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	4	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	-159924375 = -1 · 39 · 54 · 13	Discriminant
Eigenvalues	-1 3+ 5+  2 -4 13+ -4  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-218,1432]	[a1,a2,a3,a4,a6]
Generators	[8:8:1]	Generators of the group modulo torsion
j	-57960603/8125	j-invariant
L	1.3938971242677	L(r)(E,1)/r!
Ω	1.7604418017952	Real period
R	0.79178824477257	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	9360x1 37440u1 585c1 2925c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 585a1

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 585a1

-4	8	-3	5	-7	-11	13
9360x1	37440u1	585c1	2925c1	28665q1	70785c1	7605f1

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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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