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	585f	Isogeny class
Conductor	585	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-2039768874585 = -1 · 322 · 5 · 13	Discriminant
Eigenvalues	1 3- 5+  0 -4 13- -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,1890,-61479]	[a1,a2,a3,a4,a6]
Generators	[230:897:8]	Generators of the group modulo torsion
j	1023887723039/2798036865	j-invariant
L	2.3595617156492	L(r)(E,1)/r!
Ω	0.4255407264631	Real period
R	5.5448552134147	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	9360bm4 37440ca3 195a4 2925g4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 585f4

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	-	+	0	-4	-	-2	-4	-8	2	-8	6	6	-4	8	-6	12	-2	-4	0	-6	16	4	-10	18

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Quadratic twists for elliptic curve 585f4

-4	8	-3	5	-7	-11	13
9360bm4	37440ca3	195a4	2925g4	28665bq3	70785m3	7605p4

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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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