Cremona's table of elliptic curves

3362 = 2 · 41²

Field	Data	Notes
Atkin-Lehner	2+ 41+	Signs for the Atkin-Lehner involutions
Class	3362b	Isogeny class
Conductor	3362	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	6720	Modular degree for the optimal curve
Δ	779017095524 = 22 · 417	Discriminant
Eigenvalues	2+  2 -2  4  2 -4  2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-2556,24860]	[a1,a2,a3,a4,a6]
Generators	[-37:284:1]	Generators of the group modulo torsion
j	389017/164	j-invariant
L	3.4669896198044	L(r)(E,1)/r!
Ω	0.81038487587615	Real period
R	4.2782012880683	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	26896e1 107584d1 30258s1 84050n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3362b1

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	4	2	-4	2	-6	-8	0	-8	2	+	-12	-4	4	8	-14	2	-8	10	-4	12	14	-6

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Quadratic twists for elliptic curve 3362b1

-4	8	-3	5	41
26896e1	107584d1	30258s1	84050n1	82a1

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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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