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	1599a	Isogeny class
Conductor	1599	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	72	Modular degree for the optimal curve
Δ	1599 = 3 · 13 · 41	Discriminant
Eigenvalues	-1 3+ -3 -2 -1 13+  3  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-7,-10]	[a1,a2,a3,a4,a6]
Generators	[-2:1:1]	Generators of the group modulo torsion
j	38272753/1599	j-invariant
L	1.173386105281	L(r)(E,1)/r!
Ω	2.9404990705323	Real period
R	0.39904318183258	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	25584u1 102336bg1 4797a1 39975s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1599a1

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	+	-3	-2	-1	+	3	4	5	1	1	0	+	-6	5	9	0	11	-4	0	-12	-17	0	-14	3

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Quadratic twists for elliptic curve 1599a1

-4	8	-3	5	-7	13	41
25584u1	102336bg1	4797a1	39975s1	78351s1	20787c1	65559h1

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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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