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The results below are complete, since the LMFDB contains all elliptic curves with conductor at most 500000

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Conductor	Discriminant	j-invariant	Rank

Bad$\ p$	Curves per isogeny class	Complex multiplication	Torsion

Isogeny class degree	Cyclic isogeny degree	Isogeny class size	Integral points

Analytic order of Ш	$p\ $div$\ $\|Ш\|	Regulator	Reduction	Faltings height

Galois image	Adelic level	Adelic index	Adelic genus

Nonmax$\ \ell$	$abc$ quality	Szpiro ratio	Manin constant

Intrinsic torsion order

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Results (4 matches)

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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	Intrinsic torsion order	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
39.a1	39a2	39.a	39a	$4$	$4$	\( 3 \cdot 13 \)	\( 3^{4} \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.8	2B	$312$	$48$	$0$	$1$	$1$		$0$	$4$	$-0.318367$	$37159393753/1053$	$1.11616$	$6.64339$	$2$	$[1, 1, 0, -69, -252]$	\(y^2+xy=x^3+x^2-69x-252\)	2.3.0.a.1, 4.12.0-4.c.1.2, 24.24.0-24.ba.1.16, 26.6.0.b.1, 52.24.0-52.g.1.1, $\ldots$	$[ ]$	$1$
39.a2	39a3	39.a	39a	$4$	$4$	\( 3 \cdot 13 \)	\( 3 \cdot 13^{4} \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.7	2B	$312$	$48$	$0$	$1$	$1$		$2$	$4$	$-0.318367$	$822656953/85683$	$0.96086$	$5.60330$	$1$	$[1, 1, 0, -19, 22]$	\(y^2+xy=x^3+x^2-19x+22\)	2.3.0.a.1, 4.12.0-4.c.1.1, 12.24.0-12.h.1.2, 104.24.0.?, 312.48.0.?	$[ ]$	$1$
39.a3	39a1	39.a	39a	$4$	$4$	\( 3 \cdot 13 \)	\( 3^{2} \cdot 13^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	4.12.0.1	2Cs	$156$	$48$	$0$	$1$	$1$		$2$	$2$	$-0.664940$	$10218313/1521$	$0.91403$	$4.40546$	$1$	$[1, 1, 0, -4, -5]$	\(y^2+xy=x^3+x^2-4x-5\)	2.6.0.a.1, 4.12.0-2.a.1.1, 12.24.0-12.a.1.1, 52.24.0-52.b.1.2, 156.48.0.?	$[ ]$	$1$
39.a4	39a4	39.a	39a	$4$	$4$	\( 3 \cdot 13 \)	\( - 3 \cdot 13 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.12.0.6	2B	$312$	$48$	$0$	$1$	$1$		$1$	$4$	$-1.011513$	$12167/39$	$0.85844$	$2.98048$	$2$	$[1, 1, 0, 1, 0]$	\(y^2+xy=x^3+x^2+x\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0-4.c.1.5, 12.12.0-4.c.1.2, 24.24.0-24.ba.1.4, $\ldots$	$[ ]$	$2$

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