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	585b	Isogeny class
Conductor	585	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-296595 = -1 · 33 · 5 · 133	Discriminant
Eigenvalues	0 3+ 5+ -1  3 13-  3 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,12,-21]	[a1,a2,a3,a4,a6]
j	7077888/10985	j-invariant
L	1.0823993952608	L(r)(E,1)/r!
Ω	1.6235990928911	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	9360ba1 37440q1 585d2 2925a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 585b1

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
0	+	+	-1	3	-	3	-4	9	6	2	-1	3	2	6	-9	12	5	-4	-9	14	-7	0	-15	5

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Quadratic twists for elliptic curve 585b1

-4	8	-3	5	-7	-11	13
9360ba1	37440q1	585d2	2925a1	28665l1	70785a1	7605e1

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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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