Cremona's table of elliptic curves

3384 = 2³ · 3² · 47

Field	Data	Notes
Atkin-Lehner	2+ 3- 47+	Signs for the Atkin-Lehner involutions
Class	3384c	Isogeny class
Conductor	3384	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	1280	Modular degree for the optimal curve
Δ	26313984 = 28 · 37 · 47	Discriminant
Eigenvalues	2+ 3- -3 -5 -3 -6 -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-84,164]	[a1,a2,a3,a4,a6]
Generators	[-8:18:1] [-2:18:1]	Generators of the group modulo torsion
j	351232/141	j-invariant
L	3.4393736133898	L(r)(E,1)/r!
Ω	1.919969372099	Real period
R	0.11196056247598	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6768g1 27072r1 1128e1 84600bv1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3384c1

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	-5	-3	-6	-2	-2	3	1	-10	-11	-10	2	+	0	8	-10	-2	6	-2	-1	-4	14	-15

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Quadratic twists for elliptic curve 3384c1

-4	8	-3	5
6768g1	27072r1	1128e1	84600bv1

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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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