Cremona's table of elliptic curves

4422 = 2 · 3 · 11 · 67

Field	Data	Notes
Atkin-Lehner	2+ 3- 11- 67+	Signs for the Atkin-Lehner involutions
Class	4422f	Isogeny class
Conductor	4422	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	175986756 = 22 · 34 · 112 · 672	Discriminant
Eigenvalues	2+ 3-  2  0 11-  2 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-160,-454]	[a1,a2,a3,a4,a6]
Generators	[-5:17:1]	Generators of the group modulo torsion
j	448927222393/175986756	j-invariant
L	3.7030027226712	L(r)(E,1)/r!
Ω	1.3891495369285	Real period
R	1.3328308523425	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	35376o2 13266o2 110550bn2 48642x2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4422f2

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

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Quadratic twists for elliptic curve 4422f2

-4	-3	5	-11
35376o2	13266o2	110550bn2	48642x2

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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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