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
deg	384	Modular degree for the optimal curve
Δ	-965779200 = -1 · 28 · 38 · 52 · 23	Discriminant
Eigenvalues	2- 3- 5-  0  4 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-420,3600]	[a1,a2,a3,a4,a6]
j	-8194759433281/965779200	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	5520u1 22080d1 2070f1 3450d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 690k1

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 690k1

-4	8	-3	5	-7	-11	13	-23
5520u1	22080d1	2070f1	3450d1	33810ca1	83490bb1	116610y1	15870bg1

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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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