Cremona's table of elliptic curves

3381 = 3 · 7² · 23

Field	Data	Notes
Atkin-Lehner	3- 7+ 23-	Signs for the Atkin-Lehner involutions
Class	3381j	Isogeny class
Conductor	3381	Conductor
∏ cp	22	Product of Tamagawa factors cp
deg	2112	Modular degree for the optimal curve
Δ	-224999541963 = -1 · 311 · 74 · 232	Discriminant
Eigenvalues	0 3-  0 7+ -2 -3  2  3	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,327,22817]	[a1,a2,a3,a4,a6]
Generators	[39:310:1]	Generators of the group modulo torsion
j	1605632000/93710763	j-invariant
L	3.3757373070213	L(r)(E,1)/r!
Ω	0.75699941042015	Real period
R	0.20269844699013	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	54096y1 10143g1 84525a1 3381d1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3381j1

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
0	-	0	+	-2	-3	2	3	-	6	-3	-3	0	3	-10	-4	-6	-2	1	-6	1	-7	4	-14	-10

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Quadratic twists for elliptic curve 3381j1

-4	-3	5	-7	-23
54096y1	10143g1	84525a1	3381d1	77763u1

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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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