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	690c	Isogeny class
Conductor	690	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	5.0841342773437E+19	Discriminant
Eigenvalues	2+ 3+ 5- -2  2 -2  0  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-3172057,-2148591611]	[a1,a2,a3,a4,a6]
j	3529773792266261468365081/50841342773437500000	j-invariant
L	0.90580157455692	L(r)(E,1)/r!
Ω	0.11322519681962	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	5520be2 22080x2 2070o2 3450v2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 690c2

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

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Quadratic twists for elliptic curve 690c2

-4	8	-3	5	-7	-11	13	-23
5520be2	22080x2	2070o2	3450v2	33810bc2	83490br2	116610bp2	15870c2

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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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