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	128	Product of Tamagawa factors cp
Δ	428490000 = 24 · 34 · 54 · 232	Discriminant
Eigenvalues	2- 3- 5-  0  4 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-6900,220032]	[a1,a2,a3,a4,a6]
j	36330796409313601/428490000	j-invariant
L	3.0439311062815	L(r)(E,1)/r!
Ω	1.5219655531407	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	8	Number of elements in the torsion subgroup
Twists	5520u2 22080d2 2070f2 3450d2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 690k2

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 690k2

-4	8	-3	5	-7	-11	13	-23
5520u2	22080d2	2070f2	3450d2	33810ca2	83490bb2	116610y2	15870bg2

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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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