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	3939b	Isogeny class
Conductor	3939	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	1193517 = 32 · 13 · 1012	Discriminant
Eigenvalues	-1 3-  0  2  0 13-  2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-63,180]	[a1,a2,a3,a4,a6]
Generators	[3:3:1]	Generators of the group modulo torsion
j	27680640625/1193517	j-invariant
L	2.9325649278946	L(r)(E,1)/r!
Ω	2.7090100418243	Real period
R	1.0825227232896	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	63024j2 11817d2 98475b2 51207b2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3939b2

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	-	0	2	0	-	2	-8	0	-2	-8	2	-6	4	-2	-10	-4	6	-2	6	8	0	-8	-2	-10

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Quadratic twists for elliptic curve 3939b2

-4	-3	5	13
63024j2	11817d2	98475b2	51207b2

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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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