Cremona's table of elliptic curves

1599 = 3 · 13 · 41

Field	Data	Notes
Atkin-Lehner	3+ 13- 41-	Signs for the Atkin-Lehner involutions
Class	1599d	Isogeny class
Conductor	1599	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	504	Modular degree for the optimal curve
Δ	1959492951 = 37 · 13 · 413	Discriminant
Eigenvalues	1 3+ -1  2  1 13- -1  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-318,369]	[a1,a2,a3,a4,a6]
Generators	[-16:49:1]	Generators of the group modulo torsion
j	3573857582569/1959492951	j-invariant
L	2.9447859561169	L(r)(E,1)/r!
Ω	1.2842564943623	Real period
R	0.76432965144791	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	25584ba1 102336ba1 4797c1 39975r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1599d1

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	+	-1	2	1	-	-1	0	-3	5	-5	-8	-	-6	3	-3	-12	-5	4	0	-16	-13	-8	-2	13

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Quadratic twists for elliptic curve 1599d1

-4	8	-3	5	-7	13	41
25584ba1	102336ba1	4797c1	39975r1	78351l1	20787a1	65559c1

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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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