Cremona's table of elliptic curves

6489 = 3² · 7 · 103

Field	Data	Notes
Atkin-Lehner	3- 7- 103+	Signs for the Atkin-Lehner involutions
Class	6489d	Isogeny class
Conductor	6489	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	5169124311687 = 38 · 7 · 1034	Discriminant
Eigenvalues	1 3- -2 7-  0 -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-5013,83106]	[a1,a2,a3,a4,a6]
Generators	[-66:384:1]	Generators of the group modulo torsion
j	19113403497553/7090705503	j-invariant
L	4.2637551721458	L(r)(E,1)/r!
Ω	0.6999835081461	Real period
R	3.0456111626389	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	103824bw3 2163b3 45423k3	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 6489d4

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
1	-	-2	-	0	-2	6	-4	8	2	-8	6	6	0	0	10	-12	6	-8	-12	-2	-16	-12	-6	-14

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Quadratic twists for elliptic curve 6489d4

-4	-3	-7
103824bw3	2163b3	45423k3

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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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