Cremona's table of elliptic curves

3362 = 2 · 41²

Field	Data	Notes
Atkin-Lehner	2+ 41+	Signs for the Atkin-Lehner involutions
Class	3362a	Isogeny class
Conductor	3362	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	52480	Modular degree for the optimal curve
Δ	83809775204854016 = 28 · 419	Discriminant
Eigenvalues	2+  2  2 -2 -6  4  0 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-369014,-85302700]	[a1,a2,a3,a4,a6]
Generators	[-128357732225:-300237146405:356400829]	Generators of the group modulo torsion
j	16974593/256	j-invariant
L	3.6261137529654	L(r)(E,1)/r!
Ω	0.19388110319563	Real period
R	18.702770374205	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	26896d1 107584e1 30258u1 84050m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3362a1

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 3362a1

-4	8	-3	5	41
26896d1	107584e1	30258u1	84050m1	3362c1

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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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