Elliptic curves over $\Q$ of conductor 120213

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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
120213.a1	120213l1	120213.a	120213l	$1$	$1$	\( 3^{2} \cdot 19^{2} \cdot 37 \)	\( 3^{6} \cdot 19^{6} \cdot 37 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$74$	$2$	$0$	$1$	$1$		$0$	$201600$	$1.024984$	$110592/37$	$0.76978$	$3.06676$	$[0, 0, 1, -3249, 46298]$	\(y^2+y=x^3-3249x+46298\)	74.2.0.?	$[ ]$
120213.b1	120213i1	120213.b	120213i	$1$	$1$	\( 3^{2} \cdot 19^{2} \cdot 37 \)	\( - 3^{6} \cdot 19^{7} \cdot 37^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$38$	$2$	$0$	$2.643687366$	$1$		$2$	$645120$	$1.547915$	$110592/26011$	$0.86293$	$3.58013$	$[0, 0, 1, 3249, -1435246]$	\(y^2+y=x^3+3249x-1435246\)	38.2.0.a.1	$[(177, 2164)]$
120213.c1	120213d2	120213.c	120213d	$2$	$2$	\( 3^{2} \cdot 19^{2} \cdot 37 \)	\( 3^{9} \cdot 19^{6} \cdot 37^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$444$	$12$	$0$	$3.448884348$	$1$		$2$	$628992$	$1.626350$	$10503459/1369$	$0.93244$	$3.73782$	$[1, -1, 1, -44471, -3166100]$	\(y^2+xy+y=x^3-x^2-44471x-3166100\)	2.3.0.a.1, 12.6.0.a.1, 148.6.0.?, 444.12.0.?	$[(-146, 518)]$
120213.c2	120213d1	120213.c	120213d	$2$	$2$	\( 3^{2} \cdot 19^{2} \cdot 37 \)	\( - 3^{9} \cdot 19^{6} \cdot 37 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$444$	$12$	$0$	$6.897768696$	$1$		$1$	$314496$	$1.279778$	$9261/37$	$0.86736$	$3.28830$	$[1, -1, 1, 4264, -261494]$	\(y^2+xy+y=x^3-x^2+4264x-261494\)	2.3.0.a.1, 12.6.0.b.1, 148.6.0.?, 222.6.0.?, 444.12.0.?	$[(508/3, 9911/3)]$
120213.d1	120213b1	120213.d	120213b	$2$	$2$	\( 3^{2} \cdot 19^{2} \cdot 37 \)	\( 3^{9} \cdot 19^{7} \cdot 37^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$228$	$12$	$0$	$1$	$1$		$1$	$1520640$	$2.412590$	$17565861949875/26011$	$1.01226$	$4.96290$	$[1, -1, 1, -5278610, -4666637744]$	\(y^2+xy+y=x^3-x^2-5278610x-4666637744\)	2.3.0.a.1, 12.6.0.c.1, 76.6.0.?, 114.6.0.?, 228.12.0.?	$[ ]$
120213.d2	120213b2	120213.d	120213b	$2$	$2$	\( 3^{2} \cdot 19^{2} \cdot 37 \)	\( - 3^{9} \cdot 19^{8} \cdot 37^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$228$	$12$	$0$	$1$	$1$		$0$	$3041280$	$2.759163$	$-17083807243875/676572121$	$0.94492$	$4.96618$	$[1, -1, 1, -5229875, -4757070410]$	\(y^2+xy+y=x^3-x^2-5229875x-4757070410\)	2.3.0.a.1, 6.6.0.a.1, 76.6.0.?, 228.12.0.?	$[ ]$
120213.e1	120213f1	120213.e	120213f	$1$	$1$	\( 3^{2} \cdot 19^{2} \cdot 37 \)	\( - 3^{8} \cdot 19^{8} \cdot 37 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$148$	$2$	$0$	$1$	$1$		$0$	$393984$	$1.675600$	$2375/333$	$0.79965$	$3.71085$	$[1, -1, 1, 6430, -3084514]$	\(y^2+xy+y=x^3-x^2+6430x-3084514\)	148.2.0.?	$[ ]$
120213.f1	120213h3	120213.f	120213h	$3$	$9$	\( 3^{2} \cdot 19^{2} \cdot 37 \)	\( 3^{6} \cdot 19^{6} \cdot 37 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	27.36.0.1	3B	$37962$	$1296$	$43$	$18.62406696$	$1$		$0$	$1283040$	$2.243607$	$727057727488000/37$	$1.08598$	$4.99942$	$[0, 0, 1, -6086460, -5779566590]$	\(y^2+y=x^3-6086460x-5779566590\)	3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 57.8.0-3.a.1.1, 74.2.0.?, $\ldots$	$[(-408549534919/16936, -369111972243/16936)]$
120213.f2	120213h2	120213.f	120213h	$3$	$9$	\( 3^{2} \cdot 19^{2} \cdot 37 \)	\( 3^{6} \cdot 19^{6} \cdot 37^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	9.36.0.2	3Cs	$37962$	$1296$	$43$	$6.208022321$	$1$		$0$	$427680$	$1.694302$	$1404928000/50653$	$0.97274$	$3.87462$	$[0, 0, 1, -75810, -7779821]$	\(y^2+y=x^3-75810x-7779821\)	3.12.0.a.1, 9.36.0.b.1, 57.24.0-3.a.1.1, 74.2.0.?, 171.72.0.?, $\ldots$	$[(-9823/8, 250639/8)]$
