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	585d	Isogeny class
Conductor	585	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-216217755 = -1 · 39 · 5 · 133	Discriminant
Eigenvalues	0 3+ 5- -1 -3 13- -3 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,108,560]	[a1,a2,a3,a4,a6]
Generators	[30:175:1]	Generators of the group modulo torsion
j	7077888/10985	j-invariant
L	1.8522954214414	L(r)(E,1)/r!
Ω	1.2075879204524	Real period
R	0.25564673043262	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	9360bg2 37440c2 585b1 2925b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 585d2

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 585d2

-4	8	-3	5	-7	-11	13
9360bg2	37440c2	585b1	2925b2	28665c2	70785e2	7605a2

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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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