Cremona's table of elliptic curves

39 = 3 · 13

Field	Data	Notes
Atkin-Lehner	3+ 13-	Signs for the Atkin-Lehner involutions
Class	39a	Isogeny class
Conductor	39	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	85683 = 3 · 134	Discriminant
Eigenvalues	1 3+  2 -4  4 13-  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-19,22]	[a1,a2,a3,a4,a6]
j	822656953/85683	j-invariant
L	0.82668785067339	L(r)(E,1)/r!
Ω	3.3067514026935	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	624h3 2496k4 117a3 975g4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 39a3

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
1	+	2	-4	4	-	2	0	0	-10	4	-2	6	-12	0	6	12	-2	-8	0	2	8	4	-2	10

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Quadratic twists for elliptic curve 39a3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53
624h3	2496k4	117a3	975g4	1911f3	4719d3	507c4	11271f4	14079d3	20631a3	32799i3	37479d3	53391c3	65559d3	72111e3	86151a3	109551k3

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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