Cremona's table of elliptic curves

585 = 3² · 5 · 13

Field	Data	Notes
Atkin-Lehner	3+ 5+ 13+	Signs for the Atkin-Lehner involutions
Class	585a	Isogeny class
Conductor	585	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	83160675 = 39 · 52 · 132	Discriminant
Eigenvalues	-1 3+ 5+  2 -4 13+ -4  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-3593,83782]	[a1,a2,a3,a4,a6]
Generators	[28:53:1]	Generators of the group modulo torsion
j	260549802603/4225	j-invariant
L	1.3938971242677	L(r)(E,1)/r!
Ω	1.7604418017952	Real period
R	0.39589412238628	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	9360x2 37440u2 585c2 2925c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 585a2

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	+	+	2	-4	+	-4	6	0	-4	-10	-2	-6	-8	-8	-4	12	2	-10	0	-6	12	-4	14	-14

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Quadratic twists for elliptic curve 585a2

-4	8	-3	5	-7	-11	13
9360x2	37440u2	585c2	2925c2	28665q2	70785c2	7605f2

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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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