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	6622d	Isogeny class
Conductor	6622	Conductor
∏ cp	56	Product of Tamagawa factors cp
deg	26880	Modular degree for the optimal curve
Δ	-188672462691328 = -1 · 210 · 77 · 112 · 432	Discriminant
Eigenvalues	2+  0 -2 7- 11+ -6 -4 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,12112,-419584]	[a1,a2,a3,a4,a6]
Generators	[43:402:1] [64:752:1]	Generators of the group modulo torsion
j	196494830473357863/188672462691328	j-invariant
L	3.6490666147963	L(r)(E,1)/r!
Ω	0.30972007477377	Real period
R	0.84155867369284	Regulator
r	2	Rank of the group of rational points
S	0.99999999999976	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	52976t1 59598be1 46354f1 72842m1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6622d1

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	-	+	-6	-4	-6	-8	2	-4	-6	4	+	-8	6	-14	-8	4	12	-10	8	16	-12	10

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Quadratic twists for elliptic curve 6622d1

-4	-3	-7	-11
52976t1	59598be1	46354f1	72842m1

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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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