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	2	Product of Tamagawa factors cp
Δ	-31984875 = -1 · 39 · 53 · 13	Discriminant
Eigenvalues	0 3+ 5+ -1  3 13-  3 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-378,-2842]	[a1,a2,a3,a4,a6]
j	-303464448/1625	j-invariant
L	1.0823993952608	L(r)(E,1)/r!
Ω	0.54119969763038	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	9360ba2 37440q2 585d1 2925a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 585b2

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 585b2

-4	8	-3	5	-7	-11	13
9360ba2	37440q2	585d1	2925a2	28665l2	70785a2	7605e2

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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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