Elliptic curves over $\Q$ of conductor 20

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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
20.a1	20a4	20.a	20a	$4$	$6$	\( 2^{2} \cdot 5 \)	\( 2^{4} \cdot 5^{3} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.12.0.22, 3.8.0.2	2B, 3B.1.2	$120$	$384$	$9$	$1$	$1$		$1$	$6$	$-0.380644$	$488095744/125$	$1.07376$	$7.60369$	$[0, 1, 0, -41, -116]$	\(y^2=x^3+x^2-41x-116\)	2.3.0.a.1, 3.8.0-3.a.1.1, 4.6.0.b.1, 6.24.0-6.a.1.2, 8.12.0-4.b.1.2, $\ldots$	$[]$
20.a2	20a3	20.a	20a	$4$	$6$	\( 2^{2} \cdot 5 \)	\( - 2^{8} \cdot 5^{6} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.12.0.37, 3.8.0.2	2B, 3B.1.2	$120$	$384$	$9$	$1$	$1$		$1$	$3$	$-0.034070$	$-20720464/15625$	$0.95894$	$7.75305$	$[0, 1, 0, -36, -140]$	\(y^2=x^3+x^2-36x-140\)	2.3.0.a.1, 3.8.0-3.a.1.1, 4.6.0.a.1, 6.24.0-6.a.1.2, 8.12.0-4.a.1.1, $\ldots$	$[]$
20.a3	20a2	20.a	20a	$4$	$6$	\( 2^{2} \cdot 5 \)	\( 2^{4} \cdot 5 \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.12.0.22, 3.8.0.1	2B, 3B.1.1	$120$	$384$	$9$	$1$	$1$		$5$	$2$	$-0.929950$	$16384/5$	$0.95621$	$4.16481$	$[0, 1, 0, -1, 0]$	\(y^2=x^3+x^2-x\)	2.3.0.a.1, 3.8.0-3.a.1.2, 4.6.0.b.1, 6.24.0-6.a.1.4, 8.12.0-4.b.1.2, $\ldots$	$[]$
20.a4	20a1	20.a	20a	$4$	$6$	\( 2^{2} \cdot 5 \)	\( - 2^{8} \cdot 5^{2} \)	$0$	$\Z/6\Z$	$\Q$		$\mathrm{SU}(2)$			$2, 3$	8.12.0.37, 3.8.0.1	2B, 3B.1.1	$120$	$384$	$9$	$1$	$1$		$5$	$1$	$-0.583377$	$21296/25$	$0.83964$	$5.18725$	$[0, 1, 0, 4, 4]$	\(y^2=x^3+x^2+4x+4\)	2.3.0.a.1, 3.8.0-3.a.1.2, 4.6.0.a.1, 6.24.0-6.a.1.4, 8.12.0-4.a.1.1, $\ldots$	$[]$

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