Cremona's table of elliptic curves

690 = 2 · 3 · 5 · 23

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 23+	Signs for the Atkin-Lehner involutions
Class	690k	Isogeny class
Conductor	690	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	3935264062500 = 22 · 32 · 58 · 234	Discriminant
Eigenvalues	2- 3- 5-  0  4 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-7080,207900]	[a1,a2,a3,a4,a6]
j	39248884582600321/3935264062500	j-invariant
L	3.0439311062815	L(r)(E,1)/r!
Ω	0.76098277657037	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	5520u4 22080d3 2070f4 3450d3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 690k3

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

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Quadratic twists for elliptic curve 690k3

-4	8	-3	5	-7	-11	13	-23
5520u4	22080d3	2070f4	3450d3	33810ca3	83490bb3	116610y3	15870bg4

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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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