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	2	Product of Tamagawa factors cp
Δ	1053 = 34 · 13	Discriminant
Eigenvalues	1 3+  2 -4  4 13-  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-69,-252]	[a1,a2,a3,a4,a6]
j	37159393753/1053	j-invariant
L	0.82668785067339	L(r)(E,1)/r!
Ω	1.6533757013468	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	624h4 2496k3 117a4 975g3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 39a2

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 39a2

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53
624h4	2496k3	117a4	975g3	1911f4	4719d4	507c3	11271f3	14079d4	20631a4	32799i4	37479d4	53391c4	65559d4	72111e4	86151a4	109551k4

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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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