Elliptic curves over $\Q$ of conductor 392

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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
392.a1	392f1	392.a	392f	$1$	$1$	\( 2^{3} \cdot 7^{2} \)	\( 2^{4} \cdot 7^{2} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	2.2.0.1	2Cn	$28$	$12$	$0$	$0.129582864$	$1$		$8$	$24$	$-0.654362$	$48384$	$0.89152$	$2.92255$	$[0, 0, 0, -7, 7]$	\(y^2=x^3-7x+7\)	2.2.0.a.1, 14.6.0.a.1, 28.12.0-14.a.1.2	$[(1, 1)]$
392.b1	392d2	392.b	392d	$2$	$2$	\( 2^{3} \cdot 7^{2} \)	\( 2^{11} \cdot 7^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$56$	$12$	$0$	$1$	$1$		$1$	$384$	$0.738286$	$3543122/49$	$1.08036$	$5.75768$	$[0, 1, 0, -1976, 32752]$	\(y^2=x^3+x^2-1976x+32752\)	2.3.0.a.1, 8.6.0.b.1, 28.6.0.c.1, 56.12.0.k.1	$[]$
392.b2	392d1	392.b	392d	$2$	$2$	\( 2^{3} \cdot 7^{2} \)	\( - 2^{10} \cdot 7^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$56$	$12$	$0$	$1$	$1$		$1$	$192$	$0.391713$	$-4/7$	$1.03482$	$4.69045$	$[0, 1, 0, -16, 1392]$	\(y^2=x^3+x^2-16x+1392\)	2.3.0.a.1, 8.6.0.c.1, 14.6.0.b.1, 56.12.0.n.1	$[]$
392.c1	392c1	392.c	392c	$1$	$1$	\( 2^{3} \cdot 7^{2} \)	\( 2^{4} \cdot 7^{4} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.4.0.2	2Cn	$28$	$12$	$0$	$0.071541228$	$1$		$8$	$24$	$-0.376873$	$12544$	$0.83745$	$3.34824$	$[0, -1, 0, -16, 29]$	\(y^2=x^3-x^2-16x+29\)	2.2.0.a.1, 4.4.0-2.a.1.1, 14.6.0.a.1, 28.12.0-14.a.1.4	$[(-2, 7)]$
392.d1	392a3	392.d	392a	$4$	$4$	\( 2^{3} \cdot 7^{2} \)	\( 2^{11} \cdot 7^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.61	2B	$56$	$48$	$0$	$7.567836011$	$1$		$1$	$384$	$0.970922$	$1443468546/7$	$1.04654$	$6.76413$	$[0, 0, 0, -14651, -682570]$	\(y^2=x^3-14651x-682570\)	2.3.0.a.1, 4.12.0-4.c.1.2, 8.24.0-8.p.1.6, 56.48.0-56.bp.1.8	$[(1306/3, 13420/3)]$
392.d2	392a4	392.d	392a	$4$	$4$	\( 2^{3} \cdot 7^{2} \)	\( 2^{11} \cdot 7^{10} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.105	2B	$56$	$48$	$0$	$1.891959002$	$1$		$3$	$384$	$0.970922$	$11090466/2401$	$1.11706$	$5.94877$	$[0, 0, 0, -2891, 47334]$	\(y^2=x^3-2891x+47334\)	2.3.0.a.1, 4.6.0.c.1, 8.24.0-8.k.1.3, 28.12.0-4.c.1.1, 56.48.0-56.v.1.4	$[(14, 98)]$
392.d3	392a2	392.d	392a	$4$	$4$	\( 2^{3} \cdot 7^{2} \)	\( 2^{10} \cdot 7^{8} \)	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.5	2Cs	$56$	$48$	$0$	$3.783918005$	$1$		$5$	$192$	$0.624349$	$740772/49$	$1.06534$	$5.37950$	$[0, 0, 0, -931, -10290]$	\(y^2=x^3-931x-10290\)	2.6.0.a.1, 4.12.0-2.a.1.1, 8.24.0-8.a.1.3, 28.24.0-28.b.1.1, 56.48.0-56.d.1.2	$[(107, 1056)]$
392.d4	392a1	392.d	392a	$4$	$4$	\( 2^{3} \cdot 7^{2} \)	\( - 2^{8} \cdot 7^{7} \)	$1$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.51	2B	$56$	$48$	$0$	$1.891959002$	$1$		$9$	$96$	$0.277775$	$432/7$	$0.89152$	$4.45214$	$[0, 0, 0, 49, -686]$	\(y^2=x^3+49x-686\)	2.3.0.a.1, 4.12.0-4.c.1.1, 8.24.0-8.p.1.8, 14.6.0.b.1, 28.24.0-28.g.1.2, $\ldots$	$[(9, 22)]$
392.e1	392b1	392.e	392b	$1$	$1$	\( 2^{3} \cdot 7^{2} \)	\( 2^{4} \cdot 7^{10} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	2.2.0.1	2Cn	$28$	$12$	$0$	$1$	$1$		$0$	$168$	$0.596082$	$12544$	$0.83745$	$5.30352$	$[0, 1, 0, -800, -8359]$	\(y^2=x^3+x^2-800x-8359\)	2.2.0.a.1, 14.6.0.a.1, 28.12.0-14.a.1.2	$[]$
392.f1	392e1	392.f	392e	$1$	$1$	\( 2^{3} \cdot 7^{2} \)	\( 2^{4} \cdot 7^{8} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$		✓	$2$	4.4.0.2	2Cn	$28$	$12$	$0$	$1$	$1$		$0$	$168$	$0.318593$	$48384$	$0.89152$	$4.87783$	$[0, 0, 0, -343, -2401]$	\(y^2=x^3-343x-2401\)	2.2.0.a.1, 4.4.0-2.a.1.1, 14.6.0.a.1, 28.12.0-14.a.1.4	$[]$

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