.0.?	$[(127495914857798322653204542/46170203423, 1076678614447573246864537544236574226162/46170203423)]$
90972.l2	90972n1	90972.l	90972n	$2$	$3$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( - 2^{8} \cdot 3^{15} \cdot 7 \cdot 19^{10} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$1596$	$16$	$0$	$19.49477844$	$1$		$0$	$10637568$	$3.157227$	$-292571728/137781$	$0.91375$	$5.40105$	$[0, 0, 0, -14465631, -28519708282]$	\(y^2=x^3-14465631x-28519708282\)	3.4.0.a.1, 57.8.0-3.a.1.2, 84.8.0.?, 1596.16.0.?	$[(17524197007/1921, 704496898056762/1921)]$
90972.m1	90972m2	90972.m	90972m	$2$	$3$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( 2^{4} \cdot 3^{6} \cdot 7^{6} \cdot 19^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.2.0.1, 3.4.0.1	2Cn, 3B	$1596$	$96$	$2$	$2.496519936$	$1$		$2$	$116640$	$0.995531$	$1892178688/117649$	$0.88140$	$3.20662$	$[0, 0, 0, -4161, -97603]$	\(y^2=x^3-4161x-97603\)	2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 38.6.0.a.1, 57.8.0-3.a.1.1, $\ldots$	$[(188, 2401)]$
90972.m2	90972m1	90972.m	90972m	$2$	$3$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( 2^{4} \cdot 3^{6} \cdot 7^{2} \cdot 19^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.2.0.1, 3.4.0.1	2Cn, 3B	$1596$	$96$	$2$	$0.832173312$	$1$		$4$	$38880$	$0.446225$	$10686208/49$	$0.78826$	$2.75326$	$[0, 0, 0, -741, 7733]$	\(y^2=x^3-741x+7733\)	2.2.0.a.1, 3.4.0.a.1, 6.8.0.a.1, 38.6.0.a.1, 57.8.0-3.a.1.2, $\ldots$	$[(17, 7)]$
90972.n1	90972g2	90972.n	90972g	$2$	$3$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( 2^{4} \cdot 3^{6} \cdot 7^{6} \cdot 19^{8} \)	$0$	$\Z/3\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.2.0.1, 3.8.0.1	2Cn, 3B.1.1	$1596$	$96$	$2$	$1$	$4$	$2$	$2$	$2216160$	$2.467751$	$1892178688/117649$	$0.88140$	$4.75384$	$[0, 0, 0, -1502121, 669458977]$	\(y^2=x^3-1502121x+669458977\)	2.2.0.a.1, 3.8.0-3.a.1.2, 6.16.0-6.a.1.2, 38.6.0.a.1, 84.32.0.?, $\ldots$	$[]$
90972.n2	90972g1	90972.n	90972g	$2$	$3$	\( 2^{2} \cdot 3^{2} \cdot 7 \cdot 19^{2} \)	\( 2^{4} \cdot 3^{6} \cdot 7^{2} \cdot 19^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	2.2.0.1, 3.8.0.2	2Cn, 3B.1.2	$1596$	$96$	$2$	$1$	$4$	$2$	$0$	$738720$	$1.918444$	$10686208/49$	$0.78826$	$4.30048$	$[0, 0, 0, -267501, -53040647]$	\(y^2=x^3-267501x-53040647\)	2.2.0.a.1, 3.8.0-3.a.1.1, 6.16.0-6.a.1.1, 38.6.0.a.1, 84.32.0.?, $\ldots$	$[]$