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
deg	2	Modular degree for the optimal curve
Δ	1521 = 32 · 132	Discriminant
Eigenvalues	1 3+  2 -4  4 13-  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-4,-5]	[a1,a2,a3,a4,a6]
j	10218313/1521	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	624h2 2496k2 117a2 975g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 39a1

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 39a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	37	41	-43	-47	53
624h2	2496k2	117a2	975g2	1911f2	4719d2	507c2	11271f2	14079d2	20631a2	32799i2	37479d2	53391c2	65559d2	72111e2	86151a2	109551k2

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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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