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	690j	Isogeny class
Conductor	690	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	-8125440 = -1 · 210 · 3 · 5 · 232	Discriminant
Eigenvalues	2- 3- 5-  0 -2  4  6 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-245,-1503]	[a1,a2,a3,a4,a6]
j	-1626794704081/8125440	j-invariant
L	3.0158453540469	L(r)(E,1)/r!
Ω	0.60316907080938	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5520t1 22080b1 2070e1 3450c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 690j1

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

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Quadratic twists for elliptic curve 690j1

-4	8	-3	5	-7	-11	13	-23
5520t1	22080b1	2070e1	3450c1	33810by1	83490bd1	116610x1	15870bf1

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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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