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	585c	Isogeny class
Conductor	585	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	-219375 = -1 · 33 · 54 · 13	Discriminant
Eigenvalues	1 3+ 5-  2  4 13+  4  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-24,-45]	[a1,a2,a3,a4,a6]
j	-57960603/8125	j-invariant
L	2.1361696453497	L(r)(E,1)/r!
Ω	1.0680848226749	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	9360be1 37440i1 585a1 2925d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 585c1

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 585c1

-4	8	-3	5	-7	-11	13
9360be1	37440i1	585a1	2925d1	28665h1	70785h1	7605b1

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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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