Cremona's table of elliptic curves

3362 = 2 · 41²

Field	Data	Notes
Atkin-Lehner	2+ 41+	Signs for the Atkin-Lehner involutions
Class	3362c	Isogeny class
Conductor	3362	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1280	Modular degree for the optimal curve
Δ	17643776 = 28 · 413	Discriminant
Eigenvalues	2+ -2  2  2  6 -4  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-220,-1254]	[a1,a2,a3,a4,a6]
Generators	[-8:6:1]	Generators of the group modulo torsion
j	16974593/256	j-invariant
L	2.2900427422139	L(r)(E,1)/r!
Ω	1.2414447910521	Real period
R	1.8446593507175	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	26896c1 107584c1 30258t1 84050k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3362c1

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

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Quadratic twists for elliptic curve 3362c1

-4	8	-3	5	41
26896c1	107584c1	30258t1	84050k1	3362a1

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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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