Elliptic curves over $\Q$ of conductor 1224

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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
1224.a1	1224e1	1224.a	1224e	$1$	$1$	\( 2^{3} \cdot 3^{2} \cdot 17 \)	\( - 2^{8} \cdot 3^{9} \cdot 17^{5} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$102$	$2$	$0$	$0.124696278$	$1$		$10$	$1920$	$1.155319$	$57530252288/38336139$	$1.04113$	$5.19171$	$[0, 0, 0, 4596, 46676]$	\(y^2=x^3+4596x+46676\)	102.2.0.?	$[(10, 306)]$
1224.b1	1224c3	1224.b	1224c	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 17 \)	\( 2^{11} \cdot 3^{14} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$408$	$48$	$0$	$1$	$1$		$1$	$2048$	$1.001610$	$22994537186/111537$	$1.03807$	$5.35520$	$[0, 0, 0, -6771, 213550]$	\(y^2=x^3-6771x+213550\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 24.24.0-8.m.1.7, 136.24.0.?, $\ldots$	$[ ]$
1224.b2	1224c2	1224.b	1224c	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 17 \)	\( 2^{10} \cdot 3^{10} \cdot 17^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.4	2Cs	$408$	$48$	$0$	$1$	$1$		$3$	$1024$	$0.655037$	$40873252/23409$	$1.13826$	$4.36704$	$[0, 0, 0, -651, -650]$	\(y^2=x^3-651x-650\)	2.6.0.a.1, 8.12.0.b.1, 12.12.0-2.a.1.1, 24.24.0-8.b.1.2, 68.12.0.b.1, $\ldots$	$[ ]$
1224.b3	1224c1	1224.b	1224c	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 17 \)	\( 2^{8} \cdot 3^{8} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.11	2B	$408$	$48$	$0$	$1$	$1$		$1$	$512$	$0.308464$	$61918288/153$	$0.87866$	$4.23048$	$[0, 0, 0, -471, -3926]$	\(y^2=x^3-471x-3926\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.m.1, 12.12.0-4.c.1.2, 24.24.0-8.m.1.8, $\ldots$	$[ ]$
1224.b4	1224c4	1224.b	1224c	$4$	$4$	\( 2^{3} \cdot 3^{2} \cdot 17 \)	\( - 2^{11} \cdot 3^{8} \cdot 17^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.16	2B	$408$	$48$	$0$	$1$	$1$		$1$	$2048$	$1.001610$	$1285471294/751689$	$1.05433$	$4.94955$	$[0, 0, 0, 2589, -5186]$	\(y^2=x^3+2589x-5186\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.d.1, 12.12.0-4.c.1.1, 24.24.0-8.d.1.1, $\ldots$	$[ ]$
1224.c1	1224a1	1224.c	1224a	$1$	$1$	\( 2^{3} \cdot 3^{2} \cdot 17 \)	\( - 2^{8} \cdot 3^{3} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$102$	$2$	$0$	$0.149821697$	$1$		$8$	$64$	$-0.337991$	$27648/17$	$0.80344$	$2.68195$	$[0, 0, 0, 12, 4]$	\(y^2=x^3+12x+4\)	102.2.0.?	$[(2, 6)]$
1224.d1	1224d2	1224.d	1224d	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 17 \)	\( 2^{11} \cdot 3^{6} \cdot 17^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$136$	$12$	$0$	$2.459554506$	$1$		$3$	$384$	$0.417461$	$6097250/289$	$0.87700$	$4.19693$	$[0, 0, 0, -435, -3346]$	\(y^2=x^3-435x-3346\)	2.3.0.a.1, 8.6.0.b.1, 68.6.0.c.1, 136.12.0.?	$[(-10, 2)]$
1224.d2	1224d1	1224.d	1224d	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 17 \)	\( 2^{10} \cdot 3^{6} \cdot 17 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$136$	$12$	$0$	$1.229777253$	$1$		$7$	$192$	$0.070888$	$62500/17$	$0.89869$	$3.45520$	$[0, 0, 0, -75, 182]$	\(y^2=x^3-75x+182\)	2.3.0.a.1, 8.6.0.c.1, 34.6.0.a.1, 136.12.0.?	$[(-2, 18)]$
1224.e1	1224h1	1224.e	1224h	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 17 \)	\( 2^{10} \cdot 3^{8} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.4	2B	$136$	$12$	$0$	$1$	$1$		$1$	$256$	$0.355572$	$12194500/153$	$0.87537$	$4.19693$	$[0, 0, 0, -435, 3454]$	\(y^2=x^3-435x+3454\)	2.3.0.a.1, 8.6.0.d.1, 34.6.0.a.1, 136.12.0.?	$[ ]$
1224.e2	1224h2	1224.e	1224h	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 17 \)	\( - 2^{11} \cdot 3^{10} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.5	2B	$136$	$12$	$0$	$1$	$1$		$1$	$512$	$0.702146$	$-31250/23409$	$1.14865$	$4.46318$	$[0, 0, 0, -75, 8998]$	\(y^2=x^3-75x+8998\)	2.3.0.a.1, 8.6.0.a.1, 68.6.0.c.1, 136.12.0.?	$[ ]$
1224.f1	1224f1	1224.f	1224f	$1$	$1$	\( 2^{3} \cdot 3^{2} \cdot 17 \)	\( - 2^{8} \cdot 3^{9} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$102$	$2$	$0$	$0.588746284$	$1$		$4$	$192$	$0.211315$	$27648/17$	$0.80344$	$3.60906$	$[0, 0, 0, 108, -108]$	\(y^2=x^3+108x-108\)	102.2.0.?	$[(12, 54)]$
1224.g1	1224b1	1224.g	1224b	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 17 \)	\( 2^{8} \cdot 3^{6} \cdot 17 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.3	2B	$408$	$48$	$0$	$1$	$1$		$1$	$192$	$-0.058898$	$35152/17$	$0.75928$	$3.17928$	$[0, 0, 0, -39, -38]$	\(y^2=x^3-39x-38\)	2.3.0.a.1, 4.6.0.b.1, 24.12.0-4.b.1.1, 34.6.0.a.1, 68.24.0.f.1, $\ldots$	$[ ]$
1224.g2	1224b2	1224.g	1224b	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 17 \)	\( - 2^{10} \cdot 3^{6} \cdot 17^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	4.6.0.5	2B	$408$	$48$	$0$	$1$	$1$		$1$	$384$	$0.287676$	$415292/289$	$0.87236$	$3.72157$	$[0, 0, 0, 141, -290]$	\(y^2=x^3+141x-290\)	2.3.0.a.1, 4.6.0.a.1, 12.12.0-4.a.1.1, 68.12.0.d.1, 136.24.0.?, $\ldots$	$[ ]$
1224.h1	1224g1	1224.h	1224g	$1$	$1$	\( 2^{3} \cdot 3^{2} \cdot 17 \)	\( - 2^{8} \cdot 3^{11} \cdot 17 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$102$	$2$	$0$	$0.536171262$	$1$		$4$	$640$	$0.395303$	$-2249728/4131$	$0.90547$	$3.96516$	$[0, 0, 0, -156, -1532]$	\(y^2=x^3-156x-1532\)	102.2.0.?	$[(32, 162)]$

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