Cremona's table of elliptic curves

3939 = 3 · 13 · 101

Field	Data	Notes
Atkin-Lehner	3- 13- 101-	Signs for the Atkin-Lehner involutions
Class	3939d	Isogeny class
Conductor	3939	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	680	Modular degree for the optimal curve
Δ	-319059 = -1 · 35 · 13 · 101	Discriminant
Eigenvalues	2 3-  3  3  2 13-  0  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,6,-25]	[a1,a2,a3,a4,a6]
j	20123648/319059	j-invariant
L	7.458199251374	L(r)(E,1)/r!
Ω	1.4916398502748	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	63024n1 11817c1 98475i1 51207f1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3939d1

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
2	-	3	3	2	-	0	6	-2	-3	-8	-6	-4	0	-8	-5	10	-4	0	9	-7	-9	-2	6	10

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Quadratic twists for elliptic curve 3939d1

-4	-3	5	13
63024n1	11817c1	98475i1	51207f1

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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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