Cremona's table of elliptic curves

6622 = 2 · 7 · 11 · 43

Field	Data	Notes
Atkin-Lehner	2- 7- 11- 43-	Signs for the Atkin-Lehner involutions
Class	6622j	Isogeny class
Conductor	6622	Conductor
∏ cp	72	Product of Tamagawa factors cp
Δ	1646289751568 = 24 · 76 · 11 · 433	Discriminant
Eigenvalues	2- -2  0 7- 11- -4  0  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-17763,-910607]	[a1,a2,a3,a4,a6]
Generators	[-76:81:1]	Generators of the group modulo torsion
j	619832276681640625/1646289751568	j-invariant
L	4.3854290964006	L(r)(E,1)/r!
Ω	0.41360870910125	Real period
R	0.58904695292668	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	52976o3 59598i3 46354be3 72842f3	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6622j3

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	0	-	-	-4	0	8	0	-6	-4	-10	0	-	0	6	12	-10	-4	12	2	8	-18	0	-10

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Quadratic twists for elliptic curve 6622j3

-4	-3	-7	-11
52976o3	59598i3	46354be3	72842f3

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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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