Cremona's table of elliptic curves

3388 = 2² · 7 · 11²

Field	Data	Notes
Atkin-Lehner	2- 7+ 11-	Signs for the Atkin-Lehner involutions
Class	3388c	Isogeny class
Conductor	3388	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	720	Modular degree for the optimal curve
Δ	-1517824 = -1 · 28 · 72 · 112	Discriminant
Eigenvalues	2- -2  3 7+ 11-  1  3 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-84,-332]	[a1,a2,a3,a4,a6]
Generators	[11:14:1]	Generators of the group modulo torsion
j	-2141392/49	j-invariant
L	2.8947793490692	L(r)(E,1)/r!
Ω	0.78665070441396	Real period
R	1.8399394628559	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	13552bb1 54208p1 30492v1 84700r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3388c1

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	3	+	-	1	3	-8	0	3	-4	-7	-9	-8	12	9	-12	-2	-4	0	-2	-8	6	9	-19

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Quadratic twists for elliptic curve 3388c1

-4	8	-3	5	-7	-11
13552bb1	54208p1	30492v1	84700r1	23716j1	3388g1

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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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