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	2	Product of Tamagawa factors cp
deg	416	Modular degree for the optimal curve
Δ	241865 = 5 · 13 · 612	Discriminant
Eigenvalues	-1  0 5-  0 -6 13- -4  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-22,36]	[a1,a2,a3,a4,a6]
Generators	[4:-1:1]	Generators of the group modulo torsion
j	1128111921/241865	j-invariant
L	2.1754520474786	L(r)(E,1)/r!
Ω	2.9527212517538	Real period
R	1.4735234802042	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	63440m1 35685c1 19825a1 51545a1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3965b1

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 3965b1

-4	-3	5	13
63440m1	35685c1	19825a1	51545a1

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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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