Cremona's table of elliptic curves

3392 = 2⁶ · 53

Field	Data	Notes
Atkin-Lehner	2+ 53-	Signs for the Atkin-Lehner involutions
Class	3392g	Isogeny class
Conductor	3392	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	9216	Modular degree for the optimal curve
Δ	-233096465088512 = -1 · 242 · 53	Discriminant
Eigenvalues	2+ -1  0 -4  0 -5 -3  1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-18113,-1185599]	[a1,a2,a3,a4,a6]
j	-2507141976625/889192448	j-invariant
L	0.40432324181163	L(r)(E,1)/r!
Ω	0.20216162090581	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	3392p1 106c1 30528g1 84800b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3392g1

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
+	-1	0	-4	0	-5	-3	1	3	-9	-4	-5	6	10	6	-	-6	-8	4	-3	-4	-13	-3	18	-7

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Quadratic twists for elliptic curve 3392g1

-4	8	-3	5
3392p1	106c1	30528g1	84800b1

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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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