120213.f3	120213h1	120213.f	120213h	$3$	$9$	\( 3^{2} \cdot 19^{2} \cdot 37 \)	\( 3^{6} \cdot 19^{6} \cdot 37 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	27.36.0.1	3B	$37962$	$1296$	$43$	$2.069340773$	$1$		$2$	$142560$	$1.144995$	$4096000/37$	$0.88268$	$3.37555$	$[0, 0, 1, -10830, 430402]$	\(y^2+y=x^3-10830x+430402\)	3.4.0.a.1, 9.12.0.a.1, 27.36.0.a.1, 57.8.0-3.a.1.2, 74.2.0.?, $\ldots$	$[(-76, 902)]$
120213.g1	120213e1	120213.g	120213e	$1$	$1$	\( 3^{2} \cdot 19^{2} \cdot 37 \)	\( - 3^{12} \cdot 19^{3} \cdot 37^{2} \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$38$	$2$	$0$	$2.711459388$	$1$		$10$	$238080$	$1.116013$	$11239424/998001$	$0.98487$	$3.13641$	$[0, 0, 1, 798, -107127]$	\(y^2+y=x^3+798x-107127\)	38.2.0.a.1	$[(57, 351), (131, 1498)]$
120213.h1	120213g1	120213.h	120213g	$1$	$1$	\( 3^{2} \cdot 19^{2} \cdot 37 \)	\( - 3^{12} \cdot 19^{9} \cdot 37^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$38$	$2$	$0$	$3.537702921$	$1$		$2$	$4523520$	$2.588230$	$11239424/998001$	$0.98487$	$4.64677$	$[0, 0, 1, 288078, 734782378]$	\(y^2+y=x^3+288078x+734782378\)	38.2.0.a.1	$[(7942, 709906)]$
120213.i1	120213j1	120213.i	120213j	$1$	$1$	\( 3^{2} \cdot 19^{2} \cdot 37 \)	\( 3^{6} \cdot 19^{8} \cdot 37^{5} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$74$	$2$	$0$	$1$	$1$		$0$	$3628800$	$2.706715$	$44091731607552/25033168477$	$1.20826$	$4.75981$	$[0, 0, 1, -2391264, 195795299]$	\(y^2+y=x^3-2391264x+195795299\)	74.2.0.?	$[ ]$
120213.j1	120213a1	120213.j	120213a	$2$	$2$	\( 3^{2} \cdot 19^{2} \cdot 37 \)	\( 3^{3} \cdot 19^{7} \cdot 37^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$228$	$12$	$0$	$1$	$1$		$1$	$506880$	$1.863283$	$17565861949875/26011$	$1.01226$	$4.39936$	$[1, -1, 0, -586512, 173033939]$	\(y^2+xy=x^3-x^2-586512x+173033939\)	2.3.0.a.1, 12.6.0.c.1, 76.6.0.?, 114.6.0.?, 228.12.0.?	$[ ]$
120213.j2	120213a2	120213.j	120213a	$2$	$2$	\( 3^{2} \cdot 19^{2} \cdot 37 \)	\( - 3^{3} \cdot 19^{8} \cdot 37^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$228$	$12$	$0$	$1$	$1$		$0$	$1013760$	$2.209858$	$-17083807243875/676572121$	$0.94492$	$4.40264$	$[1, -1, 0, -581097, 176381492]$	\(y^2+xy=x^3-x^2-581097x+176381492\)	2.3.0.a.1, 6.6.0.a.1, 76.6.0.?, 228.12.0.?	$[ ]$
120213.k1	120213k1	120213.k	120213k	$1$	$1$	\( 3^{2} \cdot 19^{2} \cdot 37 \)	\( - 3^{8} \cdot 19^{2} \cdot 37 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$148$	$2$	$0$	$1$	$1$		$0$	$20736$	$0.203381$	$2375/333$	$0.79965$	$2.20050$	$[1, -1, 0, 18, 445]$	\(y^2+xy=x^3-x^2+18x+445\)	148.2.0.?	$[ ]$
120213.l1	120213c2	120213.l	120213c	$2$	$2$	\( 3^{2} \cdot 19^{2} \cdot 37 \)	\( 3^{3} \cdot 19^{6} \cdot 37^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$444$	$12$	$0$	$4.147680451$	$1$		$2$	$209664$	$1.077045$	$10503459/1369$	$0.93244$	$3.17429$	$[1, -1, 0, -4941, 118910]$	\(y^2+xy=x^3-x^2-4941x+118910\)	2.3.0.a.1, 12.6.0.a.1, 148.6.0.?, 444.12.0.?	$[(-62, 460)]$
120213.l2	120213c1	120213.l	120213c	$2$	$2$	\( 3^{2} \cdot 19^{2} \cdot 37 \)	\( - 3^{3} \cdot 19^{6} \cdot 37 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$444$	$12$	$0$	$8.295360903$	$1$		$1$	$104832$	$0.730472$	$9261/37$	$0.86736$	$2.72477$	$[1, -1, 0, 474, 9527]$	\(y^2+xy=x^3-x^2+474x+9527\)	2.3.0.a.1, 12.6.0.b.1, 148.6.0.?, 222.6.0.?, 444.12.0.?	$[(-1018/11, 98679/11)]$

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