Cremona's table of elliptic curves

3965 = 5 · 13 · 61

Field	Data	Notes
Atkin-Lehner	5- 13- 61+	Signs for the Atkin-Lehner involutions
Class	3965b	Isogeny class
Conductor	3965	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	257725 = 52 · 132 · 61	Discriminant
Eigenvalues	-1  0 5-  0 -6 13- -4  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-327,2354]	[a1,a2,a3,a4,a6]
Generators	[12:1:1]	Generators of the group modulo torsion
j	3855860066241/257725	j-invariant
L	2.1754520474786	L(r)(E,1)/r!
Ω	2.9527212517538	Real period
R	0.7367617401021	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	63440m2 35685c2 19825a2 51545a2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3965b2

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	-	0	-6	-	-4	4	6	6	10	2	6	-10	0	12	-10	+	-12	-6	-10	0	4	8	-2

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Quadratic twists for elliptic curve 3965b2

-4	-3	5	13
63440m2	35685c2	19825a2	51545a2

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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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