Cremona's table of elliptic curves

3392 = 2⁶ · 53

Field	Data	Notes
Atkin-Lehner	2- 53+	Signs for the Atkin-Lehner involutions
Class	3392o	Isogeny class
Conductor	3392	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	448	Modular degree for the optimal curve
Δ	-3392 = -1 · 26 · 53	Discriminant
Eigenvalues	2- -3  2  2 -6  3 -3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-19,-32]	[a1,a2,a3,a4,a6]
j	-11852352/53	j-invariant
L	1.143049309092	L(r)(E,1)/r!
Ω	1.143049309092	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3392n1 1696c1 30528bu1 84800cj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3392o1

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
-	-3	2	2	-6	3	-3	-1	5	3	8	7	6	-8	-2	+	6	-6	4	-9	-14	13	-9	6	13

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Quadratic twists for elliptic curve 3392o1

-4	8	-3	5
3392n1	1696c1	30528bu1	84800cj1

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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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