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	2	Product of Tamagawa factors cp
deg	208	Modular degree for the optimal curve
Δ	-51207 = -1 · 3 · 132 · 101	Discriminant
Eigenvalues	-1 3-  0  2  0 13-  2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,2,11]	[a1,a2,a3,a4,a6]
Generators	[7:16:1]	Generators of the group modulo torsion
j	857375/51207	j-invariant
L	2.9325649278946	L(r)(E,1)/r!
Ω	2.7090100418243	Real period
R	2.1650454465792	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	63024j1 11817d1 98475b1 51207b1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3939b1

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 3939b1

-4	-3	5	13
63024j1	11817d1	98475b1	51207b1

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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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